Chapter 7 TRANSPORT OF LIQUID WATER · behaviour • liquid water behaves in good approximation as...

TRANSPORT OF LIQUID WATER Chapter 7

1

behaviour

• liquid water behaves in good approximation as an incompressible fluid with a density of ρl ≈ 1000 kg/m3

2

materials are exposed to moisture

• during construction – construction moisture – precipitation

• weather

– rain – melting of

snow

© Jonathan Sa’adah 3

materials are exposed to moisture

• condensation – surface condensation – interstitial condensation

• ground water infiltration • by accident

– leaking pipes – broken seals – …

© DEMA

© howtobuildahouseblog.com 4

moisture content

• the moisture content is the mass of moisture per unit volume of material – symbol: w – SI unit: kg/m3

5

for stone-like materials

moisture content at saturation

• the moisture content at saturation is the maximum mass of moisture per unit volume of material – symbol: wsat

– SI unit: kg/m3

at saturation, all open pores are filled with water

6

moisture ratio

• the moisture ratio is the mass of moisture per unit mass of material – symbol: X – SI unit: kg/kg

for wood-based materials

7

volumetric moisture ratio

• the volumetric moisture ratio is the volume of moisture per unit volume of material – symbol: ψ – SI unit: m3/m3

for highly porous materials

8

relations

• moisture ratio vs. moisture content

• moisture ratio vs. volumetric moisture ratio

• summary:

ψρρ

ρρ

mat

moist

mat

moist

mat

moist

mat

moist

VV

mmX ===

wVm

mmX

matmat

moist

matmat

moist

ρρ11

===

ψρρ moistmat wX ==

9

summary

• use the moisture content w [kg/m3] for stone-like materials

• use the moisture ratio X [kg/kg] for wood-based materials

• use the volumetric moisture ratio ψ [m3/m3] for highly porous materials

10

degree of moisture saturation

• the degree of moisture saturation is the ratio between the current and the maximum amount of moisture – symbol: Sm

– SI unit: dimensionless

– formula satsatsat

m XX

wwS

ψψ

===

Sm ranges from 0 (perfectly dry) to 1 (saturated)

11

saturation degree scale

Sm = 0 Sm = 1

dry material

saturated material

w = 0 w = wsat

Sm w

≤ ≤

≤ ≤

wetting process

12

wetting process

dry material

saturated material

molecular adsorption

capillary condensation

wetting process

13

hygroscopic curve

• equilibrium Sm in an environment at RH

00.20.40.60.8

1

0 0.2 0.4 0.6 0.8 1degr

ee o

f moi

stur

e sa

tura

tion

[-]

relative humidity [-]

MORTAR

14

00.20.40.60.8

1

0 0.2 0.4 0.6 0.8 1degr

ee o

f moi

stur

e sa

tura

tion

[-]


hygroscopic curve

• hygroscopic curve is a material characteristic

hygroscopic materials take up a lot of water before RH=1. Non-hygroscopic materials do not

BRICK MORTAR

hygroscopic curve can be strongly non-linear! 15


• consider a cylindrical pore with radius r, filled partially by gas and partially by liquid :

( )( ) ( )( )rrPP lg παγπ 2cos2 =−

gP lP2r γ α

( )αγ cos2r

PP lg =−

α = contact angle γ = surface tension Pg = gas pressure Pl = liquid pressure

Laplace’s law

force equilibrium:

capillary pressure (pc [Pa]) 16


• the saturated vapor pressure above a curved meniscus differs from the one above a flat one

lP lP lP

< < ∗

satvp ,

−−=∗

TRPP

ppvl

lgsatvsatv ρ

exp,,this is described by Thompson’s law:

17


• at which RH does condensation start in a pore?

( )

−=

TrRvlcond ρ

αγϕ cos2exp

−−=

TRPP

vl

lgcond ρ

ϕ exp

satv

v

pp

,

=ϕsatv

satv

satv

v

pp

pp

,

,

,

∗

∗=satv

satvcond

pp

pp

satvv

,

,,

∗= = →

∗

ϕ

using Thompson’s law

using Laplace’s law

18


19

( )

−=

TrRvlcond ρ

αγϕ cos2exp


4.0E-09 m


• capillary condensation – starts in the small pores – occurs in large pores only at very high RH

• consequences – a material with many small pores will take up

moisture at low RH → hygroscopic materials – a material with only large pores will only take up

water at high RH → non-hygroscopic materials

20

00.20.40.60.8

1

0 0.2 0.4 0.6 0.8 1degr

ee o

f moi

stur

e sa

tura

tion

[-]


hygroscopic curve & pore size

• the pore-system determines the hyg. curve

mortar = hygroscopic => must have fine pores

BRICK MORTAR

brick = non-hygroscopic => must have large pores

21

hygroscopic curve & pore size

0

0.5

1

1.5

2

1.E-10 1.E-09 1.E-08 1.E-07 1.E-06 1.E-05 1.E-04 1.E-03

cont

ribut

ion

to S

mpe

r po

re si

ze [l

og-1

(Pa)

]

pore radius [m]

BRICK MORTAR

00.20.40.60.8

1

0 0.2 0.4 0.6 0.8 1degr

ee o

f moi

stur

e sa

tura

tion

[-]


BRICK MORTAR

22

relevance to practice

• hygroscopic curve describes the «moisture buffering capacity» of a material

• hygroscopic materials can contribute to stabilize RH in the indoor climate – adsorb moisture when RH in environment is high – release moisture when RH in environment is low

23

00.20.40.60.8

1

0 0.2 0.4 0.6 0.8 1degr

ee o

f moi

stur

e sa

tura

tion

[-]


Question

• What is the impact of moisture (condensed water) on the thermal conductivity of insulation?

24

liquid transport

• the pore-system determines the permeability

1E-20

1E-18

1E-16

1E-14

1E-12

1E-10

1E-08

1.E-10 1.E-08 1.E-06 1.E-04

liqui

d pe

rmea

bilit

y [lo

g(s)

]

pore radius [m]

25

liquid transport

• there are 3 possible transport mechanisms – due to capillarity

– due to gravity

– due to (external) pressure

26

transport due to capillarity

• imagine a tube with radius r, in contact with a water surface

2r

α gP

( ) ( )( )rghrl παγπρ 2cos2 =

h γ

gravity surface tension

( )gr

hlρ

αγ cos2=

27


• EXAMPLE: how much is the capillary rise of water in a tube with radius 0.001 m? (α=0°, ρl=1000 kg/m3, g=9.81 m/s2, γ=0.0725 J/m2)

( )gr

hlρ

αγ cos2=

( ) m 0148.0001.081.91000

0cos0725.02=

⋅⋅⋅⋅

=

© www.funsci.com 28


• EXAMPLE: how much is the capillary rise of water in a tube with radius 0.00001 m? (α=0°, ρl=1000 kg/m3, g=9.81 m/s2, γ=0.0725 J/m2)

( )gr

hlρ

αγ cos2=

© www.funsci.com 29


• capillary rise is most pronounced in materials with fine pores, such as many cementitious materials

© Ilan Kelman 2000

30


• possible problems – «bubbles» in paint – detachment of

plaster/render – decrease of material

strength – …

© Ilan Kelman 2000

31


• solution: install/foresee a moisture barrier (aka DPC – damp proofing course)

inside outside

ground basement/ground

32


• solution: install/foresee a moisture barrier

33 www.wbdg.org


new constructions

existing buildings

© abacus

quality control is an issue! © DELTA®

34


• capillarity works in all directions! – in vertical direction, it is countbalanced by gravity – in horizontal direction, … not

-20

-15

-10

-5

brick

mortar

Sm = 1 Sm = 0

log(

perm

eabi

lity)

[log

(s)]

for short-term exposure, mortar can act as barrier 35


• nowadays facades are designed as rain barrier

(1) run-off

(2) absorption in brick

(1) (2)

(3) drainage in cavity

(3) 36


• nowadays facades are designed as rain barrier

37 www.wbdg.org

liquid transport


– due to gravity


38

transport due to gravity

• in wide pores, gravitational forces dominate over capillary forces and cause flow

capillary forces

keep water island

in place

water island moves due to gravity

39


• possible problems – «bubbles» in paint – detachment of

plaster/render – decrease of material

strength – soiling – …

40


• solution

41 www.wbdg.org


• solution: – foresee a moisture barrier on horizontal surfaces – design architectural details carefully

outside

inside

42


without drip-moulding

with drip-moulding

± 1 year after construction ± 15 years after construction 43


44 www.wbdg.org


• windowsills: foresee sufficient overhang…

45


• windowsills: foresee a tiny «side-wing»…

46


• Other details

47 www.wbdg.org


• Other details

48 www.wbdg.org


• Other details

49 www.wbdg.org

liquid transport


– due to gravity


50

transport due to pressure

• the pressure at a point depends on the height of the water column above

• therefore, the water level in two connected water columns is always equal

ghPP lgl ρ+=

h

51


• solution: a water-thight barrier – at the outside: the only good solution – at the inside: only a cosmetic solution – most

likely the problems will get worse

© brehmann.de

53


• rain penetration through facade cladding

- one layer is simultaneously wind and rain barrier

- if the joint sealant degrades the pressure difference across the wall will cause leakage

−aP+

aP

56


• solution: employing a two-step system

(1) water thightness (rain)

(2) pressure equalization

(3) air thightness (wind)

(1) (2) (3)

+aP −

aP+aP

57


58 www.wbdg.org

summary transport

• capillary suction is connected to the pore width and is mainly active in small pores

• gravity is important in pores that show limited capillary suction, i.e. large pores

• air as well as water induced pressure differences are mainly important for sealants, material interfaces and fractures

59

Chapter 7 TRANSPORT OF LIQUID WATER · behaviour • liquid water behaves in good approximation as...

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