IMPACT DYNAMICS OF NEWTONIAN AND NON-NEWTONIAN

FLUID DROPLETS ON SUPER HYDROPHOBIC SUBSTRATE

A Thesis Presented

By

Yingjie Li

to

The Department of Mechanical and Industrial Engineering

in partial fulfillment of the requirements

for the degree of

Master of Science

in the field of

Mechanical Engineering

Northeastern University Boston, Massachusetts

December 2016

Copyright (©) 2016 by Yingjie Li All rights reserved. Reproduction in whole or in part in any form requires the prior written permission of Yingjie Li or designated representatives.

ACKNOWLEDGEMENTS

I hereby would like to appreciate my advisors Professors Kai-tak Wan and

Mohammad E. Taslim for their support, guidance and encouragement throughout the

process of the research. In addition, I want to thank Mr. Xiao Huang for his generous help

and continued advices for my thesis and experiments. Thanks also go to Mr. Scott Julien

and Mr, Kaizhen Zhang for their invaluable discussions and suggestions for this work.

Last but not least, I want to thank my parents for supporting my life from China. Without

their love, I am not able to complete my thesis.

TABLE OF CONTENTS

DROPLETS OF NEWTONIAN AND NON-NEWTONIAN FLUIDS IMPACTING

SUPER HYDROPHBIC SURFACE .......................................................................... i

ACKNOWLEDGEMENTS ...................................................................................... iii

1. INTRODUCTION .................................................................................................. 9 1.1 Motivation ......................................................................................................... 10 1.2 Characteristic outcomes from a droplet impact on solid surface ............. 11 1.3 Super hydrophobic surface ............................................................................ 12 1.4 Related theories ............................................................................................... 14

2. Experiments ...................................................................................................... 19 2.1 Experimental apparatus ........................................................................................ 19 2.2 Preparation of super hydrophobic surface ........................................................ 27 2.3 Droplet generation ................................................................................................. 29 2.4 Experimental procedures ..................................................................................... 31 2.5 Surface tension measurement ............................................................................. 37

3. Results and discussion ................................................................................... 38 3.1 Definition ................................................................................................................ 38 3.2 Droplet impact behaviors ..................................................................................... 45 3.3 Weber number and impact behavior ................................................................... 61 3.4 Viscosity and Spreading ....................................................................................... 67

4. Conclusion ........................................................................................................ 73

5. Suggestions and Future work ........................................................................ 73

REFERENCES ....................................................................................................... 74

Appendix ............................................................................................................... 78

LIST OF FIGURES Figure 1 : Examples of characteristic outcomes from a water droplet impact on solid

surface . .................................................................................................................12 Figure 2: Sketch of a hydrophobic surface and hydrophilic surface ...............................13 Figure 3: Water droplet with 150° contact angle ............................................................13 Figure 4: Viscosity of Newtonian, Shear Thinning and Shear Thickening fluids as a

function of shear rate .............................................................................................14 Figure 5: Experimental apparatus schematic illustration ...............................................21 Figure 5a: High speed camera ......................................................................................22 Figure 5b: Light source, RPS CoolLED 100 Studio Light RS-5610 ...............................23 Figure 5c: Rainin pipette ...............................................................................................24 Figure 5d: Conduct chamber. .......................................................................................25 Figure 5e: Tokina optical lens. ......................................................................................26 Figure 6: : Self assembled monolayer made of HDFT molecules ..................................27 Figure 7: Illustration of droplet generation .....................................................................30 Figure 8: Illustration of a micropipette positioning .........................................................33 Figure 9: Camera setting at pre-focusing stage ............................................................34 Figure 10: Camera setting at experiment stage ...........................................................35 Figure 11: Illustration of record button ..........................................................................36 Figure 12: Sketch of experiment camera locations ......................................................36 Figure 13: Pendant drop schematic ..............................................................................37 Figure 14: Illustration of pendant droplet method measurement ...................................38 Figure 15: Spreading stage of a water droplet impact on a solid surface ......................39 Figure 16: Recoiling stage of a water droplet impact on a solid surface ........................40 Figure 17: Rebound stage of a water droplet impact on a solid surface ........................40 Figure 18: Illustration of contact diameter .....................................................................41 Figure 19: Illustration of rim, spire, film and capillary waves .........................................42 Figure 20: Illustration of jet ...........................................................................................43 Figure 21: Illustration of smooth rim ..............................................................................43 Figure 22: Illustration of fragmentation ..........................................................................44 Figure 23: A water droplet with D =2.6mm and v =1.45 m/s impacted on a super

hydrophobic surface ..............................................................................................46 Figure 24: A milk droplet with D =2.75mm and v =1.91 m/s impacted on a super

hydrophobic surface ..............................................................................................49 Figure 25: A 5% corn starch droplet with D =3.41mm and v =1.72 m/s impacted on a

super hydrophobic surface .....................................................................................52 Figure 26: A 5% corn starch droplet with D =3.40mm and v =1.71 m/s impacted on a

super hydrophobic surface .....................................................................................55 Figure 27: A blood droplet with D =2.93mm and v =1.81m/s impacted on a super

hydrophobic surface ..............................................................................................57

Figure 28: A blood droplet with D =3.28m and v =1.72m/s impacted on a super hydrophobic surface ..............................................................................................59

Figure 29: Spires number K vs impact velocity v of water droplet with volume 1(3.6mm±0.1mm) and volume 2(2.6mm±0.2mm) ..................................................62

Figure 30: Spires number K vs impact velocity of milk droplet with volume 1(3.4±0.16mm) and volume 2(2.5±0.15mm) ..........................................................62

Figure 31: Spires number K vs impact velocity of 5% corn starch solution droplet with volume 1(3.4±0.13mm) and volume 2(2.5±0.22mm) ..............................................63

Figure 32: Spire number K vs velocity of 15% corn starch solution with volume 1(3.3±0.18mm) and volume 2(2.4±0.18mm) ..........................................................63

Figure 33: Spire number K vs velocity of rabbit blood with volume 1(3.3±0.2mm) and volume 2(2.97±0.13mm) .......................................................................................64

Figure 34: Spire number K vs velocity of 1:1 diluted blood with volume 1(3.25±0.1mm) and volume2 (2.78±0.2mm) ...................................................................................64

Figure 35: K vs Weber number of all experimental fluids ..............................................66 Figure 36: Illustration of pinched section and bulging section .......................................67 Figure 37: Schematic of hypothetical droplet evolution with time variation ....................69 Figure 38: Time variation of spread factor .....................................................................69 Figure 39: Impact of water droplet, milk droplet and blood droplet from t0 to t8 ..............71

ABSTRACT

Conventional rheological methods such as viscometry to characterize linear

and nonlinear viscosity behavior requires an excessive amount of sample liquid,

which is practically impractical due to the time and cost constraints, for instances,

in blood, and other scarce and expensive bio-fluids. There is an urge for a handy

tool to quickly evaluate the intrinsic properties of a liquid.

In this thesis, droplet of Newtonian (e.g. water) and non-Newtonian liquids

(e.g. shear thinning blood, shear thickening starch solution) with a desired

dimension is released by a pipette from a vertical distance. Gravitational attraction

gives rise to an impact velocity, and the droplet hits a rigid hydrophobic surface

with a liquid-substrate contact angle of 150o. An experimental set up equipped

with a manual pipette, high speed camera, and substrate holder etc. is constructed

to capture the geometrical change over the sequential the impact-spread-recoil-

rebound process. Upon impact, the droplet turns into an expanding pancake

geometry with coronal spires developing over time. In extreme conditions of high

impact velocity, splashing or fragmentation is observed. The video records are

analyzed in terms of the classical dimensionless Weber number (We) which

comprises impact velocity and surface tension. Other measurements are made:

(i) duration of droplet on the substrate, and the change in contact area at droplet-

substrate interface, prior to rebounce, (ii) critical droplet dimension and impact

velocity leading to fragmentation, (iii) jet formation at rebounce, (iv) maximum

number of spires, and (v) wavelength of radial Rayleigh wave. Comparison

between Newtonian and non-Newtonian liquids are made, and non-linear

behaviors are observed. Weber number is shown to be insufficient in describing

spire formations. Non-linear viscosity, playing an indispensable role in droplet

geometric deformation, must be incorporated in droplet dynamics.

Keywords: Droplet, Spires, Non-Newtonian fluids, Shear thinning, Shear

thickening, Blood, Viscosity, Surface tension

1. INTRODUCTION

The phenomenon of liquid droplets impacting and spreading on a solid surface —

such as rain drops falling on a windshield — is ubiquitous in daily life. The

underlying mechanics has been historically appealing to many great scientists,

including the Nobel laureate Pierre-Gilles de Gennes [1]. Many excellent works

[2-7] of water droplet impacting solid surface have been documented in the

literature. Recently, how the wettability of the solid and the viscosity [8-13] of the

fluid affecting the instability [14-16] of droplet impact and heat transfer [17-21] have

drawn extensive attention from around the globe. Numerous industrial applications

have been established, based on the fundamental understanding of the physical

processes of droplet impact. Examples include cooling of hot surfaces [18, 22, 23],

injection printing [24, 25], microfabrication [26] and laser induced transfer (LIT) [27-

29]. So far most studies have focused on Newtonian, rather than non-Newtonian,

liquids. However, a wide variety of fluids encountered in science and technology—

such as biological fluids (e.g. blood, synovial fluid, saliva), adhesives, dairy

products and polymeric fluids — do not exercise classical Newtonian fluid

behavior. A Newtonian liquid is one in which the viscosity is independent of shear

strain rate at constant pressure and temperature [30]. Non-Newtonian fluids, on

the contrary, are characterized by their non-linear and time-dependent viscosity,

which is a function of [31]

1.1 Motivation

Recently, non-Newtonian bio-fluids have attracted much interest in the

scientific community, due to their wide applications in life sciences [32, 33]. For

instance, a comprehensive understanding of the rheology of non-Newtonian fluids

will facilitate the study of pathophysiology. It is logical to presume that the viscosity

of blood, for example, changes with pathologic conditions because the apparent

viscosity is determined by hematocrit, red blood cell (RBC) aggregation and

plasma viscosity, which are influenced by such factors as infections, hypertension

and diabetes [34-36]. The pathologic conditions of blood samples from virus- or

bacteria-infected patients change rapidly with time. For example, in malaria-

infected patients, the multiplication of the plasmodium parasite and its life cycle

causes a large quantity of red blood cells (RBC) burst quickly and periodically [37].

Conventionally, in order to monitor a patient’s pathologic conditions, blood samples

are taken and prepared for cytometry and observation under optical microscope,

which are time-consuming and incapable to track the transient behavior of RBC,

that is known to change rapidly within 1-2 minutes [35, 36, 38-40]. It is highly

desirable if the transient changes in blood viscosity can be empirically quantified

to identify infection and associated pathologic conditions.

In classical fluid mechanics and droplet dynamics, Weber number and

Reynolds number play an essential role in geometric changes of droplet impact on

a surface. The sequential droplet deformation during impact, spreading, recoil and

rebound can serve as indicators of surface tension, viscosity, advancing and

receding contact angles, and, albeit, the rheological properties of fluid.

Conventional methods such as viscometry require an excessive amount of sample

liquid [34, 41], which is impractical for blood and other scarce and expensive bio-

fluids. A rigorous but quick quantification of hematology and pathophysiology is

most welcome for research in biology and medical science in general.

1.2 Droplet impact on solid surface

Six characteristic morphological stages are involved when Newtonian droplets

impact a solid surface, and are discussed by R. Rioboo [42], as shown in Fig. 1.

“Deposition” on hydrophilic surfaces and “receding break-up” are related to

wettability and lie beyond the scope of this thesis. “Prompt splash”, “corona

splash”, and “partial / complete rebounce” are expected in non-Newtonian fluid

impacting on a super hydrophobic substrate with an advancing contact angle of

150o. During “corona splash”, an impacting droplet turns into a “pancake” with

uniform thickness, followed by “spires” developing at the rim, and might ultimately

fragment or splash under special circumstances. This thesis focuses on the

experimental investigation. A high-speed camera is used to perform in-situ

observation over a range of droplet dimension and impact velocity.

Figure 1: Water droplet impacts a solid surface according to Rioboo.

1.3 Super hydrophobic surface

The natural self-cleaning ability of lotus leaves is appealing to the scientific

community. The fascinating phenomenon is strongly related to micro-/nano-scale

surface roughness and hydrophobicity, and has wide industrial applications.

Related papers are voluminous in the literature. Smooth and super-hydrophobic

surfaces are used in the present study. Contact angle is determined by the

wettability of the solid surface. A hydrophobic surface has a contact angle

exceeding 90o is hydrophobic, and becomes super-hydrophobic > 130o. In

contrary, a surface with < 90o is hydrophilic as illustrated in Figure 2. . Figure 3

shows a water droplet standing on a super hydrophobic surface with ≈150o.

Figure 2: Sketch of a hydrophobic surface and hydrophilic surface[43]

Figure 3: Water droplet with with ≈150o

1.4 Existing models 1.4.1 Newtonian and non-Newtonian behavior

In fluid mechanics, the viscosity of a Newtonian liquid is a constant

independent of the rate of change of shearing strain over time, , but depends

only on temperature and pressure [44]. Conversely, a non-Newtonian fluid

exercises nonlinear viscous behavior, as its viscosity changes as a function of ,

𝜇 = 𝑓(�̇�) (1)

as illustrated in Figure 4.

Figure 4: Viscosity of Newtonian, Shear Thinning and Shear Thickening

fluids as a function of shear rate[45].

Non-Newtonian Fluids are in general categorized into four types based on

the change of viscosity: thixotropic, rheopectic, shear thinning and shear

thickening. Shear thickening liquid has its 𝜇 increasing with �̇�, while shear thinning

fluids has a monotonic decreasing 𝜇(�̇�). Should 𝜇 changes with time, the fluid is

either thixotropic or rheopectic. Table 1 summarizes the four non-Newtonian types.

Type of

behavior Description Example

Thixotropic Viscosity decreases

with stress over time

Honey – keep stirring, and

solid honey becomes liquid

Rheopectic Viscosity increases with

stress over time

Cream – the longer you whip it

the thicker it gets

Shear thinning

or pseudoplastic

Viscosity decreases

with increased stress Blood, tomato sauce

Shear thickening

or dilatant

Viscosity increases with

increased stress Corn starch solutions

Table 1: Summary of four types of non-Newtonian liquids

This study investigates a range of Newtonian and non-Newtonian fluids.

Water is the classic representative of Newtonian liquid. Milk only simulates

Newtonian, as its viscosity is fairly constant over strain rate at room temperature.

Corn starch solution is non-Newtonian shearing thickening. Here, it comprises

100% pure corn starch from local supermarket with a concentrations of 5% and

15% by mass. Rabbit blood purchased from Innovative Research serves as shear

thinning liquid. In our droplet experiments, blood samples are either as-received

or diluted with distilled water at 1:1 volume ratio. Table 2 summarizes properties

of the liquid in this study.

Table 2: Weber number and droplet initial diameter are measured from

experiments. Surface tension is measured by Fordham’s pendant drop

method [46].

1.4.2 Non-dimensional parameters

The dimensionless Weber and Reynolds number play important roles in

droplet dynamics. Weber number is a dimensionless number useful in analyzing

fluid flows where there is an interface between two different fluids, or, in the present

context, the droplet-substrate interface. They are defined by

𝑊𝑒 =𝜌𝑣2𝐷

𝜎 (2)

𝑅𝑒 =𝜌𝑣𝐷

µ (3)

Liquid Weber number

We

Droplet diameter D(mm)

Liquid density ρ(kg/m3)

Surface tension

σ(mN/m)

Distilled water 30.82~235.38 2.4~3.7 1000 72

Whole Milk 34.83~218.95 2.35~3.56 1035 60.05

5%Corn starch solution

33.46~215.23 2.28~3.53 1052.63 67.65

15% Corn starch solution

49.75~253.27 2.22~3.48 1176.47 62.34

Blood 120.48~242.01 2.84~3.50 1082.15 56.30

Diluted blood at 1:1 volume ratio

58.54~211.68 2.58~3.35 1042.7 68.05

where ρ, σ, µ are denoted as the density, surface tension, and viscosity of the

liquid, respectively, and D and the v are denoted as droplet diameter before impact,

and impact velocity, respectively. We is a measure of the relative importance of

the fluid's inertia compared to its surface tension [49], and indicates whether the

kinetics or the surface tension energy is dominant. According to the literature,

water droplet impacting on a super hydrophobic surface with We << 1, surface

tension dominates and droplet remains roughly spherical. This study considers

only We > 1. Re is the ratio of inertial forces to viscous forces within a fluid. Bhola

and Chand [47] investigated spire formation at the rim of a molten wax droplet and

asserted that the number of coronal spires given by

𝑘 =𝑊𝑒0.5𝑅𝑒0.25

4√3 (4)

Marmanis and Thoroddsen [48] investigated a variety of liquid droplets impacting

a paper surface and found k to be a function of (We0.25Re 0.5)0.7. Such model is not

not applicable to non-Newtonian fluids as expected.

1.4.3 Related models of characteristic behaviors

The dynamic behaviors of droplet impact can be described as three stages:

spreading, recoiling and rebound, which are characterized by capillary waves, rim

instability and jetting governed by different mechanisms. There are qualitative

model discussing shock wave, moving contact line, capillary wave, Rayleigh-

Plateau instability, Rayleigh-Taylor instability, air cavity, and pinch-off dynamics.

The capillary waves observed at the early spreading stage is thought to be

depending on generation of shock wave. The wavelength is a function of surface

tension and viscosity as well as droplet kinematic input such as impact velocity.

The Rayleigh-Plateau instability is related to “break-up” of a liquid jet, while

Rayleigh-Taylor instability underlies the break up of an interface between two

dissimilar fluids of different densities. The combined model is expected to be valid

in the perturbation and fragmentation of the rim of a droplet upon impact. Jet was

first observed by Worthington when he investigated a milk droplet impact in liquid

pool, and was coined “Worthington Jet”. Similar jets are found in droplet impacting

a solid surface. Air cavity dynamics and pinch-off dynamics closely related

subjects.

In this thesis, the dynamics of droplet impact, specifically rim instability, is

investigated experimentally. The results are compared with theoretical analysis

based on Rayleigh-Plateau instability. Another graduate student in our research

group, Xiao Huang, is currently building a theoretical model in this context. From

Huang’s unpublished work, the number of the spires during a water droplet impact

is given by

𝑘 = 0.9421 ∗ [log(𝑊𝑒)]4 − 0.4122 (5)

Detailed comparison between this model and the experimental results will be

discussed in Chapter 3

2. Experiments

The experimental setup and its components for this study are outlined

below, and so are the step-by-step procedures.

2.1 Experimental apparatus

Figure 5 shows the assembled homemade apparatus and the components.

Specifications are given below:

High speed camera, Edgertronic Monochrome: The high speed camera,

Edgertronic, whose exposures are able to be down to 1/200,000 seconds,

resolution settable from 192x96 to 1280x1024, ISO 400-6400 and frame

rates up to 17,791 fps (resolution dependent)

Light source, RPS CoolLED 100 Studio Light RS-5610: The RPS Studio

LED Studio Light uses a single 100 watts (energy usage) LED that produces

light equal to 1000 watts when the 8” reflector is attached to it. The light

output is adjustable yet the color temperature of the light stays a constant

daylight (5200°K). Mounts to any standard 5/8” light stand spigot. The on/off

switch is in the 3-meter power cord. Complete with 8” Bowen’s mount style

reflector that will accept a standard umbrella, shower cap style diffuser, and

protective cap.

Pipette, Rainin Classic PR-200: The volume range of PR-200 is from 20 µL

– 200 µL, and the manual increment is 0.2 µL. Accuracy of the pipette is ±

2.5 % per 0.5 µL and precision is ± 1 % per 0.2 µL.

Aluminum experimental conduct chamber: The apparatus is designed and

assembled by an undergraduate capstone group, which is made of

assembled aluminum rack and provides adjustable impact angle and impact

velocity.

Optical lens, Tokina 100mm f/2.8: This lens is a macro lens for digital

camera, capable of life-sized (1:1) reproduction at 11.8 in. (30 cm). The

lens' multi-coating matches the highly reflective silicon based CCD and

CMOS sensors in digital SLR cameras, while the optics give full coverage

and excellent sharpness on 35mm film. The focal length is 28-70mm, close

focus up to 0.7 meter, working distance is 115mm.

Figure 5: Experimental setup comprising a frame (d) with the two

platforms (A and B) and mounting fixtures for the micropipette (c), a light

source (b), and the camera-lens assembly (a and e, respectively). The

the camera-lens assembly is mounted on Platform A, and it is height and

angle adjustable. The super hydrophobic surface is placed on Platform

B. The vertical micropipette is mounted directly above the super

hydrophobic surface and is used to dispense the sample droplet.

Figure 5a: High-speed camera. The camera has a computer

interface to record the experiments at 6000 frame per second (fps).

Recording is automatically triggered.

Figure 5b: RPS CoolLED 100 Studio Light RS-5610. The LED light is

mounted on the conduct chamber (d) and provides light in case of

recording video with high fps.

Figure 5c: Rainin pipette. Micropipette is used to dispense the sample

droplets. During an experiment, the pipette tip was filled prior to

adjust the volume adjustment knob (VAK). When it was time to

dispense the droplet, the VAK was turned in the clockwise to

decreasing volume. This gradually dispenses the fluid from the pipette

tip, forming a gradually-growing droplet pendant at the end. When

then pendant reached a critical volume, it broke free from the tip, and

fell downward.

Figure 5d: Metal frame for assembly.

Figure 5e: Tokina optical lens

2.2 Preparation of super-hydrophobic surface

There are many standard ways to create super-hydrophobic surfaces made

from polymers, metals or carbon nanotubes for different purposes. In the present

work, a copper sheet is used as the substrate. All chemicals are purchased from

Sigma-Aldrich. The surface is prepared by two consecutive steps. Two main

processes are composed to make the surfaces. First, we follow the instructions

outlined in UVA super hydrophobicity manual [49] created by Backer et al. By

silver coating with nano-scale surface roughness is produced by reacting the

copper surface with silver nitrate. The silver cations (Ag+) are reduced by copper

to metal silver. The coated copper sheet is then immersed in heptadecafluoro-1-

decanethiol (HDFT) solution, resulting in a self-assembled monolayer with non-

polar molecular segments as shown in Figure 6.

Figure 6: Self assembled monolayer made of HDFT molecules[50]

Step 1: Substrate preparation

Copper sheet (2cm x 5cm) is polished using a 500-grit pad under fingertip

pressure. The residual copper and abrasive particles are wiped off using a tissue.

The plate is examined for surface roughness using an optical microscope.

Step 2: Fine polish

Polishing is repeated using grit pads of 800, 1200, 1500 and 2000 till a mirror

surface is obtained. For the purpose of easily recognizing the polished side and

facilitating capture by tweezers, pliers are used to bend up one corner of the copper

toward polished face.

Step 3: Chemical solution preparation

Four beakers are prepared and labelled. Beaker 1 is filled with 40mL of silver

nitrate (AgNO3), Beaker 2 with 40mL of De-ionized (DI) water, Beaker 3 with 40mL

of dichloromethane (CH2CL2) and 11.5mL Heptadecafluoro-1-decanethiol

(HDFT), and Beaker 4 with 40mL of dichloromethane (CH2CL2). Gentle stirring is

applied at each stage.

Step 4: Super hydrophobic surface creation

The polished Cu sheet is placed by using the tweezers in AgNO3 (Beaker 1) with

the polished side facing up for 2 minutes. The Cu sheet is then transferred to DI

water (Beaker 2) for 20 seconds and blown dry with a nitrogen gun. The Cu sheet

is then placed in Beaker 3 for 5 minutes. The sheet is finally dropped in in

dichloromethane (Beaker 4) for 20 seconds and blown dry.

2.3 Droplet generation

A micropipette is used to generate and dispense liquid droplets. The volume

adjustment knob (VAK) is set to 20 µL before filling the disposable plastic tip with

sample liquid. Two distinct methods are used to dispense a droplet. In method

(i), the plunger is depressed to eject the droplet. There is limited control over the

velocity of the droplet. In method (ii), the pipette tip is filled prior to adjusting the

VAK. When it is time to dispense the droplet, the VAK is turned in the clockwise

direction to decrease volume. This gradually dispenses the fluid from the pipette

tip, forming a gradually-growing pendant drop at the tip. When the drop reaches

a critical size, it breaks free from the tip, and falls downward. This method,

illustrated in Fig. 7, is used to ensure a zero initial velocity.

Figure 7. Droplet generation

2.4 Experimental procedures

Step 1: Experimental apparatus assembly

The pipette (Fig. 5c) is held by a fixture vertically above the super-hydrophobic

surface on platform B. The high speed camera-lens assembly is mounted on

platform A to videotape the experiments. The light source (b) is mounted next to

platform B in a direction pointing to the target plate.

Step 2: Camera and Micropipette

The height h between the micropipette tip and the super hydrophobic surface as

shown in Fig. 8. Initially h is set to be 12.7 mm (0.5 inches) from platform B. Height

of Platform B is adjustable to vary the flight distance. Height of Platform A is also

adjustable to fine tune the camera position. Both platform A and B are kept

horizontal. The working distance L between the camera and target substrate is

set to be 600 mm.

Step 3: Camera setting

Camera is computer controlled and its setting includes two stages: pre-focusing

and experiment. At pre-focusing setting stage, camera is set as shown in Fig. 9

and lens (e) is rotate to focus. The position of the camera is adjusted to make sure

the surface is placed in the center on the screen. The setting is then switched to

experiment stage as shown in Fig. 10 and lens (e) is rotate to focus again. The

ISO, light intensity and aperture ae modulated correspondingly to make sure the

brightness is proper to see the details on the substrate.

Step 4: Experimental operations of taking horizontal view videos

Method (ii) mentioned in Chapter 2.3 is used to generation droplets. The record

button as shown in Fig. 11, is trigger at the instant of droplet impact evolution

completed. The height of h is increased by adjusting platform A with an increment

of 6.35mm (0.25 in) and limited at the elevation of 140 mm (5.5 in). Experiments

of each elevation repeat 5 times.

Step 5: Experimental operations of taking 45o view videos

The camera is regulated to the positon as shown in Fig. 12 by adjusting the height

and angle of platform A. Then septs 3 and 4 are repeated.

Figure 8: Illustration of a micropipette positioning

Figure 9: Camera setting at pre-focusing stage

Figure 10: Camera setting at experiment stage

Figure 11: Illustration of record button

Fig. 12 Sketch of experiment camera locations

2.5 Surface tension measurement

Surface tension is measured by pendant drop method [46]. The shape of

the drop a result of the relationship between the surface tension and gravity. The

pendant drop geometry is presumably universal and is independent of liquid

intrinsic properties such as surface tension. A snapshot is taken at the pipette tip

and is analyzed according to the classical theory to deduce surface tension.

Fig 13: Pendant drop schematic [51]

𝑆 =𝑑𝑠

𝑑𝑒 (6)

where 𝑑𝑒 is the droplet diameter at its maximum width and 𝑑𝑠 is the width at the

distance of 𝑑𝑒 from the bottom, and 𝑆 is the ratio of 𝑑𝑠 and 𝑑𝑒 ,as illustrated in

Fig.13. Then surface tension can be found by putting

𝜎 =∆𝜌𝑔𝑑𝑒

2

𝐻 (7)

where ∆𝜌 is the density difference between the interface, 1/H is a value dependent

on S and the calculation tables from are given in Appendix.

Figure 14: Illustration of pendant droplet method measurement

3. Results and discussion

In this section, necessary terminological names are defined. Droplet impact

behaviors of Newtonian and non-Newtonian fluids are discussed. The influence of

impact velocity, droplet diameter and Weber number on the formation of spires on

the rim are investigated. Experimental results are compared to Huang’s theoretical

model. The effects of viscosity exerted on spreading are studied.

3.1 Definition To better understand the droplet impact behaviors, necessary terminological terms

are defined in this area section prior to discussion.

3.1.1 Stage, contact diameter and impact velocity

In droplet dynamics, three stages are observed during droplet impact

evolution: spreading, recoiling and rebounce. The spreading stage, as shown in

Figure 15, begins at the instance of the droplet impacting on the target surface,

and ends when the droplet reaches its maximum lateral spreading. At this stage

the droplet spreads radially, and the contact diameter increases. The recoiling

stage, as shown in Fig. 16, begins when the droplet contracts from its extent of

maximum spread. When the contact diameter is equal to 0, the droplet lifts off the

surface. This final stage of rebounce is shown in Fig. 17. The contact diameter (Dc)

is illustrated in Fig. 18. Impact velocity is given as

𝑣 = √2𝑔ℎ (8)

where ℎ is the released height denoted at Chapter 2.4.

Figure 15: Spreading stage of a water droplet impact on a solid surface.

The spreading stage begins at the instance of the droplet impacting on

the super hydrophobic surface and ends when droplet reaches its

maximum spreading.

Figure 16: Recoiling stage of a water droplet impact on a solid

surface. The recoiling stage begins when the droplet reaches its

maximum spreading, and ends at the instance when the contact

diameter is equal to 0.

Figure 17: Rebounce of a water droplet after impact. The contact

diameter equals to 0.

Figure 18: illustration of contact diameter

3.1.2 Spires, film and jet

Corona splashing is one of the six types of droplet outcomes mentioned at

Chapter 1.2. During corona splashing, the spires are found and developed from

the perturbations around the rim. The number of the spires at its maximum

spreading is counted and denoted as k. The relation between the number of the

spires k and the liquid properties is studied and discussed in subsequent sections.

The central area of the droplet where the capillary waves are found and observed

is termed the “central film”. Illustration is shown in Fig. 19. At the recoiling stage,

the droplet shoots back in the opposite direction of the droplet impact as a pillar

and this behavior is defined as the “jet”, which is shown in Fig. 20.

Figure 19: Rim, spire, film and capillary waves

Figure 20: Jet

Figure 21: Smooth rim without spires

Figure22: Fragmentation

3.1.3 Smooth rim and fragmentation

Figure 21 shows a typical droplet with small We, the rim is smoother and no

spire is observed. with smooth rim. Figure 22 shows another droplet with high We,

fragmentation with splashing is observed.

3.2 Droplet impact behaviors

3.2.1 Droplet impact behaviors of Newtonian fluids

Most research works in the literature are based upon Newtonian water. The

present study exploits water droplet impact on super hydrophobic surface. Fig. 7

consists of an image sequence of water droplet with D = 2.6mm and 𝑣 =1.45m/s

impacting on a super hydrophobic surface. It showed the successive stages of

droplet impact evolution, with time from initial impact indicated. The water droplet

was recorded from t=0 at which right before the droplet landing on the super

hydrophobic surface. The rim of the droplet was unstable, since spires were

generated around the edge. As time went on, it continued to spread and reached

its maximum spread at t =2.33ms. At the same time, the number of spires also

reached its maximum. As the water of droplet continued flowing outward from the

center film to the rim, the thickness of the central film and contact area decrease,

while the size of the spires increased. At t=3.33ms and t=4.5ms, growth of spires

resulted in spire merging and spire number decreased. During the entire process,

surface tension acted against the increase in surface area. The spires were pulled

back together by surface tension, and eventually the droplet lifted off the surface

at t =12ms.

Figure 23: A water droplet with D =2.6mm and 𝑣 =1.45 m/s impacted

on a super hydrophobic surface. Scale bar was shown at t=0. At

t=1ms, the droplet was impacting on the substrate. At t=2.33ms, the

droplet reached its maximum spreading and 16 spires were counted.

From t=2ms to t=4.5ms, corona rim was presented. At t=12ms, the

droplet was pulled together by surface tension.

Whole milk is usually taken to be a Newtonian fluid, even though it is not a

pure substance like water. This is because it does not differ appreciably from

Newtonian behavior at room temperature during shelf life. Figure 8 shows a series

of photos of a milk droplet with v =1.91 m/s and D =2.75mm impacting on a super

hydrophobic surface. Spiky and sharp spires show up around the rim when the

droplet hit the solid surface at t = 0.67ms. The number of spires is counted as 14

when the milk droplet reached its maximum spreading at t =2.5ms. It is evident

that central fluid flows radially towards the rim, reducing the thickness and contact

area. Spires merge at t = 4ms. When t = 5ms, the spires number reduces to 8. At

t =7ms, the spires retreats towards the center, as surface tension tends to minimize

the droplet surface area. At t = 9.83ms, fragmentation occurs. Milk droplet are

observed to be more stable than water, as the rim is smoother and coronal spires

are fewer.

Figure 24: A milk droplet with D =2.75mm and 𝑣 =1.91 m/s impacted

on a super hydrophobic surface. Scale bar was shown at t=0. At

t=0.67ms, the droplet was impacting on the substrate. At t=2.5ms,

the droplet reached its maximum spreading and 14 spires were

counted. From t=2ms to t=5ms, corona rim was presented. At t=7ms,

the droplet was pulled back to the center by surface tension. At

t=9.83ms, fragmentation was observed.

3.2.2 Shear thickening and shear thinning fluids

In shear thickening fluids, viscosity increases with strain rate. When shear

is applied, the fluid thickens and its behavior becomes solid-like. Two different

concentrations of corn starch solutions — sometimes called oobleck — are

investigated in this research: 5% and 15% by mass.

Fig. 25 shows a droplet of 5% corn starch solution with v =1.72 m/s and D

= 3.41mm impacting on a super-hydrophobic surface. Spires begin to appear at t

= 0.83ms. Fluid then flows radially to the rim turning into flat pancake at t = 1.67ms.

Spires are were obtuse at the tip. At t = 3.83ms, the droplet spreads to its

maximum diameter, and 16 spires are observed around the rim. Additional minor

spires protrudes from the rim and merge with the adjacent spire from t = 5.7ms to

7.3ms. At t=15ms, the droplet pulls back together by surface tension, followed by

jetting.

Figure 25: A 5% corn starch droplet with D =3.41mm and 𝑣 =1.72 m/s

impacted on a super hydrophobic surface. Scale bar was shown at

t=0. At t=0.83ms, the droplet was impacting on the substrate. At

t=3.83ms, the droplet reached its maximum spreading and 16 spires

were counted around the rim. From t=0.83ms to t=7.33ms, corona

splash was presented. At t=9.5ms, the droplet was pulled back to the

center by surface tension. At t=15ms, the droplet jetted.

Figure 26 shows the impact of a 15% corn starch droplet with 𝑣 =1.71 m/s

and D =3.40mm. Unlike water, milk and the 5% corn starch solution, the highly

concentrated corn starch droplet spreads on the solid substrate with a smooth

round rim like a bowler hat at t = 0.33ms. Perturbation on the rim emerges as

protrusions. The protrusions grow into spires since more and more fluid flows

towards the rim. Spreading of the droplet on the solid surface is out of sync with

the spire growth. When the droplet reaches its maximum spreading at t = 4ms, no

new spire is generated, but the existing spires do not develop fully until t = 5.17ms.

The spires are obtuse and rounded. The droplet remains symmetric and is

apparently more stable. After reaching the maximum contact area, the pancake

recoils and the adjacent spires coalesce. The spires do not have sufficient inertia

to detach or the ability to detach from the mother drop to form secondary droplets.

The droplet retreats due to surface tension, followed by jetting at t =13.5ms.

Figure 26: A 5% corn starch droplet with D =3.40mm and 𝑣 =1.71 m/s

impacted on a super hydrophobic surface. Scale bar was shown at

t=0. At t=0.33ms, the droplet was impacting on the substrate. At

t=4ms, the droplet reached its maximum spreading and 14 spires

were counted around the rim. At t=5.17ms, the spires were

developed completely. From t=4ms to t=7.83ms, corona splash was

presented. At t=9.67ms, the droplet was pulled back to the center by

surface tension. At t=13.5ms, the droplet jetted.

3.2.3 Droplet impact behavior of shear thinning fluids

In shear thinning fluids (e.g. blood), viscosity decreases with strain rate. In

this work, rabbit blood as received and diluted blood are investigated. Figure 27

shows impact of a blood droplet with v =1.81m/s and D =2.93mm. The droplet

spreads with a rounded and smooth rim without perturbations at t = 1ms. At t =

2.67ms, the droplet reaches its maximum spreading, and 9 spires develop at the

rim. Upon recoil at t=5.67ms and t=6.67ms, the droplet retracts radially and

capillary waves are observed on the central film. At t=14.5ms, jetting occurs.

Figure 27: A blood droplet with D =2.93mm and v =1.81m/s impacted

on a super hydrophobic surface. Scale bar was shown at t=0. At

t=1ms, the droplet was impacting on the substrate and there was no

perturbation observed on the rim. At t=2.67ms, the droplet reached

its maximum spreading and 9 spires were counted around the rim.

At t=4ms, the spires were developed completely. From t=2.67ms to

t=4.67ms, corona splash was presented. The droplet was pulled

back to the center by surface tension at t=9.67ms and jetted at

t=14.5ms.

Figure 28 shows diluted blood droplet with D =3.28mm and v =1.72 m/s. At t = 1ms,

perturbation around the rim is seen. The spires are obtuse and regular, which are

quite different from the sharp and spiky spires in milk. These spires distribute at

approximate equidistance on the rim with similar size and shape. Symmetry

persists throughout the impact-recoil process, contrasting the irregular and

asymmetric spires in water droplet. At t = 3.17ms, the droplet reaches its maximum

contact diameter with 12. At t = 6.5ms, capillary waves are observed on the central

film. At t = 19.67ms, jetting occurs. The jet is large in cross section and comprises

most of the overall mass.

Figure 28: A blood droplet with D =3.28m and v =1.72m/s impacted

on a super hydrophobic surface. Scale bar was shown at t=0. At

t=1ms, the droplet was impacting on the substrate and there were

perturbations observed on the rim. At t=3.17ms, the droplet reached

its maximum spreading and 12 spires were counted around the rim.

At t=4.17ms, the spires were developed completely. From t=1ms to

t=6.5ms, corona splash was presented. The droplet was pulled back

to the center by surface tension at t=10.67ms and jetted at

t=19.67ms.

3.3 Weber number and impact behavior

3.3.1 Velocity and spire formation

Velocity and droplet diameter are two variables that can be varied as

desired. Two different sizes of water droplets are created and released by different

pipette tips with varying heights. Figs.29-34 show the relation of number of spires

as a function of impact velocity for droplets of two different sizes. V1 and V2

represented the volume of larger and small droplets respectively. Regardless of

the fluid nature, increase in impact velocity leads to more spires. With the same

velocity, large droplets generate more spires. From Equation (2), the square of

velocity and the diameter are directly proportional to We. Higher impact velocity

and a large droplet volume trigger more perturbation and provide more kinetic

energy to the liquid to generate more spires. The number of spires is directly

proportional to We no matter the fluid involved is Newtonian or non-Newtonian.

Fig. 29: Spires number K vs impact velocity v of water droplet with

volume 1(3.6mm±0.1𝑚𝑚) and volume 2(2.6mm±0.2𝑚𝑚)

Figure 30: Spires number K vs impact velocity of milk droplet with

volume 1(3.4±0.16𝑚𝑚) and volume 2(2.5±0.15𝑚𝑚)

0

5

10

15

20

25

0 0.5 1 1.5 2 2.5

The

nu

mb

er o

f sp

ires

k

Impact velocity v m/s

V1 Water

V2 Water

V1

V2

0

2

4

6

8

10

12

14

16

0 0.5 1 1.5 2 2.5

The

nu

mb

er o

f sp

ires

K

Impact velocity v m/s

V1 Milk

V2 Milk

V1

V2

Figure 31: Spires number K vs impact velocity of 5% corn starch

solution droplet with volume 1(3.4 ±0.13𝑚𝑚 ) and volume

2(2.5±0.22𝑚𝑚)

Figure 32: Spire number K vs velocity of 15% corn starch solution

with volume 1(3.3±0.18𝑚𝑚) and volume 2(2.4±0.18𝑚𝑚)

0

5

10

15

20

25

0 0.5 1 1.5 2 2.5

The

nu

mb

er o

f si

pre

s K

Impact velocity v m/s

V1 5% CS

V2 5% CS

V1

V2

0

2

4

6

8

10

12

14

16

18

0 0.5 1 1.5 2 2.5

The

nu

mb

er o

f si

pre

s K

Impact velocity v m/s

V1 15% CS

V2 15% CS

V1

V2

Figure 33: Spire number K vs velocity of rabbit blood with volume

1(3.3±0.2𝑚𝑚) and volume 2(2.97±0.13𝑚𝑚)

Figure 34: Spire number K vs velocity of 1:1 diluted blood with volume

1(3.25±0.1𝑚𝑚) and volume2 (2.78±0.2𝑚𝑚)

0

2

4

6

8

10

12

14

16

0 0.5 1 1.5 2 2.5

The

nu

mb

er o

f si

pre

s K

Impact velocity v m/s

V1 Blood

V2 Blood

V1

V2

0

2

4

6

8

10

12

14

16

18

0 0.5 1 1.5 2 2.5

The

nu

mb

er o

f si

pre

s K

Impact velocity v m/s

V1 1:1 DilutedBlood

V2 1:1 DilutedBlood

V1

V2

3.3.2 Weber number and spire formation

A positive correlation of k(We) is expected in both Newtonian and non-

Newtonian fluids. Figure 35 shows k(We) for water, milk, blood, 1:1 diluted blood,

5% corn starch, and 15% corn starch, along with Huang’s theoretical perdition.

Curve fitting in Figure 35 shows monotonic increasing k(We) for all liquids. From

his work, k is predictable and is a function of We. Huang’s model is capable of

predicting the number of spires in water but not the non-Newtonian fluids. The

phenomenological equations of each fluid are shown below. For

Water, 𝑘 = 6 × 10−6𝑊𝑒3 − 0.0029𝑊𝑒2 + 0.547𝑊𝑒 − 18.769

Milk, 𝑘 = −2 × 10−6𝑊𝑒3 + 0.0005𝑊𝑒2 + 0.0543𝑊𝑒 − 0.5028

5% corn starch, 𝑘 = 14.011 × 𝑙𝑛(𝑊𝑒) − 56.697

15% corn starch, 𝑘 = −3 × 10−6𝑊𝑒3 − 0.0013𝑊𝑒2 + 0.0549𝑊𝑒 − 0.5028

Blood, 𝑘 = 20.453 × 𝑙𝑛(𝑊𝑒) − 99.417

Diluted blood, 𝑘 = 6 × 10−7𝑊𝑒3 − 0.0008𝑊𝑒2 + 0.279𝑊𝑒 − 12.129

It is apparently that We alone is not sufficient to predict the impact behavior,

especially the number of spires.

Figure 35: K vs Weber number of all experimental fluids

Figure 35 shows the best fits of the liquid investigated. The higher the

surface tension the more spires are generated at the same We (c.f. Table 2). It is

worthwhile to remark that the dilute corn starch solution has roughly the same

as dilute blood, and their k(We) overlap. This is also true for the concentrated corn

starch solution and milk. Such correlation is quite consistent with the Rayleigh-

Plateau instability. The surface tension–driven instability describes a stream of

fluid that breaks into smaller droplets. When a drop impacts on a solid surface,

perturbation around the rim appears as crest and valley of waves with positive and

negative curvatures in regular intervals or wavelength [52]. Liquid with higher

tends to create more spires with the same We.

0

5

10

15

20

25

0 50 100 150 200 250 300

K

We

We Water

Weber Milk

Weber Corn starch 5%

Weber Corn starch 15%

Weber Blood

Weber 1:1 Diluted Blood

Xiao' theoretical predition

Water(72,1000)

Milk(60.05 1035)

Corn starch 5%(67.6,1052.63)

Corn starch 15%(62.34 1176.47)

Blood(56.30 1082.15)

Figure 36: Illustration of pinched section and bulging section

3.4 Viscosity and Spreading

Toivakka [53] demonstrated that both and have negative influence on

initial spreading. But how they affect the impact behavior remains unclear. The

contact diameter Dc immediately after impact should be a function of time as shown

schematically in Figure 37. If two different droplets (e.g. blood and water) with the

same We impact a super-hydrophobic surface, pushes Dc(t) to the right. Higher

prolongs the contact interval. Increase in shifts the curves up as surface

tension constrains the spreading and minimizes the surface area. Figure 38 shows

lateral spreading of water, milk and blood droplets. Since it is difficult to generate

the droplets with identical initial diameter D by the pipette, instantaneous diameter

Dc is normalized with respect to D. Here D is defined to be the diameter just before

impact at to = 0. Water, milk and blood spread from to to their maximum extent at

t2 = 3.33ms, t4 = 4.17ms and t3=3.83ms. Recoil follows immediately. At t5=7.33ms,

water droplet begins to jet and is lifted off the substrate at t8=12.5 ms. Surface

flaws on the substrate cause some droplet to stick. Blood and milk droplets jetted

at t6=9 ms and t7=10.17 ms respectively, but no complete lift-off is observed. Liquid

Table 3 summarizes the liquid properties and behavior. The measurements are

qualitatively consistently with the hypothesis: (i) maximizes spreading, and (ii)

delays spreading and prolongs contact. It is remarkable that water droplets lead

to numerous coronal spires contrasting the fairly smooth rims in blood. Viscosity

does not seem to control the spire formation directly, but apparently prolongs the

contact time and the impact-spread-recoil process. Viscosity slows down the

advancing and retreating fronts. Figure 39 shows the droplet geometry as function

of time.

Figure 37: Schematic of hypothetical droplet evolution with time variation

Figure 38: Time variation of spread factor

Liquid Water Whole Milk Blood

Weber number 122.01 122.60 120.48

Reynolds number 4224.43 1691.44 1832.72

Spire number 14 10 0

Surface tension (mN/m)

72 60.05 56.30

Viscosity (cp) 1 3[54] 2.6[55]

Initial diameter (mm) 2.75 3.38 2.67

Time of maximum spreading (ms)

3.33 4.17 3.83

Time of jetting (ms) 7.33 10.17 9

Maximum dc/Do 6.79 7.29 7.62

Table 3: Droplets properties and behavior

Figure 39: Impact of water, milk and blood droplets from t0 to t8. At

t=t1, three droplets was impacting on the super hydrophobic surface.

At t=t2, water droplet reached its maximum spreading. At t=t3, blood

droplet reached its maximum spreading. At t=t4, milk droplet

reached its maximum spreading. At t=t5, water droplet started to jet.

At t=t6, blood started to jet. At t=t7, milk started to jet. At t=t8, water

droplet lifted off the surface.

4. Conclusion

Spire generation by liquid droplet impact is investigated based on the

classical model of Weber number. Our experimental data supports a positive

correlation between Weber number and the number of spires, k, in both Newtonian

and non-Newtonian fluids. A droplet impact with higher Weber number leads to

more spires at the rim. It is also found that number of spires increases with surface

tension. Comparison between theory and experiment shows that classical model

for Newtonian liquids is inadequate to predict spire formation in non-Newtonian

fluids. Viscosity affects the droplet geometric deformations during impact

evolution, and must be incorporated into the model involving Weber number.

Nonlinear viscosity prolongs the contact time with the substrate and therefore

modifies the impact-recoil process. Droplet impact provides a tool to gauge

surface tension and nonlinear viscosity in short time.

5. Suggestions and Future work

To explore the relation between liquid intrinsic properties of the fluids and

droplet deformation upon impact, it is recommended to repeat the experiments

with corn starch and blood of a wide range of concentration. New experimental

set-up with automatic volume and impact velocity control is necessary in the long

run. Surface preparation and characterization of the super-hydrophobic substrate

are necessary to minimize the statistical variation.

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Appendix