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TPM
L P l H k H i i k D id S ld
Transport in porous media3MT130
Leo Pel, Henk Huinink, David Smeulders, Bart Erich, Hans van Duijn
Faculty of Applied Physics Mechanical Engineering
Eindhoven University of TechnologyThe Netherlands
Transport in Permeable Media
p
5 ECTS 2016
Examination : Oral
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Course + Lectures notes+ additional info
www.phys.tue.nl/nfcmr/college/college.html
Examination : oral
2 days (to be determined)
Transport in Permeable Media
2
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Surface tensions
Transport in Permeable Media
Curved surface
Pressure difference
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Single pore/capillary
Capillary pressure
wnwwnc rpppp 2
rgh
2
max
p y p
Transport in Permeable Media
rg
3
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Transport in Permeable Media
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Can surface tension really bring water from the roots up to the top?
Xylem~30μm, γ= 73 dyne/cmy μ , γ y /
Transport in Permeable Media
Sequoia ~ 100 m tall
4
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Bundle of various capillaries
Transport in Permeable Media
Look at various heights
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hA
hBhC
hD
h2 : Steighöhe in Porenklasse 2
hA hB hChD
Porenklasse i=2Hx height above free water level
Transport in Permeable Media
5
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Soil
Capillarypressure
Capillary pressure
P
• We describe the soil as a bundle of capillary tubes of
High
Moderate
rp wn
c
cos2
Transport in Permeable Media
p yvarious sizes
Low
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= 0 > 0 = n
hAhB hC
hD
Porenklasse i=2
Pc = highPc = averagePc = 0
Transport in Permeable Media
)(cc pp
Macroscopic capillary pressure
function moisture content
6
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Decreasing
Pressure
Transport in Permeable Media
TPM
)(pp
Capillary pressure (Pa)
)(cc pp
General convention (Hydrology)
Suction (m)
)(
Transport in Permeable Media
g
pc )(
(practical use in soil)
7
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Temperature dependence
pc )(
g
0-60 oC
~15%
Transport in Permeable Media
~2%
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Transport in Permeable Media
8
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Transport in Permeable Media
Local curvature ~ local capillary pressure
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Porous material : macro coefficient
wwnc pppp
Macro coef => volume averages
Transport in Permeable Media
REV
9
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on, e
tcS
uct
ion
Pot
enti
al, h
, ten
sio
Transport in Permeable Media
Water content
TPMDifferent regions
on,
etc Dry
Suc
tion
oten
tial,
h, te
nsio
Middle
Transport in Permeable Media
Water content
P
Wet
10
TPMWet region
hPore only drains if:
Big enough
Not isolated g hr
w
cos2
h
Wet
Air can get to it
Transport in Permeable Media
Air entryAir accessStructural pores
TPMA model porous medium being drained
Drainage allowed:
Poreradius:
Bigg
Transport in Permeable Media
Small
11
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Poreradius:
Big
Drainage allowed:
A model porous medium being drained
g
Transport in Permeable Media
Small
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Poreradius:
Big
Drainage allowed:
A model porous medium being drained
g
Transport in Permeable Media
Small
12
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Poreradius:
Big
Drainage allowed:
A model porous medium being drained
g
Transport in Permeable Media
Small
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Poreradius:
Big
Drainage allowed:
A model porous medium being drained
g
Transport in Permeable Media
Small
14
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Hysteresis in capillary pressure
Transport in Permeable Media
TPMTry yourself
Transport in Permeable Media
15
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MIP: Mercury Intrusion Porosimetry
Revisted
Mercury =140o, =500 10-3 Nm-1
Transport in Permeable Media
BE AWARE INK BOTTLE EFFECT(overestimation) Overestimation of
small pores
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Typical intrusion experiment
ativ
e In
tru
sio
n –
mL
/g
Transport in Permeable Media
Cu
mu
la
Diameter – micrometers
Extrusion
Intrusion
16
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Many ‘small’
hysteresis
Transport in Permeable Media
Have to know the complete history
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Transport in Permeable Media
17
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Transport in Permeable Media
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Vertical Zones of Subsurface Water
• Soil water zone: extends from the ground surface down through the g gmajor root zone, varies with soil type and vegetation but is usually a few feet in thickness
• Vadose zone (unsaturated zone): extends from the surface to the water table through the root zone, intermediate zone, and the capillary zone
Transport in Permeable Media
• Capillary zone: extends from the water table up to the limit of capillary rise, which varies inversely with the pore size of the soil and directly with the surface tension
18
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Moisture Storage Functionz What force is affecting on the
water inside the porous media?
Air pressure
pAir pressure
z What pressure is needed to force water out of a material?
Transport in Permeable Media
TPM
Moisture Storage Functionz What force is affecting on the
water inside the porous media?
0.1 bar
p
z What pressure is needed to force water out of a material?
Air pressure
Transport in Permeable Media 36
19
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Moisture Storage Function
z Capillary force is acting on the water inside the porous media?
0.5 bar
p
z What pressure is needed to remove water from a material?
Air pressure
Transport in Permeable Media
TPM
Moisture Storage Function5 bar
z Capillary force is acting on the water inside the porous media?
Air pressurep
z What pressure is needed to remove water from a material?
Transport in Permeable Media
20
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Moisture Storage Function50 bar
z Capillary force is acting on the water inside the porous media?
Pressure must be higher than the capillary pressure!
Air pressurep
z What pressure is needed to remove water from a material?
Transport in Permeable Media
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Transport in Permeable Media
21
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Membrane method (hard materials)
P )(cc pp
sample
semi-permeable membrane
Transport in Permeable Media
water drainage/wetting
Slow measurement (order weeks)
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Measurement technique: pressure plate apparatus
up to 100 bar Pressure
Transport in Permeable Media
22
TPMEmpirical & phenomenological equations
Brooks & Corey:
og hh
for 1
h
hh b
r
s at saturationr at 1.5 MPa
(“residual”)
log
lo
log
h
otherwise
h
hbrs
hb
Transport in Permeable Media
( residual )
hb bubbling pressure
fitting (“pore size distribution index”)
hb: Lowest pressure at which air can flow through the soil
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m
r
1
van Genuchten:
Empirical & phenomenological equations
nrs h
1
s at saturationr at 1.5 MPa
1/h
sr
h
Transport in Permeable Media
1/hb
n, m fitting. Often, m ≡ 1-(1/n) hb
h
23
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Transport in Permeable Media
TPM
Tensiometer for Measuring Soil Water PotentialTensiometer for Measuring Soil Water PotentialWater ReservoirWater Reservoir
Variable Tube Length (12 in- 48 in) Based on Root Zone Depth
Transport in Permeable Media
Porous Ceramic Tip
Vacuum Gauge (0Vacuum Gauge (0--100 centibar)100 centibar)
24
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Water distribution???
Transport in Permeable Media
Interface : capillary pressure continuous
suction continuous
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Θ =0.1 Θ =0.1
Material A Material B
Transport in Permeable Media
WHAT HAPPENS IF WE BRING THEM IN CONTACT ???????
27
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Θ =0.25 Θ =0.05
Transport in Permeable Media
capillary pressure is constant
=
jump in moisture content
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Towards poultice
airflow airflow
coarse
fine
fine
coarse
Transport in Permeable Media
WHAT WILL BE DRYING BEHAVIOUR ????
29
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Over boundary capillary pressure constant
)()( ll )()( rrll
)()( 11rrllll
)(1rrll
Transport in Permeable Media
)( rl f JUMP in moisture content
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Transport in Permeable Media
30
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Beach Large and small sand particles
Fine sand
Sandpres
sure
Transport in Permeable Media
Sand
Moisture content
Ca
pill
ary
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Water distribution???
Transport in Permeable Media
Interface : capillary pressure continous
suction continous
31
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Problem: different capillary pressures
Transport in Permeable Media
TPM
Phase changeswaterwater
• Sublimination• Condensation –
Evaporation• Freezing -
Transport in Permeable Media
Melting
32
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Evaporating Water into Air
Liquid water experiences dynamic departures of water
l l f i f ll d molecules from its surface, called evaporation, together with arrivals of molecules from adjacent vapor, called condensation.
When air is saturated, evaporation and condensation are in equilibrium
Transport in Permeable Media
are in equilibrium.
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Transport in Permeable Media
The partial pressure of water vapor, i.e., that portion of total atmospheric pressure that is due to the presence of H2Ov
33
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Relative humidity (RH)= partial water pressure
maximum water pressure
Transport in Permeable Media
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Relative humidity (RH)= partial water pressure
maximum water pressuremaximum water pressure
maxmaxmax
p
TR
TR
p
p
p
Transport in Permeable Media
Relative humidity (RH)= actual water vapour content
maximum water vapour content
34
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Daily Humidity Patterns
Transport in Permeable MediaFigure 7.10
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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
P=611exp[0.0829 T-0.2881 10-3 T2+4.403 10-6T3
35
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Chilled Mirror Dew Point
Mirror is chilled until dew is formed. Optical
The temperature at which saturation is achieved is determined by observing condensation on a chilled surface (mirror).
Mirror
Optical Sensor
Advantages Disadvantages
Cooler
Transport in Permeable Media
Advantages• Very high accuracy• High reliability
Disadvantages• Need clean mirror• Expensive
TPM
Flat -roof
5 oCWater+
vapour barrier
20 oCwood
gypsum board
Transport in Permeable Media
70’s energy crisis -> isolation
roofs started to collapse after few years >why??
20 oC
36
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Transport in Permeable Media Pictures by Henk Schellen
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Flat -roof
5 oCWater+
vapour barrier
wood
gypsum board
Transport in Permeable Media
20 oC, 60 %
37
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Flat -roof
5oC
Water+
vapour barrier
wood
Transport in Permeable Media
20 oC, 60 %
gypsum board
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20oC > max 2337 Pa
60% = 1402 Pa
Cool down 5oC
1402 Pa > 12oC
Transport in Permeable Media
CONDENSATION!!!
38
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Flat -roof
5oC
Water+
vapour barriercondensation
wood
120C max
Transport in Permeable Media
20 oC, 60 %
gypsum board
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Condensation
- isolation
- bathroom fungi growth
- musea (wall paintings)
- wood
Transport in Permeable Media
39
TPM
Capillary condensationIf 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!!!
Transport in Permeable Media
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
Kelvin equation
Negative pressure
Capillary pressure
Capillary
r
RTrp
ph l
vs
v
2
exp
Negative pressure
Transport in Permeable Media
p<0
h = relative humidity (0-100%)
See proof dictaat
40
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William Thomson, 1st Baron Kelvin of Largs (1824–1907)
Born26 June 1824(1824-06-26)Belfast
Died17 December 1907 (aged 83)[1]
Largs
ResidenceCambridge,Glasgow,Residence Glasgow,Belfast
Nationality British
Institutions University of Glasgow
Known for Joule–Thomson effectThomson effect (thermoelectric)Mirror galvanometerSiphon recorderKelvin materialKelvin water dropperKelvin waveKelvin–Helmholtz instabilityKelvin–Helmholtz mechanismKelvin–Helmholtz luminosity
Transport in Permeable Media
yKelvin transformKelvin's circulation theoremKelvin bridgeKelvin sensingKelvin equationMagnetoresistanceFour-terminal sensingCoining the term 'kinetic energy'
TPM
Transport in Permeable Media
41
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Transport in Permeable Media
0.001 m ~30%water
100 %
0.01 m90%
0.001 m30%
TPM
Condensation
• Dehumidifiers• Dehumidifiers
Transport in Permeable Media
42
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Transport in Permeable Media
TPM
• Warning against humidity (electronics)
Moist
Transport in Permeable Media
Silica impregnated with CoCl2
43
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Raindrop
positive pressure
rRTh
lv
v 2exp
0,
r
> 1
Transport in Permeable Media
It is very difficult to form clouds with pure water vapor (nucleation problem)
TPM
Applying Kelvin equation Drop in its vapor. The vapor pressure of a drop is higher than that of
a liquid with a planar surface. One consequence is that an aerosol of drops (fog) should be unstabledrops (fog) should be unstable
To see this let us assume that we have a box filled with many drops in a gaseous environment, some drops are larger than others
The small drops have higher vapor pressure than the large drops, hence more liquid evaporates from their surface
This tends to condense into larger drops Within a population a drops of different sizes, the bigger drops will
grow at the expense of the smaller one, these drops will sink down
Transport in Permeable Media
and at the end bulk liquid fills the bottom of the box
44
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Bubble in a liquid For a bubble, negative sign has to be used because of
the negative curvature of the liquid surfaceK
Here r is the radius of the bubble The vapor pressure inside a bubble is therefore reduced When liquids heated above the boiling point accasionally
tiny bubbles are formedI id th b bbl th i d d th
r
V
P
PRT m
K 2ln.
0
0
Transport in Permeable Media
Inside the bubble the vapor pressure is reduced, the vapor condenses and the bubble collapses
Only if a bubble larger than a certain critical size is formed, is it more likely to increase in size rather than to collapse
TPM
Porous mediawetting propeties
r
vapor0
cos2
r
Hydrophilic surfaces
r
vapor0cos2
r
Hydrophobic surfaces
Transport in Permeable Media
1
0,
v
v
liquid
liquid10,
v
v
45
TPM
R
p wnc
2
RT
ph wnv 2
exp
capillary
p<0
rpc
RTrpvs
coupled
Porous mediamacro
Transport in Permeable Media
g
pc )(
RT
Mg
p
ph
vs
v exp
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Relative
Humidity
Transport in Permeable Media
46
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Hygroscopic curve
Hysteresis
Transport in Permeable Media
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Transport in Permeable Media
Very,very slow (6 months) + temperature
47
TPMDynamic Vapour sorption
Transport in Permeable Media
TPM
Relation capillary pressure <-> RHPressure pore relative humidity
bar %
0 1000 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 vapour
liquid
Transport in Permeable Media
500 3 nm 70
1000 1.5 nm 48
5000 0.3 nm 2.6
So never in one measurement
vapour
48
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Pore size classification
Micropores r<1 nm p/po < 0.1 >1000 bar
Mesopores 1 < r < 25 nm
Transport in Permeable Media
Macro pores r>25 nm p/po >0.96 <15 bar
IN SMALL PORES (first filled)
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
49
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Autogenous Shrinkage50
OPC1, w/c = 0.40SCC1 w/c = 0 39
-150
-100
-50
0ut
ogen
ous
Shr
inka
ge (
10-6
m/m
)SCC1, w/c = 0.39SCC2, w/c = 0.33SCC3, w/c = 0.41SCC4, w/c = 0.32HPC1, w/c = 0.25SCC2-2SCC2-slag
Transport in Permeable Media
-250
-200
0 20 40 60 80 100
Age (d)
Au
TPMAutogenous shrinkage: why only low w/c?
0.50 0.50 w/cw/c
“Extra” water remains in small pores even at =1
0.50 0.50 w/cw/c
“Extra” water remains in small pores even at =1
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
Autogenous Autogenous shrinkageshrinkage
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
Autogenous Autogenous shrinkageshrinkage
Transport in Permeable Media
Pores to 50 nm emptied
Internal RH and pore fluid pressure reduced as smaller
pores are emptiedIncreasing degree of hydration
Pores to 50 nm emptied
Internal RH and pore fluid pressure reduced as smaller
pores are emptiedIncreasing degree of hydration
HPC : concrete made with low moisture content
50
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Mechanism of shrinkage
• Both autogenous and drying g y gshrinkage dominated by capillary surface tension mechanism
• As water leaves pore system, curved menisci develop, creating reduction in RH and
Hydration product
Hydration product
Transport in Permeable Media
gunderpressure within the pore fluid
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Visualize scale of mechanismCapillary stresses present in pores with radius between 2-50 nm
Note the dimensions
Transport in Permeable Media
•C-S-H makes up ~70% of hydration product•Majority of capillary stresses likely present within C-S-H network
*Micrograph take from Taylor “Cement Chemistry” (originally taken by S. Diamond 1976)
51
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BE AWARE
LOW MOISTURE CONTENT
Transport in Permeable Media
REV
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100
Representative Elementary Volume (area) REV
20
30
40
50
60
70
80
90
n (
%)
Transport in Permeable Media
0
10
0 5 10 15 20 25 30
Sqrt Area Choice error
53
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Porous media
p )( Mg
hysteresis
Transport in Permeable Media
g
pc )( )(exp f
RT
Mgh
How/What to measure in porous material
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Question ?
Transport in Permeable Media
Liquid ‘fast’ Vapour ‘slow’