Bioinspiredwatercollection methodstosupplement ... · North American Great Lakes [7]. Given that...

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ReviewCite this article: Bhushan B. 2019 Bioinspiredwater collectionmethods to supplement watersupply. Phil. Trans. R. Soc. A 377: 20190119.http://dx.doi.org/10.1098/rsta.2019.0119

Accepted: 26 April 2019

One contribution of 15 to a theme issue‘Bioinspired materials and surfaces for greenscience and technology (part 2)’.

Subject Areas:environmental engineering, mechanicalengineering, nanotechnology, materialsscience

Keywords:bioinspiration, water collection, fog,water condensation, cactus, desert beetle

Author for correspondence:Bharat Bhushane-mail: [email protected]

Bioinspired water collectionmethods to supplementwater supplyBharat Bhushan

Nanoprobe Laboratory for Bio and Nanotechnology andBiomimetics (NLBB), The Ohio State University, 201 W. 19th Avenue,Columbus, OH 43210-1142, USA

BB, 0000-0001-7161-6601

Fresh water sustains human life and is vital forhuman health. Water scarcity affects more than 40%of the global population and is projected to rise.For some of the poorest countries, 1 in 10 peopledo not have access to safe and easily accessiblewater sources. Water consumption by man continuesto grow with increasing population. Furthermore,population growth and unsafe industrial practices,as well as climate change, have put strain on‘clean’ water supply in many parts of the world,including the Americas. Current supply of freshwater needs to be supplemented to meet futureneeds. Living nature provides many lessons forwater source. It has evolved species, which cansurvive in the most arid regions of the world bywater collection from fog and condensation in thenight. Before the collected water evaporates, specieshave mechanisms to transport water for storage orconsumption. These species possess unique chemistryand structures on or within the body for collectionand transport of water. In this paper, an overview ofarid desert conditions and water collection from fog,and lessons from living nature for water collectionare provided. Data on various bioinspired surfaces forwater collection are also presented. Some bioinspiredwater purification approaches are presented. Next,consumer to military and emergency applicationsare discussed and water collection projections arepresented.

This article is part of the theme issue ‘Bioinspiredmaterials and surfaces for green science andtechnology (part 2)’.

2019 The Author(s) Published by the Royal Society. All rights reserved.

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http://dx.doi.org/10.1098/rsta/377/2150

mailto:[email protected]

http://orcid.org/0000-0001-7161-6601

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royalsocietypublishing.org/journal/rstaPhil.Trans.R.Soc.A377:20190119

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1. IntroductionAccess to a safe supply of water is a human right. Fresh water sustains human life and is vital forhuman health. Some of the arid regions of the world lack adequate water supply, figure 1 [1,2].Owing to bad economics or poor infrastructure in some parts of the world, water scarcity hasbecome even worse. More than 40% of the global population is affected by water scarcity and itis projected to rise. It is estimated that over 1.7 billion people are currently living in river basinswhere water use exceeds replenishment. In some of the poorest countries, 1 in 10 people do nothave access to safe and easily accessible water sources.

Because of global warming and an increased number of drought periods, water supplycontinues to shrink. Figure 2 shows the projected water stress by 2030 based on data from [2,3].The number of people living in areas affected by severe water stress is expected to increase from2.8 billion in 2005 to 3.9 billion by 2030, representing over 47% of the projected population [3].The majority of the people affected by water stress live in South Asia, the Middle East and NorthAfrica, but the people living in North and South America including the southwest United Statesare also increasingly being affected.

Water consumption by man continues to grow. With an ever-growing population, there isan increasing demand for food and other necessities. Food production requires a significantamount of water. Global water consumption is expected to reach 6 trillion m3 a year by 2030 as thepopulation moves towards a projected 8.2 billion, as shown in figure 3 [2,4,5]. In the USA, about600 l of water per capita is consumed; in Europe, it is about 300 l per capita and in the rest of theworld it is much less.

Roughly, 70% of the Earth’s surface is covered by water; however, the vast majority of wateris contained in the oceans with fresh water accounting for only 2.5% of all water, as shown infigure 4a [2]. Water continuously moves in a cycle due to evaporation, condensation, precipitation,surface and channel runoff and subsurface flow, as shown in figure 4b [2]. The evaporative phasecan help purify water by separating it from contaminants picked up in other phases of the cycle,including salt in the oceans. Of the 2.5% fresh water, the majority is trapped as glaciers and snow(1.74% in total). Only 0.79% (11 quadrillion m3) of all water is found as surface water in lakes andrivers (0.03% or 400 trillion m3), and as groundwater (0.76%) [6]. The distribution of this water isnot uniform across the world, with around 20% of the world’s surface fresh water found in theNorth American Great Lakes [7].

Given that about 97.5% of water is saline water, desalination has become increasinglyimportant in all parts of the world. Ocean water is contaminated by salt, as well as by bacteriaand particulates. For human consumption, ocean water must be desalinated and purified.However, desalination in which saline water is made fit for human consumption remains anenergy-intensive process [8].

Water contamination by human activity and unsafe industrial practices, as well as populationgrowth continues to grow. Water contamination is a major health issue facing the world today.Therefore, water purification becomes increasingly important. It is believed that about 800 millionpeople do not have access to ‘clean’ drinking water. That is slightly more than the population ofthe USA, Canada and continental Europe.

It is apparent that current supply of fresh water needs to be supplemented to meet futureneeds. To find new sources of water supply, living nature may provide solutions. In livingnature, after some 3.8 billion years of evolution, many plant and animal species in arid regionsexhibit efficient solutions for water collection from fog. These solutions typically involve speciespossessing unique surface structures and chemistry on or within their bodies that help to directthe movement of water before it is evaporated, to where it is consumed or stored [2]. By studyingthe surface structures and chemistries involved, bioinspired fog collectors are being developed[9–11].

The ambient temperature during desert nights is low, as low as about 4°C. This temperaturecan be lower than the dew point, which would lead to water condensation from ambient.Bioinspired water condensation can also be used for water collection. Song & Bhushan [12,13]

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>95%65–83%no data

83–95%<65%

Figure 1. Percentage of population with access to improved water sources in 2015, as defined by WHO/UNICEF (adapted from[1,2]).

no water stress low water stressmoderate water stress severe water stress

Figure 2. Projected water stress by 2030 when an estimated 47% of the world’s population will live in area of extreme waterstress [2,3].

used triangular patterns, inspired by nature, to transport water to storage after condensation toenhance water collection.

Systems in human bodies have evolved to transplant water efficiently while blocking othermolecules and ions. Inspiration can be taken to improve the efficiency of desalination and helppurify contaminated water.

Bioinspired approaches are attractive to develop materials and surfaces in an environmentallyfriendly and sustainable manner for water supply and purification. Bioinspired water collectorscan be used to provide a supplemental water source for communities in the arid regions where fogand water condensation is common, such as coastal regions of Africa, the southwestern coast ofSouth America and the southwestern United States [2,9,10,12,13]. Portable water collection unitsare also of interest for various military and emergency applications. Various bioinspired waterpurification approaches have also been developed.

In this paper, an overview of bioinspired water collection methods from fog and watercondensation from ambient, to supplement water supply, is presented. First, an overview ofarid desert conditions and water collection from fog is presented. Next, various examples ofwater collection from living nature are presented with a discussion of the surface structures

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water consumption

actual

global

Asia

AmericasAfrica

EuropeOceania

1980 1985 1990 2000 2005

year

2010 2020 2030202520151995

wat

er c

onsu

mpt

ion

(1012

m3

y–1)

6

5

4

3

2

1

0

projected

Figure 3. Water consumption based on actual (1980–2010) data [4] and projected (2030) data [2,5]. (Online version in colour.)

and chemistries used. Then, water collection data for various designs of bioinspired surfaces,both from fog and condensation from ambient, are presented, which can be used to developoptimal designs. In addition, bioinspired water desalination and water purification techniquesare briefly described. Finally, various applications are discussed and water collection projectionsare presented.

2. Overview of arid desert conditions and water collection from fogA desert is a barren area of landscape where little precipitation occurs and, consequently, livingconditions are hostile for living naure including plant and animal life. Deserts cover about one-third of the earth’s land surface area [14,15]. Deserts are formed by weathering processes; largevariations in temperature between day and night put strains on the rocks which consequentlybreak in pieces. A map of the world’s deserts with relative degrees of aridness is shown in figure 5.

The Namib Desert in southwest Africa is one of the most arid regions in the world with anaverage annual rainfall of only 1.8 cm, and it is not uncommon to experience consecutive yearswith no rainfall at all. Despite the low rainfall, prevailing southwesterly winds form fog along thecoast from 60–200 days per year, which can be blown inland for up to 50 km [16].

Species surviving in the deserts need water to survive. Water appears in deserts from varioussources including groundwater from roots, metabolic water, rainwater, snow, fog and watercondensation. During low rainfall months, the species survive on fog (figure 6a). Mean rainfalland fog water collection is presented in figure 6b, based on 2 years of fog collection and 30 yearsof rainwater collection in the California central coast (Big Sur, CA, USA) [17]. Fog depositionoccurs primarily during the months of June through October. It should be noted that the ambienttemperature during desert nights is low, as low as about 4°C. This temperature can be lower thanthe dew point and can lead to water condensation from ambient.

In arid and semi-arid regions, fog dominates as a water source. This source of water isclean from impurities [18]. Fog is essentially a visible aerosol consisting of tiny water dropletssuspended in air, which is found close to the land surface or water. The amount of fog dependsupon the geographical position of the desert as well as to offshore ocean current. Thick fog isformed near coastal deserts [19]. It is typically formed when warm, moist air from the land movesabove the cold water and condenses, and the winds bring the condensed moist air or fog back tothe land. Visibility in fog is generally limited to distances on the order of 1 km or maybe much lessthan that, only a few metres. Fog is formed by small water droplets whose size is on the order of

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(a)

(b)

96.5%oceans

1.74%glaciers and snow

0.03%surface water

0.001%atmosphere

0.76%groundwater

2.5%fresh water

cloud formation

snow

surface run-off

channel run-off

condensing water vapour

evaporation

ocean salt waterintrusion

lakes

river

subsurface flow

impervious layer

groundwaterpenetration

precipitation

97.5%saline water

1%brackish

groundwater

Figure 4. (a) Percentage breakdown of all water on Earth; 2.5% is fresh water, with surface water in rivers and lakes onlyaccounting for 0.03% of all water (400 trillion m3) and groundwater only 0.79% of all water (11 quadrillion m3) [6], and (b) thewater cycle where of all water the evaporative phase helps purify water via separation from contaminants picked up in otherphases of the cycle (adapted from [2]). (Online version in colour.)

10–50 µm, with a concentration on the order of 10–100 microdroplets per cubic centimetre [14,20].Air in fog has a relative humidity (RH) generally above 95%.

Fog occurs on a wide range of days per year dependent upon the desert location. Table 1presents data for occurrence and duration of fog in the very arid central Namib Desert during a12 month period [21]. The fog occurrence in the less arid central California coast desert is reportedto be more frequent, on the order of 80% of days per year [17].

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world map of deserts

distribution of non-polararid land (after Meigs, 1953)

extremely arid

arid

semi-arid

0 1000 2000 km

Figure 5. World map of deserts. Arid deserts exist in parts of Africa, the Middle East, Southwestern South America andSouthwestern United States.

fog(a) (b)

Jan

Feb

Mar

Apr

May

June

July

Aug Sep

Oct

Nov

Dec

month

mean rainfall and fog water collection inCalifornia central coast (Hiatt et al. [17])

mea

n m

onth

ly r

ainf

all (

cm)

fog

wat

er c

olle

ctio

n (l

m–2

h–1

)

30

20

10

0 0

0.2

0.4

0.6

Figure 6. (a) Photograph of fog near coastal desert; (b) mean monthly rainfall for years 1981–2010 and hourly fog watercollection for the 2010 and 2011 fog collection periods in the California central coast (Big Sur, CA, USA) (adapted from [17]).(Online version in colour.)

The amount of water collection from fog and duration of fog is dependent upon the desertregion and the period. Figure 7 shows the rate of fog water collected in different regions andthe number of days fog occurs annually [22]. The rate of fog water collected ranges from 1.5 to12 l m−2 d−1. The detailed data on fog deposition in the California central coast has been presentedby Hiatt et al. [17]. They reported that in 2010, 73% of days recorded fog deposition. The totalamount of fog deposition was about 290 l m−2 with a daily average of about 2.3 l m−2 and a dailymaximum of about 13 l m−2, and an hourly average of about 0.1 l m−2 and an hourly maximum ofabout 2.3 l m−2. Similar data were reported for 2011. Figure 8a shows data for fog water collectionin 2010 and 2011 during June to September. During summer months, the amount and duration ofthe fog is highest. Most fog deposition occurs during the night and early morning hours. Averagefog water collection was about 0.16 l m−2 between 8.00 and 2.00 increasing to a peak of about0.2 l m−2 between 3.00 and 9.00. After 9.00, it steeply declined to nearly 0 between 2.00 and 6.00.

To sum up, the daily average fog water collection is on the order of 2 l m−2 and the hourlyaverage is on the order of 0.1 l m−2, dependent upon the location. The highest fog collectionoccurs when the temperature of the land is hot, which occurs during the months of June andJuly, during nights and early mornings. As a reference, a consumer humidifier produces fog with

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rate of fog water collection and number of days fog occurs annually at various locations (Fessehaye et al. [22])

Cape Verde, Serra Malgagueta (365)Peru, Mejia (210)

Chile, Alto Patache (365)Canary Islands, Tenerife (354)

Eritrea, Arborobu (166)Guatemala, Tojquia (210)

S. Africa, Lepelfontein (184)Yemen, Hajja (121)

Ecuador, P. Grande (210)Nepal, Pathivara (122)Spain, Valencia (142)

Eritrea, Nefasit (90)S. Africa, Soutpansberg (200)

Chile, El Tofo (365)Chile, Padre Hurtado (365)

Colombia, Andes mountain (210)in parantheses are the numberof days fog occured annually

rate of fog water collection (l m–2 d–1)0 12108642

Chile, Falda Verde (365)

Figure 7. Rate of fog water collection and number of days fog occurs annually at various desert locations (adapted from [22]).(Online version in colour.)

Table 1. Occurrence and duration of fogs at Central Namib Desert during a 12 month period (adapted from [21]).

no. fog days duration of fog (h) time fogs begin

mean range earliest latest

1977. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

September 9 3.8 3–7 24.00 06.00. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

October 7 3.0 1–5 02.00 06.30. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

November 11 3.2 1–5 12.30 06.30. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

December 9 3.4 1–7 01.00 06.00. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1978. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

January 12 3.6 1–8 22.00 06.00. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

February 4 3.2 1–5 23.00 08.00. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

March 5 1.2 1–2 05.00 07.00. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

April 8 2.1 1–7 02.00 07.00. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

May 2 2.5 1–4 04.00 06.00. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

June 0 — — — —.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

July 4 4.2 1–7 02.00 07.00. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

August 7 2.9 1–7 24.30 07.00. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

water content on the order of 50–1000 l m−2 h−1 with nozzle diameter on the order of a couple ofcentimetres. The fog emitted by the humidifier is dissipated over a large area.

The water collection depends on various environmental factors including the differencebetween air temperature and dew point temperature, wind speed, wind direction and landtemperature [17]. The difference between air temperature and dew point temperature, termed the

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average hourly fog water collection by month fog water collection versus wind speed (at 4°C)

fog

wat

er c

olle

ctio

n (l

m–2

h–1

)

fog

wat

er c

olle

ctio

n (l

m–2

h–1

)

June

2010

0.3

0.2

0

2.0

0

0 864wind speed (m s–1)

2

0.5

1.0

1.5

0.1

2011

July Augmonth

Sep

(a) (b)

Figure 8. (a) Average hourly fog water collection by month in 2010 and 2011 and (b) and fog water collection as a function ofwind speed during prevailing winds in the California central coast (adapted from [17]).

Table 2. Weight gain expressed as a percentageweight change of bodyweight of tenebrionid beetle after a head-down stanceto collect water in fogs of various strengths on the Namib Desert (adapted from [23]).

date fog (mm) mean weight gain (%)

14 October 1975 0.50 14.50. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5 November 1975 0.35 1.63. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25 November 1975 0.10 5.47. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29 November 1975 0.65 8.39. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 December 1975 0.10 2.11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

dew point depression, is a strong indicator of fog. The lower the dew point depression, the higherthe fog density and vice versa. The wind speed of fog is typically on the order of a few cm s−1

[20] to as high as a couple of m s−1 in the California central coast [17]. Fog water collection is afunction of wind speed during prevailing winds. An example of data collected in the Californiacentral coast is shown in figure 8b. The higher the wind speed, the higher is fog collection. Thoughthe wind direction is random, for maximum collection, the wind should be perpendicular to thecollecting surface.

Fog is one of the major reasons for many species’ survival in arid regions. Examples of watercollection of flora and fauna are presented next. Data for the weight gain for tenebrionid beetles(13–22 mm) after a head-down stance to collect water are shown in table 2 [23]. The beetles beingmobile, consume fog water in two different ways: by consuming fog-water droplets condensed ondifferent vegetation, stones and soil, and by using a fog-basking stance and drinking the fog-watercondensed on its body [21]. The water collected on Stipagrostis sabulicola, Namib dune bushmangrass, is presented in figure 9, measured at 4.00, a few hours after the onset of the fog, and at 8.00.After 8.00, no substantial fog collection could be measured. Measurements were taken of 10 fogevents for five set of samples [24]. Total fog collected per leaf area was about 5 l m−2.

3. Water collection: lessons from living natureFog is composed of micrometre-sized water droplets that form when air becomes saturated withwater vapour. Fog is a thick cloud that remains suspended in the atmosphere. Dew is the depositof water droplets that are formed on cold surfaces by condensation of water vapour in air or fog.In many flora and fauna, living nature uses fog as a vital source of water, particularly in aridareas that receive little rainfall [2]. Fog and dew always exist when the temperature decreases late

9


...............................................................

Namib dune bushman grass (Ebner et al. [24])

stem

flo

w r

ate

(l m

–2)

10

01 2 543

4.00 8.00time of day

1 2 543

2

4

6

8

Figure 9. Measured stem flow rates for S. sabulicola, Namib dune bushman grass, measured at 4.00 and 8.00. Measurementswere taken on 10 fog events for five plants. After 8.00, no substantial fog harvesting could be observed. The vertical lines indicatethe highest and lowest values and the cross line indicates the median (adapted from [24]).

5 mm

(a) (b)

Figure 10. Net-based water collectors currently available from (a) FogQuest (photograph by Anne Lummerich, inset adaptedfrom [26], and (b) Warka Water (photograph by Architecture and Vision). (Online version in colour.)

at night and in the early morning. There is evidence that over 5000 years ago, hunter–gatherergroups were able to populate arid areas along the southern coast of Peru by using fresh waterfrom fog, though the collection method is unknown [25].

Since the earlier attempts by Carlos Espinosa in Chile in 1957, net-based fog collectors havebeen built in several countries. During fog collection, fog drops are deposited on the net filamenton the towers and travel by gravity to a collection dish at the bottom. In North America,many organizations such as FogQuest use two-dimensional (2D) nets for fog interception andharvesting that are able to provide a supplemental source of water in arid regions, figure 10 [2]. Toovercome the limitations of a 2D net, new designs were developed, such as a tower by the charityWarka Water, figure 10 [2]. However, the nets in these devices are typically made of material thathas not been optimized for water collection.

In living nature, several flora and fauna in arid regions have evolved surface structures andchemistries that enable them to collect water from fog, figure 11 [2]. These include Namib Desertbeetles, several lizard species, spider webs, and various types of cacti, grasses, bushes and otherplants. External structures typically feature areas where fog droplets can deposit and grow before

10


...............................................................

inspirations for water-collecting device

mechanism

hydrophilic

knot

barb

spine

hydrophobicwater droplets grow onwax-free hydrophilic bumpsbefore being transportedtowards the mouth by the waxyhydrophobic surround(Hamilton & Seely [23] Parker &Lawrence [27])

a hydrophilic surface supportsa thin water film and capillaryaction directs water throughasymmetric channels, favouringtransport towards the mouth(Comanns et al. [31])

due to Laplace pressure andsurface energy gradients, waterdroplets move along hydrophilicsilk towards knots(Zheng et al. [32])

water droplets grow on tips ofsmall barbs before movingdown onto spine and travellingtowards base, due to Laplacepressure gradident where theyare absorbed (Mooney et al. [36],Ju et al. [39])

water droplets are channelleddown the hydrophilic leavestowards the base of the plantand eventually reaching theroots (Ebner et al. [24];Roth-Nebelsick et al. [41])

water droplets grow on tinyhairs before dropping downfurther into the plant structurewhen they get too heavy andeventually reaching the roots(Andrews et al. [43])

commentsspecies

Stenocara gracilipes (beetle)

Moloch horridus (lizard)

Araneae (spider web)

Opuntia microdasys (cactus)

plan

tan

imal

Stipagrostis sabulicola (grass)

Cotula fallax (bush)

Figure 11. Summary of animal and plant species found to collect water from fog. A combination of surface structure andchemistry results in interception of water from fog and transport to themouth, roots or another area where it can be consumedor stored (adapted from [2]). (Online version in colour.)

eventually being transported to where it is consumed or stored. For example, in the case ofdesert beetles and lizards, collected water is transported towards their mouth for consumption.In the case of some plants, the collected water is transported towards roots or trunk forstorage. High droplet velocity is needed for water collection purposes to minimize water loss toevaporation.

11


...............................................................

(a) Namib Desert beetlesThe Namib Desert in southern Africa is one of the most arid regions in the world with an averageannual rainfall of only 1.8 cm, and it is not uncommon to experience consecutive years withno rainfall at all [16]. Stenocara gracilipes and Onymacris unguicularis are beetles native to thisregion. The beetles survive as a result of collection of water from fog. The first observation offog harvesting in the Namib Desert was made by Hamilton & Seely [23], with beetles emergingduring nocturnal fogs and lowering their heads while oriented into the wind. The water wasfound to trickle down the body of the beetle and into the mouth.

Parker & Lawrence [27] presented the mechanism for fog collection. They reported that theback of the beetle comprised a random array of 0.5 mm diameter bumps spaced 0.5–1.5 mmapart, figure 11. The bumps were found to be smooth, while the surrounding area was coveredin microstructured wax. Water from the fog is observed to land on the bumps and droplets beginto grow. The droplet continues to grow (up to 4–5 mm) until the weight of the droplet overcomesthe capillary force and the droplet detaches and rolls down the tilted beetle’s back. The bumpswere found to be hydrophilic while the background wax was hydrophobic. They created a modelsurface comprising 0.6 mm glass beads fixed in wax and found that the surface collected morewater than the wax or glass surfaces alone. This experiment verified that an array of hydrophilicbumps on a hydrophobic background is responsible for fog harvesting.

(b) LizardsMoloch horridus is a species of lizard native to arid regions in Western and Southern Australia,figure 11. Bentley & Blumer [28] reported that water droplets spread out over the skin beforereaching the mouth. Water movement occurs due to capillary action along open channels in theskin. Similarly, in the case of Phrynocephalus helioscopus, a species of lizard native to arid regionsin Asia, the lizard adopted a posture where the head was depressed and the hindquarters wereelevated, which helped guide the water to the mouth [29].

Comanns et al. [30] studied numerous species of lizards. In the case of Phrynosoma cornutum orthe Texas horned lizard, they found that water placed on the skin flowed preferentially towardsthe mouth, with capillary forces dominating over gravitational and viscous forces, figure 12[2,31]. They reported a network of capillary channels with a narrowing of individual channelsin the direction of the mouth (longitudinal), figure 11. An abrupt widening from one channelto the next, in addition to an interconnecting narrower channel running laterally, would follow.The narrowing of the channel results in favourable water transport in that direction due to thecurvature of the liquid–air interface. The lateral interconnecting channels overcome the effects ofthe abrupt widening and help maintain an advancing liquid front [31]. In the backward direction,liquid flow is stopped as the channel widens and pressure would need to be applied to force theliquid in that direction [2].

(c) Spider websSpider webs are known to collect water, as evidenced by capturing a dew-glistened web, figure 11.Dry webs undergo moisture-induced structural reorganization. First, the hygroscopic nature ofthe proteins contained within the silk results in the condensation of water droplets and theswelling of the cylindrical silk thread. This cylinder is then broken up due to Rayleigh instability,where a cylinder of fluid will break up into smaller drops to lower its surface area, resulting inthe formation of a ‘beads on a string’ structure with a series of knots periodically spaced alongthe thread, figure 13a [2,33]. It is believed that this rebuilding of the web structure and subsequentwater capture is beneficial for the spider, as not only does it provide a source of drinking water butit also results in improved capture of prey due to the water-swollen knots possessing enhancedadhesive properties [33].

12


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directional spreading of water droplet on lizard skin

snout +26%

+70%+48%

1.6 s0 s

3.3 s 5.0 s

Figure 12. Time-lapse images showing directional spreading of water droplets deposited on lizard skin. Preferential watertransport occurs towards the snout (adapted from [31]).

(c)

(b)

(a)

(e)

(h)

( f )

(i)

(g)

( j )

(d)

water droplet collection on spider webs

joint

200 mm

30 mm

1 mm1 mm

100 mm

t = 7.708 s

stretched porous structure random porous structure

t = 7.955 s t = 8.116 s

t = 8.427 s t = 8.588 s t = 8.717 s

spindle-knot

Figure 13. (a) Image of spiderwebs, afterwater-induced structural changes, comprising thick knots connected by thinner jointsdue to Rayleigh instability; (b–d) SEM images showing morphology of knot and joint; and (e–j) time-lapse images showingpreferential transport of water droplets from joints to knots (adapted from [32]).

13


...............................................................

Laplace pressure gradient driving droplet against gravity on cactus spine

0 s

gravity

100 mm

dropletmoving up

10 s 20 s 30 s

Figure 14. Photographs of water droplets initially collected at the barb tip, climbing up over the cactus spine due to Laplacepressure gradient. Droplets defy gravity.

Web knots are known to be composed of randomly oriented porous nanofibrils, whilethe interconnecting joints are composed of stretched porous nanofibrils aligned parallel tothe thread (figure 13b–d) [32]. When water condensed on the wet-rebuilt spider thread, thedroplets condensing on the joints were found to move to the knots (figure 13e–j). A combinationof a surface tension gradient and a Laplace pressure gradient is believed to be responsiblefor the water movement [32]. Surface tension gradient occurs due to the knots displaying arougher surface because of the randomly oriented nanofibrils. The roughness enhances theirhydrophilicity, since the droplets are in the Wenzel state of wetting. Laplace pressure gradientoccurs due to the higher radius of curvature of the joints compared to the larger knots.

Laplace pressure gradient present on a conical surface with curvature gradient is discussed inappendix A [34].

(d) CactiCacti are commonly found in arid regions. They are mostly succulents, a type of plant withthick, fleshy and swollen parts that are adapted to store water and minimize water loss [35].Mooney et al. [36] reported that cacti species use fog as a supplemental source of water. Copiapoahaseltoniana, a species native to the Atacama Desert, was found to use the run off from nightlyfog events to survive in what is the driest non-polar desert in the world [37]. More recently,Gymnocalycium baldianum, a species in neighbouring Argentina, was found to collect and transportwater through microcapillaries [38].

Opuntia microdasys is a species of water-collecting cacti endemic to Mexico, which featuressmall barbs atop conical spines that help in the collection of water [39], figure 11. Water dropletscollect on the tips of the small barbs and once they reach critical size, they move onto the conicalspine. On the spine, the droplets move towards the base due to the curvature gradient, providingthe Laplace pressure gradient (appendix A). Once at the base of the spine, the plant absorbs thewater [2]. Laplace pressure gradient is large enough that water droplets can defy gravity andclimb up, figure 14.

(e) Other plant speciesOther plant species adapted to collect water from fog include Stipagrostis sabulicola, a grassendemic to the Namib Desert [2]. Water droplets collect on the leaf before coalescing and runningdown towards the base of the plant [24,40]. The leaves feature longitudinal ridges, which dictatethis fluid flow, figure 11 [41]. Another type of grass, Setaria viridis, is found to collect water with asimilar structure and mechanism to that found on the Opuntia microdasys cacti [42].

Cotula fallax bush is native to South Africa and is known to collect water from fog. Finehairs on the leaves of the plant intercept fog droplets where they coalesce and grow before

14


...............................................................

Table 3. Selected dimensions describing three water-collecting species (adapted from [9]).

water-collecting species dimensions references

desert beetle hydrophilic spot diameter: 0.2–0.5 mm,pitch: 0.5–1.5 mm

Parker & Lawrence [27]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

cactus spine length: approximately 1.5 mm,base diameter: approximately 50µm,tip angle: 10°,barbed length: top one-fourth of the spine length,groove length: bottom three-fourths of the spine length,groove width: approximately 2µm,groove pitch: approximately 20µm

Ju et al. [39]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

desert grass Cross section: C-shaped,width: approximately 2 mm,length:<2000 mm,groove width: approximately 0.3 mm,groove pitch: approximately 0.4 mm

Roth-Nebelsick et al. [41]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

dropping down into the plant structure when they become too heavy, and eventually reach theroots, figure 11 [43].

(f) SummaryMany flora and fauna commonly found in arid regions exhibit the ability to collect water from fog,summarized in figure 11 [2]. These examples typically contain a combination of surface structureand chemistry to achieve efficient interception, transport and collection of water. A beetle shellcomprises a random array of bumps. These bumps are hydrophilic, while the rest of the beetleback is hydrophobic. Therefore, water droplets collect on these bumps and once they are largeenough, travel over the body of the beetle and into its mouth. In some species of lizards, waterdroplets spread out over the skin before reaching the mouth. The water movement occurs due tocapillary action along the open channels in the skin. Spider webs are also known to collect water.First, the hygroscopic nature of the proteins contained within the silk results in condensation ofwater droplets and swelling of the cylindrical silk thread. This cylinder is then broken up due toRayleigh instability, resulting in smaller drops to lower its surface area leading to the ‘formationon a string’ structure. Species of cacti have conical barbs upon which water droplets preferentiallyflow towards the base due to Laplace pressure gradients. Certain grasses contain grooved surfaceswith anisotropic wetting characteristics, which direct water down towards the roots. Finally,some bushes contain fine hairs on the leaves of the plant which intercept fog droplets wherethey coalesce, grow and drop down into the plant structure when they become heavy, eventuallyreaching to the roots.

Selected dimensions of desert beetle, cactus and desert grass are presented in table 3 [9].

4. Bioinspired surfaces for water collection from fogThere have been many attempts to produce surfaces for water collection from fog, inspired by thebeetle [9,44,45], grass [9,10,46] and cactus [47]; Gurera & Bhushan [9,10,48]. The methods usedin nature include—heterogeneous wettability, curvature gradient (Laplace pressure gradient)and/or grooves.

In this section, an overview of a systematic study of bioinspired water collectors carriedout by Gurera & Bhushan [9,10] is presented. Heterogeneous wettability, Laplace pressuregradient and grooved surfaces were investigated on flat and conical water collectors. The flat

15


...............................................................

surfaces with different wettability and surface roughness as well as heterogeneous wettabilitywere characterized for their water collection abilities. Conical surfaces with different geometry,ungrooved and grooved, and different wettability were characterized for droplet movement andtheir water collection abilities at different inclination angles. Based on the data, design guidelinesfor water collection towers with heterogeneous wettability and/or consisting of conical arrays arepresented.

(a) Experimental methodThis section describes fabrication of various surfaces, and the experimental set-up used for watercollection measurements [9–11].

(i) Fabrication of water collector surfaces

Flat surfaces with homogeneous wettability and beetle-inspired surfaces. Flat surfaces withhomogeneous wettability included superhydrophobicity, hydrophobicity, hydrophilicity andsuperhydrophilicity [49,50]. Beetle-inspired surfaces consisted of superhydrophilic spots over asuperhydrophobic background. A spot size of 0.5 mm and a pitch of 1 mm were chosen, whichwas inspired from the desert beetle’s dimensions, as given in table 3 [9]. The effect of two surfaceroughnesses was also investigated, which was introduced by spray coating the surface withdifferent nanoparticles and binder. Two sizes of nanoparticles of 10 µm and 7 nm were used, sothat the pitch between the nanoparticles’ asperities could be varied. As stated earlier, fog haswater droplets of diameter on the order of 10 µm which will interact with the surface based onthe surface roughness and surface energy. Therefore, two sizes of nanoparticles were chosen, onecomparable to the fog droplet size and one smaller [9].

The substrate used was polycarbonate (PC) because it is a tough material and is commonlyused in the fabrication of water bottles. PC substrate is hydrophilic. It was made hydrophobicby vapour deposition of fluorosilane (448931, Sigma Aldrich). The 20 mm × 20 mm samples wereplaced upside down and a droplet of fluorosilane was placed 1 cm below in an enclosure, andwas left for 30 min [51]. A superhydrophobic surface was fabricated by spray coating a mixtureof hydrophobic silica particles and methylphenyl silicone (SR355S, Momentive PerformanceMaterials) binder on the uncoated PC [50,52,53] (figure 15). Two different sizes of particles wereused, 10 µm (Aerosil VM2270) and 7 nm (Aerosil RX300). The coating mixture was prepared bymixing 375 mg of the particles and 150 mg of the binder in 30 ml of solvent in an ultrasonifier(Branson Sonifier 450A, Emerson Electric Co., St Louis, Missouri) for 30 min. The solvent used was40% tetrahydrofuran (THF, Fisher Scientific) and 60% isopropyl alcohol (IPA, Fisher Scientific).Superhydrophilicity was introduced by treating the PC surface with ultraviolet-ozone (UVO)light. The UVO lamp used was a U-shaped lamp (18.4 W, Model G18T5VH-U, Atlantic UltravioletCo.), and the samples were kept directly underneath the light source for 60 min.

To fabricate a beetle-inspired surface, superhydrophilic spots were introduced on thesuperhydrophobic surface by irradiating the spray coated surface using UVO light through amask. Schematic of the mask is shown in figure 15.

Beetle-, grass- and cactus-inspired surfaces. Bioinspired conical surfaces with and without grooveswere fabricated using additive manufacturing or 3D printing (Objet30 Prime, Stratasys) thatallows flexibility in designing and scalability [9,10]. The machine uses PolyJet 3D printingtechnology, which is similar to inkjet printing, and jets layers of curable liquid photopolymeronto a build tray. It has an accuracy of 0.1 mm. The material used was acrylic polymer, RGD720.Surface wettability was modified by surface treatment and/or coating deposition.

Cylinder versus cone: Conical and cylindrical surfaces were fabricated to study the effect ofconical geometry. Schematics of cylindrical and conical geometries are presented in figure 16. Thedesign was based on the dimensions of natural species, summarized in table 3. A base cylinderdiameter of 3 mm was chosen in an effort to mimic the grass’s diameter. The length was chosen to

16


...............................................................

beetle-inspired water collectors

fabrication approach

polycarbonate

superhydrophobic

superhydrophilic spots

superhydrophilicspots

UVO irradiationthrough a mask

water CA: polycarbonate - 75° ± 2°, superhydrophobic - 163° ± 2°, superhydrophilic - wet

spray coating ofmethylphenylsilicone resin +10 mm or 7 nmSiO2 NP

mask

20 mm

hole diameter - 0.5 mmpitch - 2 × hole dia.hexagonal arrayno. holes - 449

20 m

m

Figure 15. Fabrication of surfaces with heterogeneous wettability for beetle-inspired water collectors (adapted from [9]). NP,nanoparticle.

cylindrical and cactus-inspiredconical water collectors

material - hydrophilic acrylic polymer,water CA - 61° ± 2°

cylinder and cone

35 mm

3 mmdia.

6 mmdia.

surface area 330 mm2

10°

Figure 16. Schematic of 3D printed cylinder and a cone with equal surface area (adapted from [9]).

17


...............................................................

be 35 mm. To keep the surface area and the length constant, the base diameter of the cone, 6 mm,was doubled to that of the cylinder, and the tip angle was kept at 10°, as seen in cactus spines [9].

Single cone. (a) Geometry. To study the effect of conical geometry, two tip angles were chosen:10° and 45°. Cacti conical spines have a tip angle of about 10°, as mentioned in table 3. Forcomparison, a larger tip angle of 45° was chosen [10]. When considering the collection of waterfrom fog, a comparison between cones of different tip angles and the same surface area is neededbecause fog intercepts the entire surface and droplets are formed across the whole surface.Therefore, having a similar number of water nucleation sites presents a fair comparison. It isknown that a droplet moves from the tip to the base under a fog flow. Therefore, comparing tipangles with same lengths, presents another fair comparison. This results in the travelling distancefor droplets to be the same on each cone.

Two pairs of cones with two tip angles were fabricated—one with the same surface area(330 mm2) and another with the same length (15 mm), as shown in figure 17a [10]. The surfacearea, A, is given by π l2(tan(θ/2)/cos(θ/2)), where l is the cone length, and θ is the tip angle.

(b) Grooves. A representative cone of 45° tip angle and 15 mm length, was chosen to investigatethe effect of grooves inspired by desert grass and cactus, as shown in figure 17b [10]. The numberof grooves selected was 8; they were spaced equidistantly, and ran up to three-quarters of thecone’s length, as inspired from cactus. The thin grooves found on a cactus spine could not befabricated using the 3D printer. Therefore, the grooves’ cross-sectional dimension, 0.4 mm by0.4 mm, inspired from grass (table 3), was used.

(c) Heterogeneity. A representative cone of 45° tip angle and 15 mm length, was chosen toinvestigate the effect of heterogeneity, as shown in figure 17b [10]. Heterogeneous wettabilityin grass and cactus does not exist in nature. It was incorporated with inspiration coming fromthe desert beetle. Heterogeneous wettability in the conical surfaces included a hydrophobic tipwith a superhydrophilic base. A hydrophobic tip was selected as it can collect more water,and a superhydrophilic base because it can transport the collected water quickly to the base.Superhydrophobic tips are not recommended because droplets will not stick to the surface andwill fly away instead, because of the low tilt angle.

For fabrication, the complete cone was made superhydrophilic under a UVO lamp. Thebottom three-quarters was then covered with Teflon tape and the entire object was subjectedto fluorination; afterwards, the tape was removed. The fluorination was achieved via vapourdeposition of fluorosilane (448931, Sigma Aldrich). The samples were placed upside down and adroplet of fluorosilane was placed 1 cm below the tip in an enclosure, and was left for 30 min [51].

Conical array: To design arrays, a representative cone of 45° tip angle and 15 mm length waschosen. Seven cones were selected in the array, with end-to-end spacing between two adjacentcones of about 2 mm, as shown in figure 17c.

(ii) Experimental set-up

Single droplet experiments. For fundamental understanding of droplet dynamics on cones, thesingle droplet experiments were carried out to investigate the effect of the tip angle of cones andtheir orientation on the movement of droplets of known volume. Two tip angles were chosen: 10°and 45°. The cones were placed with either sideline or centreline in the horizontal orientation.Sideline in the horizontal orientation was used to study the role of Laplace pressure gradient onthe movement of the droplets. Whereas with centreline in the horizontal orientation, gravitationalforce also contributed to the movement. Using a pipette, a droplet was placed at the tip of the coneand its motion was photographed [10,48].

Droplets were fed in increments of 5 µl volume (about 2 mm diameter), which is a smallenough volume for them to stick to the surface, rather than fall off when ejected from the pipette.Dependent upon the size of the droplet, it moved for some distance and stopped. After the firstdroplet had stopped, the pipette was pointed at the current location of the droplet, not the tipof the cone. The increments were added until the droplets detached and fell off the cone surface.

18


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cone

conical array

45°

10°

10°

6 mm dia.

330 mm2 65 mm2 330 mm2 410 mm2

3 mm dia.

2 mm

surface area - 3500 mm2

no. cones - 7, hexagonal array

15 mm

13 mm dia.

13 mm dia.

8 grooves hydrophobic: vapourdeposited fluorosilane

superhydrophilic:UVO etched

superhydrophilic

hydrophobic

45° 45°

4 mm (1/4)

11 mm (3/4)

35 m

m

15 m

m

15 m

m

grooved

beetle-, grass- and cactus-inspired water collectorsmaterial - hydrophilic acrylic polymer, water CA - 61° ± 2°

heterogeneouswettability

(a) (b)

(c)

Figure 17. Schematic of 3D printed beetle-, grass- and cactus-inspired water collectors. (a) Single cones with 10° or 45° tipangles and either equal lengths (15 mm) or equal surface areas (330 mm2), (b) grooved cone with eight grooves running up to3/4 of the length starting from thebase anda conewithheterogeneouswettabilitywithbottom3/4of the cone superhydrophilicand top 1/4 hydrophobic, and (c) a conical array with seven cones of 45° tip angle [10].

Droplets fall because at higher volumes, gravitational forces dominate the capillary forces. Forthe cones used in this study, droplets detached at deposition of total water volume of about 40 µl.

The distance travelled as a function of droplet volume on the two cones was recorded. Thedistance was measured from the tip of the cone to the centre of the droplet. Experiments wererepeated three times for each cone. The average and standard deviation of the distance wasreported at every 10 µl increment [10].

Water collection from fog. Figure 18a shows a schematic of the experimental apparatus [9,10].A commercial humidifier (EE-3186, Crane, Itasca, IL, USA) was used to produce a stream of fogonto a surface and water collected was measured using an analytical balance (B044038, DenverInvestment Company, Bohemia, New York) underneath. The minimum weight the balance couldmeasure was 1 mg. The humidifier, which emits fog at about 10 cm s−1, was kept about 20 cmaway from the surface. The flow speed was calculated by measuring the volume of water lostover time, and by knowing the diameter of the pipe through which the fog was blown out.

19


...............................................................

1200

0 543time (h)

wat

er c

olle

ctio

n (m

g)

21

300

600

900

20 cm

fog flow

container

surface area - 330 mm2

cone(tip angle 10°)(hydrophilic) flat

(hydrophilic)

analyticalbalance

humidifier

0.0000 g

q°bioinspiredcollector

(a)

(b)

Figure 18. (a) Schematic of apparatus for water collection from fog. A commercial humidifier throws a stream of fog on abioinspired water collector. The collector base was inclined at either 0° or 45° from vertical axis (θ ). Inclination angle of 0°means that the cone axis is parallel to the fog flow (horizontal). The collected water was measured by an analytical balanceunderneath. (b) A representativewater collection (milligram) versus time (hour) plot for hydrophilic flat surface, and hydrophiliccone surface of 10° tip angle and 35 mm length, both at 45° inclination (adapted fromGurera & Bhushan [9,10]). (Online versionin colour.)

When the fog is turned on, droplets form all across the intercepted surface area. There aretwo forces which drive these droplets to the base—gravity and force due to the Laplace pressuregradient. To characterize the effect of both forces individually, two inclination angles were chosen– 0° and 45°; here 0° means the cone axis is parallel to the fog flow (horizontal). At 0° inclinationangle, the only driving force is the Laplace pressure gradient. At 45° inclination angle, the forcedue to both gravity and the Laplace pressure gradient act on the droplets. In the experiments, theweight range of each collected drop was about 30–60 mg.

Water collected by a surface was measured as a function of time [9,10]. A straight line was fittedthrough the points and the slope of the line was referred to as the water collection rate (mg h−1).A minimum of five droplets were allowed to fall before a straight line was fitted. The amountof water collected after a certain amount of initial collection period was believed to be a moreaccurate representation of the water collection; some published studies calculate the rate from thebeginning of the time. The average and the standard deviation calculated from a minimum of 15data points were reported [9,10].

There are three other parameters by which the collected data can be characterized. First isthe initial wait time—the time to get the first droplet in the beaker. Typically, the higher thewater collection rate, the lower the initial wait time. The second parameter is the frequency ofthe droplets dropping (droplets h−1), which is the sum of the inverse of the wait-time for everydroplet except the first droplet. This parameter gives an idea of how fast the surface is collectingwater. The third parameter is average weight of the collected droplet (mg). It is the averageof every droplet dropped in the beaker. This could be measured since a balance reading wasrecorded before and after the falling of every droplet. This allows one to observe the mass of thedroplets being collected by the surface. Ideally, high frequency and high average droplet weightare desired [10].

A representative data of the amount of water collection as a function of time for two surfaces ispresented in figure 18b. The two surfaces were cones with a 10° tip angle and a flat surface. Bothwere hydrophilic, had the same surface area of about 330 mm2, and were inclined at a 45° angle.

(b) Results and discussionWater collection data for flat, cylindrical and conical surfaces are presented in this section [9,10].First, water collection data by flat surfaces of various wettability and beetle-inspired surfaces atdifferent inclinations and surface roughness (nanoparticle sizes) are presented. This is followedby a cylinder versus cone with same surface area and two inclination angles.

20


...............................................................

flat surfaces with various wettabilities at 45° inclination with two NP sizes

1.5

wat

er c

olle

ctio

n ra

te

(mg

mm

–2 h

–1)

400 mm2, 2 h

(10 mm NP)superhydrophobic

(7 nm NP) (7 nm NP)

supe

rhyd

roph

obic

supe

rhyd

roph

ilic

hydr

opho

bic

hydr

ophi

lic(u

ncoa

ted)

10 mm NP 7 nm NP

0beetle-

inspired

beetle-inspired

beetle-inspired

homogeneous

homogeneous

superhydrophobic(10 µm NP)

1 mm

large droplets formwhich roll down

droplets spread over the surfaceand lead to some evaporation

droplets roll/slidedown because of

heterogeneity

smaller particles provide morenucleation sites and largernumber of smaller droplets

small dropletslost by wind

droplets roll/slidedown because of

heterogeneity

hydrophilic superhydrophilic

homogeneous

differences in droplet formation on various surfaces after 1 h

0.5

1.0

(a)

(b)

Figure 19. (a)Water collection rates per unit surface area for flat surfaceswith variouswettability and beetle-inspired surfaces,at 45° inclination. The wettability includes superhydrophobic, hydrophobic, hydrophilic (uncoated), and superhydrophilicsurfaces, and a beetle-inspired surface (which includes 0.5 mm diameter circular superhydrophilic spots surrounded bysuperhydrophobic surface). The superhydrophobic and beetle-inspired surfaces were created using two different sizes of NP—10 µm and 7 nm. (b) Optical images showing differences in droplet formation on various surfaces after about 1 h (adaptedfrom [9]).

Next, data on single droplet transport experiments on two cones with different orientationsare presented, followed by water collection from fog data on cones with various geometriesand wettability at different inclination angles and arrays. Finally, design guidelines for watercollection tower are presented.

(i) Flat surfaces with various wettability and beetle-inspired surfaces at 45°and 0° inclination angles

To study the effect of various wettability and heterogeneity on flat surfaces, water collectionrate per unit area was measured at a 45° inclination. The date are shown in figure 19a.Superhydrophobic and beetle-inspired surfaces were prepared using 10 µm and 7 nm particles.The size of the particles affects the surface morphology and droplet interaction. Figure 19b showsdifferences in size and shape of droplets on various surfaces after 1 h [9].

The data show that the higher the repellency (higher CA) on the flat surface, the higherthe water collection. The decreasing order of the water collection rate per unit area on flatsurfaces with homogeneous wettability is superhydrophobic surface using 10 µm, hydrophobic,hydrophilic and superhydrophilic. This is attributed to the fact that the higher the repellency,the more spherical the droplet shape will be, which results in a lower contact area between the

21


...............................................................

Table 4. Summary of water collection rates by flat surfaces with various wettability and beetle-inspired surfaces at twoinclination angles, and some fabricated with two nanoparticle (NP) sizes (adapted from [9]).

wettability water collection rate (mg mm−2 h−1)

inclination angle

45° 0°

10 µmNP 7 nm NP 10 µmNP 7 nm NP

homogeneous Superhydrophobic 0.7± 0.1 — 0.5± 0.1 0.5± 0.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

hydrophobic 0.5± 0.1 0.4± 0.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

hydrophilic (uncoated) 0.4± 0.1 0.3± 0.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

superhydrophilic 0.4± 0.1 0.3± 0.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

beetle-inspired 0.5 mm spot diameter 0.8± 0.1 0.9± 0.1 0.7± 0.1 0.8± 0.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

droplet and the surface. Therefore, less heat will be transferred to the droplet and less evaporationwill be observed. As shown in the optical images, large spherical droplets are formed on thesuperhydrophobic surface which roll down. In the case of hydrophilic and superhydrophilicsurfaces, the droplets spread across the surface leading to higher evaporation [9].

A beetle-inspired surface was found to collect more water than flat surfaces with homogeneouswettability. This is because of the heterogeneity: droplets can slide/roll at a faster rate, andmaintain a spherical droplet shape, leading to lesser evaporation [9].

Next, the effect of smaller particles was investigated. A coating with smaller particles resultsin a surface with lower pitch of asperities when compared with the larger particles, whichaffects the number of nucleation sites. A coating with smaller particles is believed to increasethe water collection rate because of more nucleation sites leading to a larger number of smallerdroplets coalescing faster. There was an increase in the water collection on the beetle-inspiredsurface because the droplets sitting on superhydrophobic spots roll off to superhydrophilic spots.However, the superhydrophobic surface resulted in no water collection. This is because of the factthat smaller particles nucleate smaller droplets, as shown in the optical images, which could leadto losing droplets to the wind [9].

Gurera & Bhushan [9] also performed experiments on various surfaces at 0° inclination angle.The data are summarized at two inclination angles in table 4. There was no significant differencebetween 45° and 0° inclination angles, except for the superhydrophobic surface using 7 nmparticles. It was because there was little water collection because the droplets were not lost tothe wind at 0° inclination, instead they fell in the beaker [9].

To summarize, it was found that higher water repellency in flat surfaces resulted in a higherwater collection rate. The inclination angle (with respect to the vertical axis) had little effect.Surfaces with heterogeneous wettability had a higher water collection rate than surfaces withhomogeneous wettability.

(ii) Cylinder versus cone at 0° inclination angle

To study the role of conical geometry, water collection rates on a cylinder and a cone weremeasured. Figure 20a shows the water collection data for single cylindrical and conical surfaces,with the same surface area and length, at 0° inclination angle [9]. The 0° angle was chosen toeliminate the effect of gravity on the movement of the droplets along the length. The left part ofthe bar chart shows water collection for the complete object. However, in nature, the collectedwater that matters is that which reaches the base; therefore, the right part of the bar chart presentsthe water collection rate per unit area at base half-length. The complete water collection rate perunit area by cylinder and cone was found to be comparable. However, it was negligible at the

22


...............................................................

0.05

0.10

homogeneous wettability(hydrophilic)

wat

er c

olle

ctio

n ra

te(m

g m

m–2

h–1

)

drop

let w

eigh

t (m

g)

0.15

0.20

cylinder

cylinder

droplet grows at the tip anddrops and no force is pushing

droplet to the base

droplets form, coalesce andtravel to the base, due to Laplace

pressure gradient, and fall

complete collection

completecollection

completecollection

half lengthcollection at base

cone

cone

cylinder conecylinder cone

330 mm2, 5 h

0 0

20

40

60

80 4

3

2

1

freq

uenc

y (d

ropl

ets

h–1)

0

(b)(a)

(c)

0 h

1 h 1 h

2 h 2 h

0 h

5 mm

Figure 20. (a) Water collection rates for a cylinder and a cone at 0° inclination. The left part of the bar chart shows the datawhen water was collected under the entire surface (complete collection). The right part shows the data when the water wascollected under the half-length near the base (as in nature), (b) weights and frequency of falling droplets on a cylinder and acone in complete collection and (c) the optical images showing movement of the water droplets on a cylinder and a cone incomplete collection (adapted from [9]). (Online version in colour.)

base half-length for a cylinder. Figure 20b shows comparison of weight and frequency of dropletson complete collection. Cones collect heavier droplets with a lower frequency.

Figure 20c shows optical images of droplets growing and moving on a cylinder and a cone atthree time steps [9]. On the cylinder, water droplets nucleate at the tip, grow, attain a critical size,then fall. Droplets mostly nucleate at the tip because it intercepts the fog flow perpendicularly.On the rest of the curved surface, little to no droplets were observed since the surface is parallelto the fog flow. The smaller droplets became visible much later, at about the 4 h mark. Since thedroplets are small and sit on the surface for a long time, a significant amount of their volume islost to evaporation. Therefore, the droplets nucleating at the cylinder’s tip are mostly responsiblefor the water collection rate per unit surface area [9].

The droplets growing at the cylinder’s tip do not move along the length, since there is no forceacting in that direction. However, this is not the case in cones. Droplets nucleate at the tip, growand move along its length. For a droplet resting on a conical surface, the changing radius results ina pressure difference inside the droplet (appendix A). Laplace pressure gradient causes dropletsto move on a cone from regions of low radius to regions of higher radius.

Irrespective of the motion of the droplet, both a cylinder and a cone have similar watercollection rates per unit area. As mentioned earlier, in nature, the water collection that matters isat the base. A cylinder does not achieve any water collection at the base, whereas a cone achievesthe same water collection at the base that was observed in complete collection. As a result, coneshave an advantage over cylinders in water collection at the base.

23


...............................................................

250 mm

droplets movement on cone and cylinder

on cone, droplets coalesce and move upward due to Laplace pressure gradient.On cylinder, droplets grow but do not move

10° cone

cylinder

0 s 15 s 28 s 29 s7 s

0 s 15 s 28 s 29 s7 s

250 mm

Figure 21. Video stills of water droplets on a cone with 10° tip angle, pointed downward, and a cylinder, both inclined in thevertical direction. Water droplets grew larger but did not move on a cylinder; however, droplets grew, coalesced and climbedupward on a cone due to Laplace pressure gradient, defying gravity. (Online version in colour.)

flat cone

hydr

ophi

lic

hydr

ophi

lic

beet

le-

insp

ired

0.5

0

1.0

1.52 h

summary of various surfaces at 45° inclination

wat

er c

olle

ctio

n ra

te(m

g m

m–2

h–1

)

Figure 22. Summary of water collection rates for flat hydrophilic and beetle-inspired surfaces and a hydrophilic cone at 45°inclination (adapted from [9]).

To illustrate that Laplace pressure gradient defies gravity, figure 21 shows video stills ofdroplets on a cone with 10° tip angle pointed downwards and a cylinder. It can be seen thatdroplets grew larger but did not move on the cylinder. However, droplets grew, coalesced andclimbed upwards on a cone, defying gravity.

(iii) Cone at 45° inclination angle and comparison with flat surfaces

To study the effect of the inclination angle, water collection rates on a cone at 45° inclinationangle were measured at the base. Data are shown in figure 22 [9]. The water collection rate at45° inclination is about an order of magnitude higher that that at 0° inclination (figure 20a). At45° inclination angle, the entire surfaces intercept the fog flow, not just its tip. Droplets nucleate,

24


...............................................................

grow, slide along the length and drop at the base. Droplets fall at the base because there is gravity(g sin θ ) in addition to Laplace pressure gradient, aiding the movement of the droplets towardsthe base. It was reported by Gurera & Bhushan [9] that at 45° inclination angle, the frequency ofthe droplets falling was about 6–8 times higher when compared with the 0° inclination. However,aid by gravity did not increase the weight of the droplets falling. To summarize, higher inclinationincreased the water collection rate.

The cone data are also compared with the data for flat and beetle-inspired surfaces, presentedearlier. A cone surface collects about twice as much water as that for a flat surface.

It is noted that a surface covered with cones (conical array) would provide flexibility inincreasing surface area to increase collection by several fold, a factor of 10–100 or even more.

(iv) Cones with various geometries and inclination

Single droplet experiments. To develop fundamental understanding of droplet dynamics, singledroplet experiments were conducted on cones with two tip angles of 10° and 45° with sidelineor centreline in the horizontal direction. On a cone with the sideline in the horizontal direction,only Laplace pressure gradient due to curvature gradient drives the droplet, whereas on a conewith the centreline in the horizontal direction, in addition to Laplace pressure gradient, thegravitational forces due to inclination of the cone surface with respect to horizontal axis drivethe droplet.

Figure 23a shows the relationship between droplet volume and distance travelled by thedroplet for cones of two tip angles, 10° and 45°, with the sideline in the horizontal orientation[10]. Figure 23c shows the four images, (top) during the moment of the first droplet depositionand just after deposition, and (bottom) equilibrium stages of a 10 µl droplet and a 40 µl droplet,for cones of 10° tip angle [9].

Figure 23a shows that for any cone, a droplet will move towards the base if the droplet volumeis increased. On increasing the volume, a droplet instantaneously moves a certain distance andthen stops. The droplet moves due to the Laplace pressure gradient resulting from the underlyingcurvature gradient. As the curvature decreases, the Laplace pressure inside the droplet decreases.The droplet stops because the force due to the Laplace pressure becomes less than the adhesionforce between the surface and the droplet. Figure 23a also shows that a droplet of known volumetravels further on a cone with tip angle of 10°, when compared with on a cone of tip angle of 45°.

The curvature gradient was calculated using the expression (1/R1 − 1/R2), where R1 and R2are the two local radii of the cone at two ends of the droplet. As the droplet moves, R1 and R2change. For a cone with a tip angle of θ , radius, R, at a given distance from the tip, d, is given byd tan(θ/2). The curvature gradient was plotted as a function of distance from the tip of the coneto the centre of the droplet, along the cone axis. Two droplets with lengths of 0.5 mm and 2 mmmeasured along sideline of cones were selected because they are typical large droplet lengthsobserved in water collection measurements. Figure 24 shows calculated curvature gradient as afunction of distance for two cones with tip angles of 10° and 45°. An increase in the droplet lengthincreases the curvature gradient because of the larger change in the radii. The curvature gradientdecreases with the distance from the tip. The curvature gradient of a cone with a smaller tip angleis larger and remains so for a longer distance. Therefore, the droplet on a cone with smaller tipangle travels farther. Since curvature gradient decreases with distance, the droplet stops aftersome distance.

Figure 23b shows the relationship between droplet volume and distance travelled by thedroplet for cones of two tip angles, 10° and 45°, with centreline in horizontal orientation.Figure 23d shows the two images at equilibrium stages of a 10 µl droplet and a 40 µl droplet,for cones of 10° tip angle [10]. Droplets on both cones travelled further, compared to that of coneswith sideline in the horizontal direction. A droplet of 40 µl on a 45° tip angle cone travelled theentire cone length and reached its base.

At centreline in the horizontal orientation, a component of gravity along the side of the conealso drives the droplets. The gravitational force acting on the droplets is given by (V ρ)g sin(θ/2),

25


...............................................................

1 mm

1 mm

effect of tip angle on droplet movement using single droplet experiment at two orientations

60

40

20

0

sideline horizontal

time taken to reach equilibrium: <1 s

tip angle

45° 10°

gravity 90°

gravity

tip angle 45°tip angle 10°

90°

centreline

Laplacepressure gradient

8distance (mm)

a droplet of fixed volume travels farther in smaller tip angle cone

(a)

(c)

(d)

10

centreline horizontal 60

length = 15 mm length = 15 mm

40

20

02 4 6 2 4 6 14 16 distance (mm)

gravity increases the distance travelled by the droplets. The effect is more prominent at higher volumes and

higher tip angle cones

drop

let v

olum

e (µ

l)

(b)

tip angle 10°at deposition

pipette

distancetravelled

distancetravelled

1 mm

cone

at time = 0

at equilibrium droplet volume - 10 µl droplet volume - 40 µl

tip angle 10° at equilibrium

droplet volume - 10 µl droplet volume - 40 µl

Figure 23. Droplet volume as a function of the distance travelled for cones with 10° and 45° tip angles, when (a) a cone placedwith the sideline in horizontal orientation, as shown in the insert, to study the effect of Laplace pressure gradient and to removethe gravitational force in driving the droplet, and (b) a cone placed with the centreline in the horizontal orientation, as shownin the insert, to add gravitational effects in driving the droplet. (c) The four images shown are (top) during the moment of thefirst droplet deposition and just after deposition, and (bottom) equilibrium stages of 10µl and 40 µl droplets on a 10° tip anglecone with sideline in horizontal orientation, and (d) the two images shown at equilibrium stages of 10µl and a 40 µl dropletson a 10° tip angle cone with centreline in horizontal orientation (adapted from [10]). (Online version in colour.)

where V is volume of the droplet, ρ is mass density of water and g is the gravitational constant(9.8 m s−2). It increases the distance travelled by the droplets along the cone. The effect is morepronounced for larger volume droplets and larger tip angles.

Gurera & Bhushan [10] also conducted single droplet experiments in the presence of fog. Fogcontinuously deposits droplets on the entire cone. These droplets coalesce with each other and theincreased volume of the droplet increases the distance travelled. It is the continuous depositionof fog droplets which maintains the droplet motion. Otherwise, in the absence of fog deposition,any deposited droplets only travel a certain distance during which Laplace force is high enoughto overcome adhesion to the surface.

To sum up, for efficient water transport, it is important to maximize the effects of Laplacepressure gradient, gravity and droplet coalescence.

26


...............................................................

0 1 2 3 4 5

10° 10°45° 45°

2

4

6

8

10effect of tip angle on curvature gradient

droplet length 0.5 mm 2 mm

distance (mm)

curvature gradient increases with decreasing tip angle and increasing droplet length

curv

atur

e gr

adie

nt (

mm

–1)

Figure 24. Calculated curvature gradient as a function of distance from the tip of two cones with tip angles of 10° and 45° fortwo droplets with lengths of 0.5 and 2 mm. (Online version in colour.)

effect of tip angle on cone at 0° inclination same surface area: 330 mm2

400

300

20035 mm

100

0

drop

let w

eigh

t (m

g)

wat

er c

olle

ctio

n ra

te (

mg

h–1)

80

60

40length 15 mm

20

0 10°

shorter length provides higher water collection rate, because of shorter travel time for water droplets

freq

uenc

y (d

ropl

ets

h–1) 4

3

2

1

45°0

tip angle 10° 45°

tip angle

Figure 25. Water collection rates, and weight and frequency of falling droplets for cones with the same surface area and tipangles of 10° and 45°, at 0° inclination angle (adapted from [10]).

Water collection from fog. Two sets of cones were tested to evaluate the effect of tip angles—onewith the same surface area and another with the same length at two inclination angles. Coneswith grooves and heterogeneity were also studied. Finally, a conical array was tested.

Two tip angles with the same surface area: Figure 25 shows the water collection rate forcones with two tip angles and with the same surface areas at 0° inclination [10]. The left bar chartshows the water collection rate (mg h−1). The right bar chart shows the average droplet weight(milligrams) and frequency (droplet h−1) for the two cones. The cone with higher tip angle hashigher water collection rate. This is because cone length of the larger tip angle cone is shorter anddroplets take less time to reach to the base. Although the weight of the falling droplets is similar,the cone with a larger tip angle has a higher frequency of falling droplets.

Figure 26 shows a sequence of optical images of water droplets moving from tip to base forboth tip angles [10]. A sequence for the first droplet is presented. It was reported that the firstdroplet takes a longer time to fall when compared with the subsequent droplets. Optical imagesof water droplets just before they completely detached from the cones are also shown. The size ofthe droplets appears to be similar, independent of the tip angle. This is the reason that the weightsof the fallen droplets were found to be similar. As the droplet starts from the tip and reaches the

27


...............................................................

0 h

3 mm

3 mm

0 h

1 h

0.2 h

0.9 h

1 h

1.4 h

1.5 h

first droplet takes longer timethan subsequent droplets


droplet movement on cone at 0° inclination

first falling droplet

Figure 26. Optical images showing the movement of water droplets from tip to base on the 10° and 45° tip angle cones anddroplets just before and after they detach from the surface and fall. The sizes of the falling droplets on the two cones appearto be similar. It was reported that the first droplet takes a longer time to fall when compared with the subsequent droplets(adapted from [10]). (Online version in colour.)

end of the cone, it sits there and elongates. As the elongation reaches a critical length, the dropletstarts to break away, as shown in the images.

Two tip angles with same length: Figure 27a shows water collection rates for cones withtwo tip angles of the same length at 0° inclination [10]. The bar chart on the left side showsthe water collection rate data (mg h−1). The bar chart on the right shows the average dropletweight (milligrams) and frequency (droplet h−1) for the two cones. The cones of same lengthwere found to have similar water collection rates. From the single droplet experiment, Laplace

28


...............................................................

0 h 0.6 h

0.3 h 0.8 h

0.5 h 0.9 h

3 mm

effect of tip angle on cone at 0° inclination same length: 15 mm

400 80 4

300

200

100

0

wat

er c

olle

ctio

n ra

te (

mg

h–1)

surface area 65 mm2 330 mm2

10° 45°

60

40

20

010°

tip angle tip angle same length results in same water collection rate,

regardless of the surface area

3

2

1

45°0 fr

eque

ncy

(dro

plet

s h–1

)

drop

let w

eigh

t (m

g)

(a)

(b) tip angle 10°first falling droplet second falling droplet

first droplet takes longer time than subsequent droplets

Figure 27. (a)Water collection rates, andweight and frequency of falling droplets for coneswith the same length and tip anglesof 10° and 45°, at 0° inclination angle. (b) Optical images showing the movement of water droplets from tip to base on a conewith tip angle of 10°. The first droplet took longer time to fall when comparedwith the subsequent droplets (adapted from [10]).(Online version in colour.)

pressure gradient was found to be more effective in a smaller tip angle cone. However, due to thedifference in surface areas, more water droplets are formed on the surface of the 45° tip angle cone.This makes the water collection rate for both the cones similar. Droplet weight and frequency werereported to be similar for the two cones.

Figure 27b shows a sequence of optical images of the first and second water droplets movingfrom tip to base for the cone with 10° tip angle [10]. The first droplet takes the longer time to fallwhen compared with the subsequent droplets.

Inclination angle: Figure 28 shows water collection rates for cones with two tip angles at twoinclination angles [10]. The cones of 10° and 45° tip angles, having either the same surface area orsame length, were compared at two inclination angles of 0° and 45°.

29


...............................................................

35 mm,330 mm2

15 mm,65 mm2

15 mm,330 mm2

15 mm,330 mm2

15 mm,65 mm2

35 mm,330 mm2

0°0

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effect of inclination angle on cone


wat

er c

olle

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te (

mg

h–1)

0

100

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400w

ater

col

lect

ion

rate

(m

g h–1

)

inclination angle inclination angle

at 0° inclination, length dictates water collection rateat 45° inclination, surface area dictates water collection rate

Figure 28. Summary of water collection rates for cones of tip angles of 10° and 45°, with either the same lengths or the samesurface areas, and at two inclination angles of 0° and 45° (adapted from [10]).

As was mentioned before, there are two forces driving droplets on the conical surface dueto Laplace pressure gradient and gravity. In the previous section, it was established that in theabsence of driving gravitational force, at 0° inclination angle, the cone length dictates the watercollection rate. The shorter the cone, the higher the water collection rate, irrespective of the tipangle. This is because the distance travelled by the droplets from the tip to the base is shorter inshorter cones.

At a 45° inclination angle, gravity also drives droplets. Therefore, increasing the inclinationangle increases the water collection rate, irrespective of the cone tip angle. The increase is morefor cones with a larger surface area. At a 45° inclination angle, it is logical to expect that therequired volume for a droplet to move towards the base is much lower than the required volumerequired at a 0° inclination angle. Therefore, at a higher inclination angle it is the number ofdroplets formed on the surface that dictates the water collection rate, not the length. Moreover,same as before, the tip angle is not a contributing factor in collecting water from fog.

Velocity of droplets: High droplet velocity is needed for water collection purposes to minimizewater loss to evaporation. For velocity measurements, the distance between the centre of thedroplet from the tip of the cone was measured as a function of time. The centre of the dropletwas located by taking the midpoint of the distance between the left edge and the right edge of thedroplet. Measurements were performed by using a video camera to record a video that startedwhen the second droplet was deposited and ended when the second droplet reached the conebase or detached from the cone. Screenshots were taken with timestamps to document dropletmovement. These screenshots were then analysed by software included with the video camera toaccurately determine droplet distance on the cone at certain periods of time. These time/distancedatapoints were plotted and a second-order polynomial equation trendline was fitted to the data.The derivative of this time/distance equation was then calculated to determine the velocity/timeequation. The droplet velocity at any length on the cone could be found by entering the timeassociated with a distance measurement into the velocity equation [48].

Velocities of droplets as a function of distance moving on cones of 10° and 45° tip angles, at 0°inclination are shown in figure 29 [48]. The initial velocity of the cone with 10° tip angle was higherthan that of the cone with a 45° tip angle because of larger Laplace pressure gradient. For the 10°tip angle cone, the velocity decreases with distance because of the decreasing curvature gradientresponsible for the Laplace pressure gradient. However, for the 45° tip angle cone, velocity doesnot decrease with distance because gravity plays a larger role. This cone also benefits from largersurface area because of the additional water droplets formed on its whole surface [48].

Nonlinear cones: Nonlinear profile of a cone can be used to increase the curvature gradientnear the tip and higher slope later, in order to maximize water collection for a cone with a given

30


...............................................................

velocity of droplets on cone at 0° inclination

length = 15 mm tip angle 10°

0.08

0.06

0.04

0.02

0

0.08

0.06

0.04

0.02

0 5 10 15distance (mm)

velo

city

(m

m s

–1)

velo

city

(m

m s

–1)

distance (mm)

tip angle 45°

5 10

velocity at tip of the 10° tip angle cone is higher because of larger Laplace pressure gradientvelocity decreases with length on 10° tip angle cone because of decreasing curvature gradient

however, velocity increases with length on 45° tip angle cone because gravity dominates

15

Figure 29. Velocity of droplets on cones with 10° and 45° tip angle, at 0° inclination angle as a function of distance from thetip over the length of cones (adapted from [48]).

length and base area. Gurera & Bhushan [11] proposed a design of diameter of 13 mm cone witha concave profile with low tip angle of 10° to increase the Laplace pressure gradient near the tipand nonlinearly increase the radius to have higher gravitational forces for higher slope. Watercollection rate for the nonlinear cone was reported to be higher than that for a linear cone with10° tip angle and another cone with the base diameter of 13 mm.

Grooves: To study the effect of grooves, a representative cone with a tip angle of 45° anda length of about 15 mm was selected. Figure 30a shows the water collection rates (mg h−1) ofungrooved and grooved cones at two inclination angles, 0° and 45° [10]. At a 0° inclination angle,grooves help in increasing the water collection rate. This is because grooves help in channellingthe water. It is believed that they also create an increased Laplace pressure gradient via thegradient in grooves spacing. However, at a 45° inclination angle, the improvement due to groovesis not observed. That is probably because the gravitational force is overpowering the advantageof grooves.

To study the differences in the channelling of a water droplet on the ungrooved and groovedcones, a fixed volume of water droplet, 5 µl, was placed on the cones at similar locations [10].The optical images are shown in figure 30b. The droplets between the grooves appear to be morechannelled towards the base. This elongation of the droplet is the reason for the increase in thewater collection rate in the grooved cone.

Heterogeneity in wettability: To study the effect of heterogeneity in wettability, arepresentative cone with a tip angle of 45° and a length of about 15 mm was selected. Figure 31shows the effect of heterogeneity on water collection rate (mg h−1) at two inclination angles of0° and 45° [10]. At a 0° inclination angle, the heterogeneity increases the water collection rate.This is because the heterogeneity assists in transporting the water quickly. However, at a 45°inclination angle, an improvement due to heterogeneity is not observed. This is probably becausethe gravitational force dominates the transport due to heterogeneity.

Arrays: Arrays with cones with a tip angle of 45° and a length of about 15 mm were selectedto evaluate effects of arrays at two inclination angles of 0° and 45°. Figure 32a shows a watercollection rate (mg h−1) for an array [10]. The array data are presented as water collection rateper number of cones. The data are compared with a single cone with a tip angle of 45°. At a 0°inclination angle, having an array increased the water collection rate per number of cones. It isbelieved that this increase is due to a cascading effect on a falling droplet. This is because a droplet

31


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5 ml droplet

3 mm

ungrooved

ungrooved grooved ungrooved grooved

grooved

0° 45°

wat

er c

olle

ctio

n ra

te (

mg

h–1)

0° inclination

inclination angle

channelling of water droplets

3 mm

0

100

200

300

400

(a)

(b)

effect of grooved cone

tip angle 45°

length = 15 mm, surface area = 330 mm2

at 0° inclination, grooves contributeat 45° inclination, gravity dominates and grooves do not contribute

Figure 30. (a) Water collection rates for ungrooved and grooved cones with tip angle of 45°, at 0° and 45° inclination angles.(b) Awater droplet of volumeof 5 µlwas placedonungroovedandgrooved cones to demonstrate the channelling in thegroovedcone (adapted from [10]). (Online version in colour.)

falling from the top cone collects the droplets stuck to the cone underneath, increasing the netwater collection rate per cone, as shown in figure 32b [10]. At a 45° inclination angle, the data fora single cone and the array per cone is comparable. Water collection rates at 45° inclination angleis larger than at 0° inclination angles. As suggested earlier, this occurs because the gravitationalforces dominate the water transport at a higher inclination.

Summary. In a single droplet test for a cone with sideline in the horizontal orientation, the lowertip angle transports a water droplet further along the cone. This is because, for a lower tip angle,the curvature gradient is larger. For a cone in centreline horizontal orientation, gravity increasesthe distance travelled by droplets. Water droplets travel further along the cone when comparedwith that with sideline in the horizontal orientation.

32


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0homo

0° 45°

hetero homo hetero

100

200

300

400

inclination angle

at 0° inclination, heterogeneity contributeat 45° inclination, gravity dominates andheterogeneity do not contribute

wat

er c

olle

ctio

n ra

te (

mg

h–1)

effect of homogeneous wettability on cone

tip angle 45°

length = 15 mm, surface area = 330 mm2

Figure 31. Water collection rates for cones with a tip angle of 45° and homogeneous and heterogeneous wettability, and at 0°and 45° inclination angles (adapted from [10]).

For water collection from fog, the following were observed. Collected water droplets aredriven by the Laplace pressure gradient and gravity. During travel, droplets coalesce and travelfurther because of larger mass. The Laplace pressure gradient dominates at 0° inclination angle,which results in higher water collection rate for shorter length. Gravity dominates the watercollection rate at 45° inclination angle, which results in higher water collection rate for largersurface area. The water collection rate remains independent of the tip angle for the same lengthbut larger at larger tip angles for the same surface area, irrespective of the inclination angle.The water collection rate always increases with an increase in inclination angle, regardless of thecone, because of gravity effects. Grooves and heterogeneous wettability also increase the watercollection rate. In arrays, water collection per cone is higher at 0° inclination angle than a singlecone. However, it is similar at 45° inclination.

(c) Design guidelines for water collection systemsIt was shown that both beetle-inspired and conical surfaces have about twice the water collectionrate per unit area than that of homogeneous wettable, flat surfaces.

In cones, both the Laplace pressure gradient and gravity are the important factors in drivingwater droplets towards the base. The Laplace pressure gradient dominates at 0° inclinationangle, and a shorter cone length will provide a higher water collection rate at the base. Gravitydominates at 45° inclination angle, and higher surface area will provide a higher water collectionrate at the base. Higher inclination angle provides a higher water collection rate, when comparedwith a lower inclination angle because of the contributions of gravity. Therefore, for a high watercollection rate, a higher surface area, inclined at a higher inclination angle is desired. With cones,one can increase the surface area which would increase water collection by several fold, an orderof magnitude or more. The surface area can be maximized by having a larger number of conesper unit base area and longer cones. The dimensions of the cones are limited by their structuralintegrity. Grooves and heterogeneous wettability can also increase water collection rates. Theheterogeneity includes a hydrophobic tip and a superhydrophilic base.

33


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45°0°

array singlesingle array0

100

200

300

400

(a)

(b)

wat

er c

olle

ctio

n ra

te (

mg

h–1)

tip angle 45°

effect of array

single cone surface area = 330 mm2

array data per cone

length = 15 mm,

inclination angle

droplets falling from the top cone coalesce withdroplets stuck to cone underneath

3 mm

Figure 32. (a) Water collection rate of a single cone and an array at 0° and 45° inclination angles. The array data are presentedas water collection rate per cone. (b) Optical images of falling droplets on array at 0° inclination angle showing coalescence(adapted from [10]). (Online version in colour.)

Designs of beetle-inspired and beetle-, grass- and cactus-inspired water collectors is shownin figure 33 [50]. Beetle-inspired surfaces consist of superhydrophilic spots over a flatsuperhydrophobic surface. Beetle-, grass- and cactus-inspired surfaces consist of an array ofcones with heterogeneity and grooves. The heterogeneity includes a hydrophobic tip and asuperhydrophilic base. The surfaces can be inclined at 45° to the wind for high water collection.

For scale-up, nets or towers can be designed based on the beetle-inspired or beetle-, grass-and cactus-inspired designs. For beetle-inspired designs, the junctions of the nets should have

34


...............................................................

bioinspired water collector designs

beetle-inspired

superhydrophilic superhydrophobic

beetle-, grass- and cactus-inspired

wettability gradient

Figure 33. Proposed bioinspired water collector designs (adapted from [50]).

45°

(b)

(a)

45°

beetle-inspired water collector 2D net

beetle-, grass- and cactus-inspired

water collector 2D net water collector 3D tower

Figure 34. Schematics of (a) beetle-inspired water collector 2D net, and (b) beetle-, grass- and cactus-inspired water collector2D net and a 3D tower. (Online version in colour.)

superhydrophilic spots. For beetle-, grass- and cactus-inspired designs, the junctions of the netsshould have heterogeneous wettable cones with grooves and inclined at 45°. The heterogeneityincludes a hydrophobic tip and a superhydrophilic base. Figure 34a,b shows 2D water collectornets and a three-dimensional (3D) tower. Three-dimensional towers consist of a cylindrical towercovered with cones. For maximum water collection, large 3D towers can be used.

35


...............................................................

5. Bioinspired surfaces for water condensationWater condensation can also be used for water collection. Water condensation occurs whensubstrate temperature is below the dew point [54,55]. A low temperature decreases the saturatedpartial pressure of water vapour in the ambient air, which is desirable for a higher amount ofwater condensation [56,57].

For water collection, condensed water needs to be transported to storage before it evaporates.As mentioned earlier, cactus spines take advantage of the conical geometry to drive water dropletsby Laplace pressure gradient. For bioinspired flat surfaces, triangular patterns can be used. Forthe first time, Song & Bhushan [12,13] used bioinspired triangular patterns to transport condensedwater in the pattern, facilitated by Laplace pressure gradient in the longitudinal direction.

The wettability of the triangular pattern affects the water condensation process and thehydrophilic pattern has been shown to be good for water transport compared to superhydrophilicand hydrophobic patterns [12]. In the case of a hydrophobic pattern, droplets are more sphericaland do not spread and touch the pattern boundaries readily, necessary for droplet movement. Inthe case of superhydrophilic and hydrophilic patterns, droplets spread and touch the patternboundaries to facilitate droplet movement. However, in the case of superhydrohydrophilicpatterns, condensed water spreads in the form of a thin film, which then evaporates; this is notdesirable. Furthermore, adhesion of the droplet is high and impedes droplet movement.

Hydrophilic triangular patterns of various geometry were investigated to maximizecondensation and transport. Patterns of various geometry were surrounded with a region of lesswettability to constrain condensed water droplets inside the pattern. Details follow.

(a) Experimental methodA low temperature of 5°C was used to decrease saturated vapour pressure to promote watercondensation. The triangular patterns of various geometry were made hydrophilic. Surroundingregions with less wettability than the triangular patterns were selected to constrain condensedwater in the pattern.

(i) Experimental apparatus

Figure 35a shows a schematic of the water collection apparatus used to collect water condensationand provide transport [12,13]. The bioinspired samples were placed on top of an aluminium blockon a horizontal table and cooled by a thermoelectric Peltier cooler (GeekTeches) to about 5 ± 1°C.

When the sample is placed on a cold substrate (5°C), water vapour in the air will condenseon the surface if the partial pressure of ambient is higher than the saturation vapour pressure atthe surface temperature. An empirical formula of the saturation vapour pressure of water as afunction of temperature is given as [58]

psat(T) = 0.611 exp(

17.625 T243 + T

)kPa, (5.1)

where T is the temperature in °C. Using equation (5.1), the saturation vapour pressure at 5°C iscalculated to be 0.87 kPa. Next, we calculate the partial pressure of water vapour in ambient (22°C,50% RH). The saturated vapour at ambient temperature of 22°C is calculated to be 2.64 kPa. RH ofair–water mixture is defined as the partial pressure of water vapour in the mixture divided by thesaturation vapour pressure [54,55]. Therefore, the partial pressure of water vapour in ambient at50% RH is given as 2.64 × 0.50 = 1.32 kPa. This value is higher than the saturation vapour pressureat the surface temperature of 5°C, a necessary condition for water condensation.

36


...............................................................

(a)

(b)

A: hydrophilic B: superhydrophobic

B BA

A

A

a

L = 20 mm 17m

m

La La5 mm

triangular array(c)

~5°C

water

heater

moist air

air

apparatus for water collection from condensation

single triangular pattern withheterogeneous wettability

CCDvideo

sample

aluminium block

Peltier cooler

Figure 35. Schematic of (a) water condensation apparatus, (b) sample with a single triangular pattern and (c) reservoir withan array of triangular patterns (adapted from [13]).

Another property of interest in water condensation is the dew point, which is the temperatureto which air must be cooled to become saturated with water vapour. If the surface temperature isbelow the dew point, airborne water vapour will condense on the surface and deposit drops ofwater (dew). The dew point temperature, Td, can be calculated using the following equation [59]:

Td = T − 100 − RH5

. (5.2)

Using equation (5.2), the dew point temperature at the ambient (22°C and 50% RH) is about 12°C,higher than the sample tempearture of 5 ± 1°C.

The samples were housed in an acrylic chamber (1 m × 0.5 m × 0.8 m). The air temperaturein the chamber was 22 ± 1°C. RH was controlled by injection of humid air. The humid air wasproduced by an air stream that passed through a tank of hot water. By changing the temperatureof the hot water and the flow rate of the air stream, RH in the chamber could be controlled between30% and 95%. A digital microscope CCD camera (Koolertron, 5MP 20–300X) was used to capturethe condensation process.

Experiments were conducted at an RH of 85%, except those performed to study the effect ofRH. When the sample was cooled to 5°C at RH greater than 50%, which is lower than the dewpoint of the ambient air, water vapour continuously condensed on the triangular region.

37


...............................................................

(ii) Fabrication method

Two types of samples were fabricated. One type of sample contained a single triangular pattern,which was used to investigate the movement of the condensed droplets (figure 35b) [12,13]. Thesingle triangular pattern with a 20 mm length, with region A being hydrophilic, was surroundedby a superhydrophobic rim (0.5 mm wide). The superhydrophobic rim was produced to serve asa dam to the condensed liquid in the triangular pattern. Three included angles (α = 5°, 9° and 17°)were selected to investigate the effect of α on the droplet condensation and transport process. Theother type of sample contained an array of triangular patterns that were located on both sides of arectangular reservoir, to increase the amount of the collected water for better accuracy (figure 35c).An array with an included angle of 9° and length of 10 mm was used. To study the effect of theincluded angle, arrays with four included angles of 9°, 17°, 22° and 30°, with a length of 10 mm,were selected. To study the effect of length, arrays with four lengths of 5, 10, 20 and 30 mm withan included angle of 9° were selected.

The triangular patterns were fabricated on a hydrophilic glass slide. To fabricate the patternedsample, the boundaries of pattern B were printed on a paper that was placed under the glass slideand a piece of adhesive tape was put on top of the glass slide. Next, region B was cut onto theadhesive tape, guided by the pattern on the paper underneath, so that region B was exposedto air and region A was protected by the tape. Then a superhydrophobic coating was spraycoated on the glass slide, followed by removal of the adhesive tape that covered region A. Thesuperhydrophobic coating consisted of 10 nm hydrophobic SiO2 nanoparticles (Aerosil RX300)and a binder of methylphenyl silicone resin (SR355S, Momentive Performance Materials), bothof which were pre-mixed in acetone before spraying [50,52]. Region B after coating becamesuperhydrophobic and region A remained hydrophilic.

To compare a triangular pattern with that of a rectangular pattern, glass slides withhydrophobic, triangular and rectangular patterns surrounded by superhydrophobic surfaceswere also produced [12]. To produce a hydrophobic pattern, a monolayer of perfluorodecyltrichlo-rosilane (FTDS) (448931, Sigma-Aldrich) was deposited using a vapour deposition method [50].

(iii) Water collection measurements

To measure the mass of the collected water for both types of samples, a piece of paper tissue wasused to absorb the water in the reservoir and was weighed by a microbalance (Denver InstrumentCompany no. B044038) after the condensation tests. The microbalance could measure a minimumweight of 1 mg.

(b) Results and discussionTo compare the effect the triangular and rectangular patterns on droplet mobility, experimentswere conducted on these two patterns. To study the effect of wettability, a triangular patternwith different wettability was studied. To understand the droplet transport mechanism, singledroplets of different volumes were deposited on a triangular pattern at room temperature, andthe droplet movements were observed. Next, to study the effect of included angle, length and RHon the water condensation and transport, water condensation experiments were performed usingpatterns with different geometry at various values of RH.

(i) Rectangular versus triangular pattern and role of wettability

To compare the effect of rectangular and triangular patterns on droplet condensation andmobility, droplet condensation on hydrophobic rectangular and triangular patterns surroundedby superhydrophobic surfaces was studied as a function of time. The data are shown infigure 36 [12]. In the rectangular pattern, the micro-sized droplets form rather uniformly inthe hydrophobic area. With time, the microdroplets grew due to continuous condensation andcoalesced into bigger ones (numbered 1–6). When the droplets were big enough to reach each

38


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18 min 85 min

triangular (a = 9°)

rectangular

A: hydrophobic, B: superhydrophobic

rectangular versus triangular patterns with heterogeneous wettabilityRH = 85%

86 min 93 min

14 min

2 mm

2 mm

all

A

A

B

B

36 min 51 min 57 min

1 2 3 4 5 6 1 2 3 4 5+6 1+2 3+4 5+6+

1 2 3 4 5 76 1 2 3 4 5 76+ +

Figure 36. Selected optical images of condensation on hydrophobic rectangular and triangular patterns surrounded bysuperhydrophobic coatings. On the rectangular pattern, the condensed droplets do not move, but grow and coalesce with asize larger than the pattern. However, the droplets on the triangular pattern move in the direction with a larger triangularwidthwhen tiny droplets coalesce into one droplet with a size larger than the local triangular width. Arrows shown below somedroplets are based on the droplet movement observed in videos (adapted from [12]).

other, they coalesced into even bigger ones (1 + 2, 3 + 4 and 5 + 6). However, the centre positionof the merged droplets did not change, which means that there was no transportation aftercoalescence.

In the triangular pattern, the initial formation of the micro-sized droplets was the same as theone with a rectangular pattern. It was observed that when tiny droplets (1, 2 and 3) coalesced toa bigger one (1 + 2 + 3), which was much bigger than the local width of the triangular pattern,the merged droplet moved in the direction with a wider triangular width. Condensation andcoalescence continued, the newly formed droplets kept on growing and a new cycle of coalescencemade the droplet move even further.

To study the effect of wettability of the triangular regions with heterogeneous surroundingregions, another triangular sample with hydrophilic triangular pattern surrounded by asuperhydrophilic region was studied. The data are shown in figure 37a [12]. Wettability ofthe triangular patterns was found to affect the droplet shapes as well as the condensationprocess. On the hydrophobic triangular pattern, as expected the droplets were more sphericalcompared to the hydrophilic pattern, where the droplets were elongated to form a stripe. Thehydrophilic triangular pattern was more efficient for transport. Schematically, water condensationand movement at various times is shown in figure 37b [12]. The droplets nucleate and coalesce.Once they touch the two sides, they start to move because of Laplace pressure gradient.

The time it takes to initiate movement is affected by the wettability as well (figures 36 and 37).On the hydrophilic triangular pattern, it takes about 25 min for condensed droplets to move fromtip to about 5.5 mm, whereas it takes about 93 min on the hydrophobic pattern to move the samedistance. Therefore, hydrophilic triangular patterns surrounded by superhydrophobic regions aremore efficient in transport of the two wettability patterns [12].

(ii) Single droplet experiments on hydrophilic triangular patterns

To understand the droplet transport mechanism, single droplet experiments were conducted bydepositing a droplet using a pipette at the tip inside the triangular pattern with varying volume

39


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A

B 1

1 2 3 34 1+ +21+2 4

2 3 4 1 2 3 3

microdroplets

1 2 4+ + 1 2 4+ ++

2 mm

16 min12 min

triangular pattern (a = 9°) with heterogeneous wettabilityRH = 85%

schematic showing droplet nucleation and movement

droplets touch boundaries and move because of Laplace pressure gradient

A: hydrophilic, B: superhydrophobic

25 min8 min

(a)

(b)

Figure 37. (a) Selected optical images of condensation on a hydrophilic triangular pattern surrounded by superhydrophobiccoating. The condensed droplets on the triangular patternmove in the directionwith larger triangular widthwhen tiny dropletscoalesce into one droplet with a size larger than the local triangular width. Arrows shown below some droplets are based on thedroplet movement observed in the videos. This hydrophilic triangular pattern is more efficient in transport than hydrophobictriangular patterns in figure 35. (b) Schematic showing droplet nucleation and movement on a hydrophilic triangular patternsurrounded by a superhydrophobic region (adapted from [12]). (Online version in colour.)

from 10 to 100 µl with increments of 5 µl ranging between 10 µl and 50 µl and increments of 10 µlranging between 50 µl and 100 µl. After deposition, the droplet moved along the pattern dueto Laplace pressure gradient, and stopped after travelling some distance. Figure 38a shows theoptical images of the locations of the stopped droplets of different volumes for a triangular patternwith an included angle of 17° [13]. A droplet with larger volume travelled further.

To mathematically understand the role of Laplace pressure gradient on the droplet movementand the distance travelled, a droplet placed on the hydrophilic triangular area, as shown infigure 39, was analysed [13]. In this example, w(x) is the local width of the triangle at a distancex from the tip of the triangle. The droplet was constrained by the superhydrophobic region andbecame wedged shaped. The local radius of the curvature of the droplet along the triangle can bewritten as R(x) ∼ w(x)/(2sinθ (x)), where θ (x) is the contact angle at the boundaries. The Laplacepressure generated by the local curvature can be simplified as �P ∼ γ /R(x) ∼ 2γ sinθ (x)/w(x),where γ is the surface tension of water in the air [60]. For the constrained droplet, w(x) increasesfrom the narrower side to the wider side, and hence the Laplace pressure at the narrower side islarger than the wider side. As a result, a driving force is generated to transport the droplet withthe direction pointing to the wider side. The driving force of the Laplace pressure exists as long asthe droplet is large enough to contact both boundaries of the triangular pattern. When the dropletmoved further in the triangular pattern, the magnitude of the driving force decreased because ofthe decrease in the curvature gradient. The droplet stopped when the driving force was smallerthan the adhesion force.

Figure 38b shows a plot of the droplet volume as a function of travel distance, measuredfrom the tip of the triangle to the right-hand edge of the droplet (xr) at various included angles[13]. The distance was measured when the droplet stopped. A droplet with a larger volumetravelled further. A droplet with a given volume was transported further by a triangle with asmaller included angle. For example, to move a droplet 20 mm to the right, the droplet volumehad to reach 82, 29 and 20 µl on the triangular pattern with the included angle α = 17, 9 and 5°,respectively.

40


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droplet length versus travel distancedroplet volume versus travel distance150

a: 17°

10 µl

10 mm

20 µl 50 µl 80 µl

9° 5°

100

50

0 0

2.50

7.50

5.00

10.00

effect of volume of deposited droplet on its position and length a = 17°

5 10 15

Xr (mm)

Xr

2520 5 10 15

Xr (mm)

2520

drop

let v

olum

e (µ

l)

drop

let l

engt

h, l

(mm

)

(b)

(a)

Figure 38. (a) Selected optical images of the deposited droplets with different volumes transported along the triangularpattern when they stop. (b) Droplet volume and its length as a function of travel distance. These data were measured whenthe droplet stopped (adapted from [13]).

droplet constrained within a triangular pattern

w(x)R(x) q(x)

xxr

l

Figure 39. An optical image and schematic of a droplet constrained within the triangular pattern (adapted from [13]).

Figure 38b also shows the relationship between the length of the stopped droplet (l) and (xr)[13]. The data showed that l increased linearly with xr and the included angle had little effect. Itwas observed that the droplets were elongated along their travel direction. The droplet elongationwas believed to occur due to the adhesion force, which is directly related to the contact anglehysteresis (difference between advancing and receding contact angles) on the triangular area.

(iii) Water condensation and transport on hydrophilic triangular patterns

Effect of included angle. Figure 40 shows water condensation on triangular patterns with differentincluded angles [13]. At the beginning of condensation, the condensed droplets were relativelysmall, as shown in the first column of figure 39a. As condensation continued, the growingdroplets started to coalesce into bigger droplets. Eventually, they were big enough to touch thesuperhydrophobic borders, which triggered motion driven by the Laplace pressure gradient, asshown in the second and third columns of figure 40. For example, at 45 min after the start ofcondensation on the triangular pattern with α = 9°, there were 5 mm sized droplets (numbered1–5) that touched the borders. At 76 min, droplets 1 and 2 coalesced into one big droplet (1 + 2)and droplets 3 and 4 coalesced into another (3 + 4). After the coalescence of droplets 1 and 2, the

41


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effect of included angle of triangular patterns on water condesation and transportRH = 85%

26 min

10.mm

1 2 3

1 4 52 3 1 + 2 3 + 4 5

1 + 2 + 3 all

all

23 min 45 min 76 min 111 min

29 min

10.0

effect of a on mass of first droplet atreservoir

effect of a on mass of first droplettravelling through pattern

droplet length versus travel distance

a: 17° 9° 5°7.5

rese

rvoi

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ea

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75

50

25

0 5 10 15a (º) a (º)

20 5 10 15 20

0 5 10 15 20 25

37 min 45 min

xr (mm)

68 min


a = 17º

a = 9º

a = 5º

(b)

(a)

(c)

all1 + 2 + 3 4 + 51 4 52 3

Figure 40. (a) Selected optical images of the condensation on a single triangular pattern with different included angles atdifferent times. Arrows shown below some droplets are based on droplet movement observed in videos. (b) Length of thecoalesced droplet as a function of the travel distance, xr, when it stops. (c) Effect of included angle on the mass of the firstdroplet on the reservoir and the time taken for the droplet travelling through the pattern (adapted from [13]).

droplet volume increased and the Laplace pressure gradient was able to drive the droplet. Owingto adhesion, the droplet (1 + 2) was elongated and stopped after moving 1.4 mm based on thecalculation of the centre of the droplet area. It is further noted that the position of the centre ofdroplets 3 and 4 did not change after their coalescence. This is because the size of the coalesceddroplet (3 + 4) was too small and the Laplace pressure gradient along the coalesced droplet couldnot overcome the adhesion.

42


...............................................................

51 min

10 mm

23 min

drop

let m

ass

(mg)

time

to r

eser

voir

(m

in)

75

100 400

300

200

100

0

50

25

0 20 40 60RH (%) RH (%)

80 100 20 40 60 80 100

effect of humidity on mass of the firstdroplet at reservoir

effect of humidity on time for droplettravelling through pattern


127 min

1 1 + 2 + 3 4 + 5

1 + 2 3 + 4 5

all

all

2 3 4 5

1 23 4 5

effect of humidity on water condensation and transporta = 9º

RH = 85%

RH = 50%

183 min 241 min

(b)

(a)

Figure 41. (a) Selected optical images of the condensation on a single triangular pattern in different relative humidity atdifferent times. Arrows shown below some droplets are based on droplet movement observed in videos. (b) Effect of relativehumidity on the mass of the first droplet on the reservoir and the time taken for the droplet travelling through the pattern(adapted from [13]).

The length of the droplet as a function of distance travelled xr when it stops is shown infigure 40b [13]. Similar to figure 38b, the length of the elongated droplet increases linearly with itsposition xr, and the included angle has little effect on the length.

To study condensation rate, one needs to know the size (mass or volume) of the droplet andtime taken to reach the reservoir. Figure 40c shows the droplet mass and time needed for thedroplet to reach the reservoir through the whole triangular pattern with different included angles[13]. As α increases, it takes more time for the droplet to be transported to the reservoir. However,for larger α, the mass of a coalesced droplet which starts to move is larger, as shown in figure 40.

The transport efficiency of the condensed droplet across the triangular pattern needs furtherinvestigation. It was carried out using an array of triangular patterns to increase the amount ofcollected water for high accuracy, and will be presented below.

Effect of relative humidity. The effect of RH on condensation and transport was investigated.Figure 41a shows the condensed droplets at two different values of RH on a triangular patternwith an included angle of 9° [12,13].

The droplets coalesced and started to move. The coalesced droplets eventually moved tothe reservoir and the sizes of the droplets were weighed by soaking a slice of paper tissue andweighing it. Figure 41b shows the mass of the final droplet just before reaching the reservoir. RHdid not affect the mass of the final droplet before reaching the reservoir. Figure 41b also showsthe time it takes for the droplet to reach the reservoir at different values of RH. The travel timethrough the reservoir decreased with an increase in RH because of increased condensation [13].

43


...............................................................

effect of humidity, included angle and length of triangularpatterns on water condensation rate

1.00

5 mm

wat

er c

onde

nsat

ion

rate

(mg

mm

–2 h

–1) 0.75

0.50

0.25

1.00

0.75

wat

er c

onde

nsat

ion

rate

(mg

mm

–2 h

–1)

wat

er c

onde

nsat

ion

rate

(mg

mm

–2 h

–1)

0.50

0.25

1.00

0.75

0.50

0.25

0 10 20

a (º)30 40 0 10

La (mm)20 30 40

20 40 60

RH (%)

80 1000

reservoir with 16 triangular patterns, a = 9º, La = 10 mmRH = 50%, at 450 min

effect of humidity on water condensation ratea = 9º, La = 10 mm

effect of included angle on water condensationrate La = 10 mm, RH = 85%

effect of length on water condensationrate a = 9º, RH = 85%

(b)

(a)

(c)

Figure42. (a) An optical image of the condensedwater in the reservoir and array of triangular patterns. (b)Water condensationrate as a function of relative humidity. (c) Water condensation rate as a function of included angle and length of the triangularpatterns (adapted from [13]).

(iv) Water condensation and transport on an array of hydrophilic triangular patterns

Figure 42a shows water condensation on a sample containing an array of triangular patternssurrounding a rectangular reservoir [13]. The condensed water on the triangular area wastransported to the reservoir whose weight was measured via a paper tissue. To evaluate theadditional mass of water condensed at the reservoir area, a rectangular hydrophilic area wasplaced beside the array and the mass of the condensed water was measured as well. When

44


...............................................................

calculating the condensation rate on the triangular patterns, the mass of the water on therectangular region was deducted from the mass of the water on the reservoir with array.

The effect of RH on the condensation rate is shown in figure 42b [13]. The condensation rateincreased linearly with RH in the measured range of 50% and 85%.

Next, the effect of the included angle, α, and the length of the triangular patterns, La, werestudied. As shown in figure 42c, the included angle did not affect the condensation rate [13].Even though the droplet transported slowly on a triangle with a larger included angle, the sizeof the droplet was larger, which may provide similar condensation rates. Figure 42c also showsthe condensation rate as a function of the length of the triangular patterns. The condensation ratedecreased when the length increased. Since a shorter distance requires less time to transport thecondensed droplets and though droplets being removed are expected to be smaller, the removalrate increased the condensation rate.

(v) Summary

The water condensation and transport ability of bioinspired triangular patterns were investigated.Hydrophilic triangular patterns were surrounded by superhydrophobic regions. It was found thatwhen the droplets were constrained within the triangular patterns, they started to move once theyreached a critical size and touched both sides. The triangular pattern with a larger included angleneeded more time to transport condensed droplets, and the mass was larger. A water collectionreservoir was fabricated with multiple triangular patterns to measure the condensation rate. TheRH increased the condensation rate. The included angle did not affect the condensation rate. Thelength of the pattern decreased the condensation rate [12,13].

To design a condensation water collection tower, a hydrophilic pattern surrounded by asuperhydrophobic region should be used. Since the included angle had no effect on condensationrate and a shorter length promoted condensation, a larger number of triangular patterns withsmaller included angles and shorter lengths can be used for a higher condensation rate. AlthoughRH of the ambient air increased the condensation rate, it could not be controlled [12,13].

6. Bioinspired water desalination and water purification approachesAs discussed earlier, 97.5% of water is saline water; therefore, water desalination has becomeincreasingly important in some parts of the world. In addition, water contamination from humanactivity affects clean water supply. Water purification from all contaminants including salt inocean water is important.

For water desalination and water purification, a commonly used commercial technique isreverse osmosis (RO). Normally, if two aqueous solutions with varying solute concentrations areplaced either side of a semipermeable membrane, water will move through the membrane froma region of low solute concentration to a region of higher solute concentration in an attempt toequalize the concentrations, figure 43 [2]. This process is known as osmosis and the tendency fora solution to take in water is defined as the osmotic pressure. In RO, external pressure is appliedto overcome this osmotic pressure, preventing the flow of water into the region of higher soluteconcentration. Additional pressure above the osmotic pressure will instead cause water to moveinto the region of lower solute concentration. The requirement for this applied pressure meansthat separation via a RO membrane can be energy intensive, consuming at least 2 kWh m−3 [61],whereas the theoretical minimum energy required for desalination should be around 1 kWh m−3

[8]. This excess pressure is due to the low permeability of the membranes involved. A membranewith low water permeability will require additional applied pressure, above that required tobalance the osmotic pressure in order to result in reasonable water fluxes [8].

For water purification from various contaminants, various techniques are used, includingadsorbents such as activated carbon [62], biomaterials [63] and zeolites (porous minerals) [64]to remove organics from wastewater [2]. However, adsorbents are inefficienct due to contaminantremoval and regeneration of the adsorbent. Ultraviolet treatments have been used to disinfect

45


...............................................................

osmosis reverese osmosis

osmosis and reverse osmosis

semipermeablemembrane

water moves through semi-permeable membrane into region with

higher salt concentration in an attempt to equalize solute

concentrations on both sides

external pressure is applied toovercome osmotic pressure

causing water to move throughsemipermeable membrane to

region with lower salt concentration

semipermeablemembrane

osmoticpressure

externalpressure

Na+

Cl–

H2OH2O

Figure 43. Two water purification approaches—osmosis and reverse osmosis. In osmosis, water travels across asemipermeable membrane to equalize solute concentrations. In reverse osmosis, external pressure is applied to prevent waterfrom travelling into regions of higher solute concentration. Additional pressure, instead, causes water to travel into regions oflower solute concentrations (adapted from [2]). (Online version in colour.)

targetsolute

microporous

length scales of various target solutes and porous materials

water colloidal solids

proteins bacteria

viruses

surfacelayer

proteins

aquaporins

ions

carbon nanotubespore-

formingmolecules

0.1 nm 1 nm 10 nm 100 nm

block copolymers

templated metal oxides

bacterialthreads

eggshell

oil emulsions

0.1 nm 1 nm 10 nm 100 nm 1 mm 10 mm

1 mm 10 mm

mesoporous macroporous

naturalporous

material

bioinspiredporous

material

Figure 44. Comparison of length scales of target solutes, natural porous materials and bioinspired porous materials (adaptedfrom [2]). (Online version in colour.)

water [65], and can be combined with metal oxide catalysts for improved oxidation rates.However, the use of use of ultraviolet light cannot remove heavy metal or other non-livingcontaminants, the process can be expensive, and ineffective on cloudy or turbid water [2].

Micro- and nanoporous membranes are commonly used for separation of salt as well ascontaminants [2]. There are two mechanisms that dictate water transport through a membrane,both of which can occur together. One mechanism is solution–diffusion, where water molecules

46


...............................................................

Table 5. Examples of target solute, natural materials and bioinspired equivalents sorted bymembrane pore size (adapted from[2]).

pore size target solute natural porous material bioinspired porous material

macropores,(>50 nm)

bacteria (0.2–750µm),oil emulsions (0.1–10 µm)

eggshell, bacterialthreads

carbon nanotubes, templatedsilica

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

mesopores,(2–50 nm)

colloidal solids (0.01–1 µm),viruses (20–400 nm),proteins (2–10 nm)

surface layer proteins carbon nanotubes,self-assembled blockcopolymers

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

micropores,(0.2–2 nm)

inorganic ions (0.2–0.4 nm),water (0.2 nm)

aquaporins carbon nanotubes, amphiphilicdipeptides, cyclic peptides,crown ethers

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

dissolve into the membrane and diffuse through the membrane to desorb from the other side.Another mechanism is pore flow, where the size of the pores is smaller than the contaminant beingremoved [66]. Microporous membranes are typically made of polymers and ceramic materials.Nanoporous membranes are typically made of graphene [67] or etched silicon [68].

Porous materials are classified into three main categories depending upon their pore size.A summary of the various pore sizes, including solutes that can be targeted in this size range,examples in nature and their bioinspired equivalents is provided in figure 44 and table 5 [2].Microporous materials contain pore diameters less than 2 nm, which are required for desalination.Ocean water (and other water sources) also contains many contaminants other than salt thatare typically many orders of magnitude larger than the inorganic ions found in salt. Whensalt removal is not required, membranes with larger pores would likely be sufficient forthese applications. In addition to separation applications, ordered macroporous (pore diameters2–50 nm) or mesoporous (pore diameters greater than 50 nm) materials could also find use in ionexchange [69], catalysis [70] and battery technology [71].

Living nature provides examples of membranes with higher separation rates andpermeabilities than man-made equivalents. A steel wire mesh or nanofibrous polymermembrane can be coated with bioinspired material, which allows water flow but repels organiccontaminants, which can be used for water purification and oil–water separation. These coatedmeshes can be used for water purification [2,50,51].

7. Commercial applications and projections for bioinspired water collectionBioinspired large water collection towers and portable water collection units are of commercialinterest. Large water collection towers can be used to supply water to a community. Portable unitscan be used to supply a home or a camper. Cost will be an important consideration for economicviability. In addition, portable units can be used for various military and emergency applications.For example, military applications include use by soldiers in combat and military bases in combatzones. Various emergency applications, such as natural disasters could also benefit from portableunits which could be dropped from air. The cost of clean water and fuel in forward operatingbases (FOBs) in a combat zone such as in Afghanistan can be as much as US $350/gallon becauseof the dangers posed in transportation. In emergency applications, human life is at stake. In theseapplications, cost will be less of an issue.

Next, water collection rates for bioinspired collectors are projected and compared with thecollection rates on flat surfaces and living species in deserts. In arid deserts, water collectionrates are on the order of 2 l m−2 d−1. Bioinspired surfaces covered with conical arrays can providecollection rates one to several orders of magnitude larger than that of a flat hydrophilic surface.This means that bioinspired surfaces can collect water on the order of 20 l m−2 d−1 or more. For anexample of 20 l m−2 d−1, a medium sized tower covered with a bioinspired surface with a surface

47


...............................................................

area of 100 m2 and total surface area of both sides of 200 m2, the water collected would be about4000 l d−1. If the water consumption per capita is 100 l d−1, a tower can provide sufficient water forabout 10 families.

8. ConclusionWater is vital for the survival of all living things. Various desert species have evolved ingeniousways to collect water from fog and transport it for consumption or storage. By studying thelessons from nature, from beetles to cacti, various surface structures and chemistries can bedeveloped for efficient fog harvesting.

The ambient temperature during desert nights is low, as low as about 4°C. This temperaturecan be lower than the dew point and can lead to water condensation from ambient. Bioinspiredwater condensation approaches can also be used.

Bioinspired designs are proposed for water collection from fog and/or water condensationfor the use of a household or a small community. Portable units are also of interest for variousmilitary and emergency applications.

Water collection systems will be covered by dust. They will require filters to keep the activecollection area clean. Filters may require high-pressure air.

Bioinspired water desalination and water purification approaches were also discussed.Desalination of water from the oceans or brackish groundwater is essential in some parts of theworld for water supply. With population growth and industrial revolution, contamination of thewater supply is a concern. Nature has evolved efficient pathways in our own body to facilitatethe transport of water while blocking contaminants. It is hoped that by taking inspiration fromthe chemistries and surface structures of these natural species, artificial ones can be created thatcan improve desalination as well as water purification from contamination.

Data accessibility. This article has no additional data.Competing interests. I declare I have no competing interests.Funding. I received no funding for this study.Acknowledgements. This perspective paper is inspired from two major public lectures: (1) Science Sundays PublicLecture on ‘Lessons from Nature: Bioinspired Surfaces for Green Science and Technology’ part of the Free Artsand Sciences Public Lecture Series at The Ohio State University, Columbus, Ohio, on 14 October 2018, and (2)TEDx talk, ‘Lessons from Nature: Bioinspired Surfaces for Green Technology’ at 2019 TEDx Event: Fuse inColumbus, Ohio on 23 February 2019. The author would like to thank Dev Gurera for insightful discussions.

Appendix A. Laplace pressure gradient on a conical surfaceFor a spherical droplet sitting on a surface, capillary pressure or Laplace pressure in the liquidpL is proportional to the surface tension of the liquid in air (γ LA) divided by the local radius, R[60,72],

pL = γLA

R. (A 1)

The Laplace pressure can be attractive or repulsive depending on whether the surface ishydrophilic or hydrophobic, respectively. The pL remains constant on a flat surface.

Next, we consider a liquid droplet sitting on a conical object. We consider two adjacentlocations A and B with the local radii of the cone, as RA and RB, respectively, figure 45 [50]. Thesubstrate curvature gradient results in the Laplace pressure difference between the two oppositeends of the droplet along the surface. The Laplace pressure difference is given as

�pL = γLA

(1

R′A− 1

R′B

), (A 2)

where R′A and R′

B are the radii of curvature at the front and rear contact lines of the droplet,respectively. The curvature gradient leading to Laplace pressure difference that acts on the contact

48


...............................................................

Laplace force acting on a water droplet

contact area between water droplet and cone(top view)

L

R¢AR¢B

FL

RBRA

AB

Figure 45. Schematic of a liquid droplet on a conical object with a cone angle of 2α and local radii RA and RB at two locationsof A and B, respectively. Shown is the Laplace force (FL) which helps in driving the droplet towards a larger radius (adapted from[50]). (Online version in colour.)

area A, produces the Laplace force FL,

FL =∫∫

A

�pLdA, (A 3)

where the contact area is approximately equal to volume of the droplet, Vdroplet divided by thelength L of the droplet,

A ∼ sin α

(RB − RA)Vdroplet, (A 4)

where α is the half-apex angle of the cone. Combining equations 17.A.2 to 17.A.4, we get

FL ∼ γLA

(1

R′A

− 1R′

B

)sin α

RB − RAVdroplet, (A 5)

The Laplace force acting on a conical object drives the droplet from regions of lower radius tolarger radius as long as the Laplace force is larger than the adhesion force. During this dropletmovement, new droplets may be deposited in the path, which coalesce resulting in a large liquidvolume and provide the additional movement.

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