course + lectures notes - applied physics · general convention (hydrology) ... mip: mercury...

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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

[email protected]

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)


2

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Surface tensions


Curved surface

Pressure difference

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Single pore/capillary

Capillary pressure

wnwwnc rpppp 2

rgh

2

max

p y p


rg

3

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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 /


Sequoia ~ 100 m tall

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Bundle of various capillaries


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


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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


p yvarious sizes

Low

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= 0 > 0 = n

hAhB hC

hD

Porenklasse i=2

Pc = highPc = averagePc = 0


)(cc pp

Macroscopic capillary pressure

function moisture content

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Decreasing

Pressure


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)(pp

Capillary pressure (Pa)

)(cc pp

General convention (Hydrology)

Suction (m)

)(


g

pc )(

(practical use in soil)

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Temperature dependence

pc )(

g

0-60 oC

~15%


~2%

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Local curvature ~ local capillary pressure

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Porous material : macro coefficient

wwnc pppp

Macro coef => volume averages


REV

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on, e

tcS

uct

ion

Pot

enti

al, h

, ten

sio


Water content

TPMDifferent regions

on,

etc Dry

Suc

tion

oten

tial,

h, te

nsio

Middle


Water content

P

Wet

10

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hPore only drains if:

Big enough

Not isolated g hr

w

cos2

h

Wet

Air can get to it


Air entryAir accessStructural pores

TPMA model porous medium being drained

Drainage allowed:

Poreradius:

Bigg


Small

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Poreradius:

Big

Drainage allowed:

A model porous medium being drained

g


Small

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Poreradius:

Big

Drainage allowed:


g


Small

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Poreradius:

Big

Drainage allowed:


g


Small

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Poreradius:

Big

Drainage allowed:


g


Small

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Pc


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hysteresis


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Hysteresis in capillary pressure


TPMTry yourself


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MIP: Mercury Intrusion Porosimetry

Revisted

Mercury =140o, =500 10-3 Nm-1


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


Cu

mu

la

Diameter – micrometers

Extrusion

Intrusion

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Many ‘small’

hysteresis


Have to know the complete history

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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


• 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

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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?


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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

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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


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Moisture Storage Function5 bar


Air pressurep



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Moisture Storage Function50 bar


Pressure must be higher than the capillary pressure!

Air pressurep



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Membrane method (hard materials)

P )(cc pp

sample

semi-permeable membrane


water drainage/wetting

Slow measurement (order weeks)

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Measurement technique: pressure plate apparatus

up to 100 bar Pressure


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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


( 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


1/hb

n, m fitting. Often, m ≡ 1-(1/n) hb

h

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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


Porous Ceramic Tip

Vacuum Gauge (0Vacuum Gauge (0--100 centibar)100 centibar)

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Water distribution???


Interface : capillary pressure continuous

suction continuous

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Θ =0.1 Θ =0.1

Material A Material B


WHAT HAPPENS IF WE BRING THEM IN CONTACT ???????

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Θ =0.1 Θ =0.1


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Θ =0.1 Θ =0.1


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Θ =0.15 Θ =0.08


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Θ =0.2 Θ =0.2


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Θ =0.25 Θ =0.05


capillary pressure is constant

=

jump in moisture content

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Towards poultice

airflow airflow

coarse

fine

fine

coarse


WHAT WILL BE DRYING BEHAVIOUR ????

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Over boundary capillary pressure constant

)()( ll )()( rrll

)()( 11rrllll

)(1rrll


)( rl f JUMP in moisture content

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Beach Large and small sand particles

Fine sand

Sandpres

sure


Sand

Moisture content

Ca

pill

ary

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Water distribution???


Interface : capillary pressure continous

suction continous

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Problem: different capillary pressures


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Phase changeswaterwater

• Sublimination• Condensation –

Evaporation• Freezing -


Melting

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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


are in equilibrium.

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The partial pressure of water vapor, i.e., that portion of total atmospheric pressure that is due to the presence of H2Ov

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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 pressuremaximum 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

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


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

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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


Advantages• Very high accuracy• High reliability

Disadvantages• Need clean mirror• Expensive

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Flat -roof

5 oCWater+

vapour barrier

20 oCwood

gypsum board


70’s energy crisis -> isolation

roofs started to collapse after few years >why??

20 oC

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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


20 oC, 60 %

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Flat -roof

5oC

Water+

vapour barrier

wood


20 oC, 60 %

gypsum board

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20oC > max 2337 Pa

60% = 1402 Pa

Cool down 5oC

1402 Pa > 12oC


CONDENSATION!!!

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Flat -roof

5oC

Water+

vapour barriercondensation

wood

120C max


20 oC, 60 %

gypsum board

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Condensation

- isolation

- bathroom fungi growth

- musea (wall paintings)

- wood


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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!!!


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


p<0

h = relative humidity (0-100%)

See proof dictaat

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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


yKelvin transformKelvin's circulation theoremKelvin bridgeKelvin sensingKelvin equationMagnetoresistanceFour-terminal sensingCoining the term 'kinetic energy'

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0.001 m ~30%water

100 %

0.01 m90%

0.001 m30%

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Condensation

• Dehumidifiers• Dehumidifiers


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• Warning against humidity (electronics)

Moist


Silica impregnated with CoCl2

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Raindrop

positive pressure

rRTh

lv

v 2exp

0,

r

> 1


It is very difficult to form clouds with pure water vapor (nucleation problem)

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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


and at the end bulk liquid fills the bottom of the box

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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


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

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Porous mediawetting propeties

r

vapor0

cos2

r

Hydrophilic surfaces

r

vapor0cos2

r

Hydrophobic surfaces


1

0,

v

v

liquid

liquid10,

v

v

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R

p wnc

2

RT

ph wnv 2

exp

capillary

p<0

rpc

RTrpvs

coupled

Porous mediamacro


g

pc )(

RT

Mg

p

ph

vs

v exp

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Relative

Humidity


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Hygroscopic curve

Hysteresis


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Very,very slow (6 months) + temperature

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TPMDynamic Vapour sorption


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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


500 3 nm 70

1000 1.5 nm 48

5000 0.3 nm 2.6

So never in one measurement

vapour

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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


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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


-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


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

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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


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


•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)

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BE AWARE

LOW MOISTURE CONTENT


REV

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100

Representative Elementary Volume (area) REV

20

30

40

50

60

70

80

90

n (

%)


0

10

0 5 10 15 20 25 30

Sqrt Area Choice error

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Same moisture content


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RH


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Porous media

p )( Mg

hysteresis


g

pc )( )(exp f

RT

Mgh

How/What to measure in porous material

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Question ?


Liquid ‘fast’ Vapour ‘slow’

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Membrane method (hard materials)

P )(cc pp

sample

semi-permeable membrane


water drainage/wetting

Slow measurement (order weeks)

Comination liquid/vapour

course + lectures notes - applied physics · general convention (hydrology) ... mip: mercury...

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