transport in porous media 3mt130

Transport in Permeable Media

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Transport in porous media3MT130

Cap II part B: capillary condensation


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Problem: different capillary pressures


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Phase changeswater

• Sublimination

• Condensation –Evaporation

• Freezing -Melting


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Relative humidity (RH)= partial water pressure

maximum water pressure


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Relative humidity (RH)= partial water pressure

maximum water pressure

maxmaxmax

===

p

TR

TR

p

p

p

Relative humidity (RH)= actual water vapour content

maximum water vapour content


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Daily Humidity

Patterns


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P=611exp[0.0829 T-0.2881 10-3 T2+4.403 10-6T3

The temperature to which the air must be cooled (at constant pressure and without changing the moisture) for it to become saturated

Dew point temperature


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70’s energy crisis -> isolation

roofs started to collapse after few years >why??

Flat -roof

20 oC

5 oC

wood

Water+

vapour barrier

gypsum board

A


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Pictures by Henk Schellen


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Capillary condensation

If the vapour pressure of water within a porous eventually filling the pores. This process is known as capillary condensation.

For capillary condensation to occur, the water vapour pressure must exceed its saturation vapour pressure.

BUT: in porous materials the saturation vapour pressure varies!!!

This is due to the pressure drop across a curved liquid surface, and is described by the Kelvin equation


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Capillary

r

p<0

−==

RTrp

ph l

vs

v

2exp

h = relative humidity (0-100%)

Kelvin equation

Negative pressure

See proof book/dictaat

Capillary pressure


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0.001 m ~30%

water

100 %

0.01 m90%

0.001 m30%


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Condensation

• Dehumidifiers


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Porous mediawetting propeties

q

r

vapor

0cos2

−r

q

10,

v

v

Hydrophilic surfaces

liquid

q

r

vapor

liquid

0cos2

−r

q

10,

v

v

Hydrophobic surfaces


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R

p<0

rp wn

c

2=

−==

RTrp

ph wn

vs

v

2exp

coupled

capillary

Porous media

q

g

pc )(=

==

RT

Mg

p

ph

vs

v exp

macro

Kelvin in porous media


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Relative

Humidity


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Hygroscopic curve

Hysteresis


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Very,very slow (6 months) + temperature


TPMDynamic Vapour sorption (DVS)


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Relation capillary pressure <-> RH

Pressure pore relative humidity

bar %

0 100

0.1 15 m 99.993

1 1.5 m 99.93

15 100 nm 98.9

100 15 nm 93

500 3 nm 70

1000 1.5 nm 48

5000 0.3 nm 2.6

So never in one measurement

vapour

liquid


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Pore size classification

Micropores r<1 nm p/po < 0.1 >1000 bar

Mesopores 1 < r < 25 nm

Macro pores r>25 nm p/po >0.96 <15 bar

IN SMALL PORES (first filled)


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Drying cracks concreteespecially: high performance concrete (HPC)

• Early age pavement cracking is a persistent problem

– Runway at Willard Airport (7/21/98)

– Early cracking within 18 hrs and additional cracking at 3-8 days


TPMAutogenous shrinkage: why only low w/c?

0.50 0.50

w/cw/c

0.30 0.30

w/cw/c

Cement grains

initially separated by

water

Initial set locks in

paste structure

Chemical shrinkage

ensures some porosity

remains even at =

“Extra” water remains in

small pores even at =1

Pores to 50 nm

emptied

Internal RH and pore fluid

pressure reduced as smaller

pores are emptied

Autogenous Autogenous

shrinkageshrinkage

Increasing degree of hydration

0.50 0.50

w/cw/c

0.30 0.30

w/cw/c

Cement grains

initially separated by

water

Initial set locks in

paste structure

Chemical shrinkage

ensures some porosity

remains even at =

“Extra” water remains in

small pores even at =1

Pores to 50 nm

emptied

Internal RH and pore fluid

pressure reduced as smaller

pores are emptied

Autogenous Autogenous

shrinkageshrinkage

Increasing degree of hydration

HPC : concrete made with low moisture content


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Mechanism of shrinkage

• Both autogenous and drying shrinkage dominated by capillary surface tension mechanism

• As water leaves pore system, curved menisci develop, creating reduction in RH and underpressure within the pore fluid

Hydratio

productHydration

product


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BE AWARE

LOW MOISTURE CONTENT

REV


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0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20 25 30

Sqrt Area

n (

%)

Representative Elementary Volume (area) REV

Choice error


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Same moisture content


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Porous media

q

g

pc )(= )(exp q f

RT

Mgh =

=

q

hysteresis

How/What to measure in porous material??


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Membrane method (hard materials)

sample

P

semi- permeable membrane

water drainage/wetting

Slow measurement (order weeks)

)(qcc pp =

Combination liquid/vapour

transport in porous media 3mt130

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