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Transport in Permeable Media
TPM
Transport in porous media3MT130
Cap II part B: capillary condensation
Transport in Permeable Media
TPM
Phase changeswater
• Sublimination
• Condensation –Evaporation
• Freezing -Melting
Transport in Permeable Media
TPM
Relative humidity (RH)= partial water pressure
maximum water pressure
Transport in Permeable Media
TPM
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
Transport in Permeable Media
TPM
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
Transport in Permeable Media
TPM
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
Transport in Permeable Media
TPM
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
Transport in Permeable Media
TPM
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
Transport in Permeable Media
TPM
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
Transport in Permeable Media
TPM
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
Transport in Permeable Media
TPM
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
Transport in Permeable Media
TPM
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)
Transport in Permeable Media
TPM
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
Transport in Permeable Media
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
Transport in Permeable Media
TPM
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
Transport in Permeable Media
TPM
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
Transport in Permeable Media
TPM
Porous media
q
g
pc )(= )(exp q f
RT
Mgh =
=
q
hysteresis
How/What to measure in porous material??