course + lectures notesporousmedia.nl/nfcmr/college/college-week2a-2016.pdf · tu19‐4‐2016...

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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)


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Week 1tu 19‐4‐2016 13:45 15:30 Leo Introduction + REVth 21‐4‐2016 08:45 10:30 NO lectureWeek 2 tu 26‐4‐2016 13:45 15:30 Leo Capillary forces Ith 30‐4‐2016 08:45 10:30 Leo Capillary forces IIWeek 3Week 3 tu 3‐5‐2016 13:45 15:30 Leo Darcy’s law (sat + unsat)th 5‐5‐2016 08:45 10:30 PUBLIC HOLIDAYAfter week 3: all basicsWeek 4tu 10‐5‐2016 13:45 15:30 David: Dupuit + akoestiekth 12‐5‐2016 08:45 10:30 Leo: component transportWeek 5 tu 17‐5‐2016 13:45 15:30 Henk: Multiphase flow (oil/water)th 19‐5‐2016 08:45 10:30 Bart: NMR porous media


Week 6 tu 24‐5‐2016 13:45 15:30 Hans: density driven flow or hysteresisth 28‐5‐2016 08:45 10:30 Leo: fire spallingWeek 7 tu 31‐5‐2016 13:45 15:30 Henk: Phase change in porous mediath 2‐6‐2016 08:45 10:30 ? een reserve datum

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Silicate brick (Light weight)

Speed

60% fast / 40% slow

Height

Cellular concrete

2xSilicate brick

3xFired clay brick

Fast

Middle

Slow

Lowest


Stone Sicilia

Concrete

Slow

Fast

Highest small pores

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PorosityPorosity TransportTransportPermeabilityPermeability

BE AWARE


Ability to hold water Ability to transmit water

Size, Shape, Interconnectedness

PorosityPorosity PermeabilityPermeability

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How is the moisture distributed??


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WHY ?

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SURFACETENSION


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What’s going onat the surfaceof a liquid?of a liquid?


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What’s going onat the surfaceof a liquid?of a liquid?

Let’s takea look!


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Particles that make up a liquid are in constant random motion; they are randomly arranged.


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You might expect the particles at the surface,at the micro level, to form a random surface,as shown below.


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You might expect the particles at the surface,at the micro level, to form a random surface,as shown below.


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= intermolecularattractionsCOHESION

But how do intermolecular forcesinfluence the surface?


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Under the surface, intermolecular attractions pull onindividual molecules in all directions



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At the surface, pull on the molecules is laterally and downward;there is negligible intermolecular attractions above the molecules (from the medium above, such as air).SO, the net force on surface molecules is downward.


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The result of this downward force is thatsurface particles are pulled down untilcounter-balanced by the compressionresistance of the liquid:


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Surface molecules are compressedmore tightly together, forming a sort of skin on the surface, with less distance between themcompared to the molecules below=surface skincompared to the molecules below=surface skin


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Surface molecules also form a much smoother surface than one would expect from randomlymoving molecules.


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This explains the characteristic rounded shape that liquids form when dropping through the air: The molecules are all being pulled toward the center.


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This explains the characteristic rounded shape that liquids form when dropping through the air: The molecules are all being pulled toward the center.


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The overall result of this asymmetric force on surface molecules is that:

• The surface of the liquid will rearrange until the least number of molecules are present on the surface

In other words the surface area will be minimized– In other words the surface area will be minimized – A sphere has the smallest surface area to volume

ratio • The surface molecules will pack somewhat closer

together than the rest of the molecules in the liquid – The surface molecules will be somewhat more

ordered and resistant to molecular disruptions Th th f ill t h " ki "


– Thus, the surface will seem to have a "skin" • The "inward" molecular attraction forces, which must be

overcome to increase the surface area, are termed the "surface tension"

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Surface tension = N/m

Surface tension is the intensity of the molecular attraction per unit length along any line in the surface

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Zero gravity


http://spaceflightsystems.grc.nasa.gov/WaterBalloon/

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Surface Tension


Emperor penguin huddle, Antarctica© Doug Allan/Naturepl.com

http://www.arkive.org/education/

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Thomas Young

In 1804: founded the theory of capillary phenomena on the principle ofs urface tension.

He also observed the constancy of the angle of contact of a liquid surface with a solid, and showed how to deduce from these two principles the phenomena of capillary action.

The Young–Laplace equation is the

Thomas Young

13 June 1773


The Young Laplace equation is the formula for capillary action independently discovered by Laplace in 1805.

Young was the first to define the term "energy" in the modern sense.

Born13 June 1773England

Died 10 May 1829 (aged 55)

FieldsPhysics, Physiology, Egyptology

Religion Quaker

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Formation of a SurfaceFormation of a Surface


Separation of liquid to create a new surface requireswork to overcome cohesion forces

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Surface Energy of Liquids

The work (w) required to create a new surface is proportional to the # molecules at the surface, and hence the area (A):

Where :

is the proportionality constant defined as the specific surface free

Aw


energy. It has units of (energy/unit area, J/m2).

acts as a restoring force to resist any increase in area, for liquids it is numerically equal to the surface tension.

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Units of measurement

Surface Tension Surface Energy

(force/unit length) (energy/unit area)

(N/m) (J/m2)

1 Joule = 1 Nm(Nm/m2)


(N/m)

• For Liquid/Liquid Interface, usually termed Interfacial Tension

• For Gas/Liquid interface usually termed Surface Tension

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F2


l

F2

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DEMO

Transport in Permeable Media movie

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Release of a Liquid drop from a capillary

Surface Tension MeasurementSurface Tension Measurement-- Drop--


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Drop-weight Method • Here the liquid is allowed to flow out from the

bottom of a capillary tube.p y• Drops are formed which detach when they reach

a critical dimension, the weight of a drop falling out of a capillary is measured

• As long as the drop is still hanging at the end of the capillary, its weight is more than balanced by the surface tension

• A drop falls off when the gravitational force mg


• A drop falls off when the gravitational force mg determined by the mass of the drop is no longer balanced by the surface tension

mg = 2rc

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TPMSurface Tension MeasurementSurface Tension Measurement-- Wilhelmy Plate --

l2

)bwt(wt)cos( platetotal

= surface tension wtplate = plate weight


= contact angle

wttotal = total weight

p

b = buoyancy force

l = width of plate

• Normally platinum is used to have q 0 and plate just touches liquid so buoyancy is small

TPMSurface Tension MeasurementSurface Tension Measurement-- Ring--


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Wtot = Wring + 4R F

2R

where Wring is the weight of the ring, R is the radius of the ring, and g the surface tension.

• Still commonly used but values may be as much as 25%


• However, the shape of the liquid supported by the ring is complex and the direction of tension forces are non-vertical. The correction factor should be introduced.

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The surface or interfacial tension

R

F

4

r

F

2R

R4

Where is the correction factor, calculated from the equation of Zuidema and Waters

cR

F

R

ba

2122

2

4

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Oil

water

(Liquid-Vapor) (Liquid-Water)

water

oil


Where 1 and 2 are the densities

of the lower and upper phases;

a=0.725, b=0.09075m-1s2; c=0.04534-1.679r/R

The first column shows the surface tensionBetween a liquid and its own vapor

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Surface tension (10-3 Nm-1)

alcohol 23

benzene 29benzene 29

glycerol 62

kwik 500

milk 45

water 73


influence surfactants (soap)

(often dynes/cm dyne=10-5 N)

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Water high surface tension ???

asymmetrical molecule:

dipole moment


dipole moment

hydrogen bonding:

polar liquidWater is polar so there are intermolecular forces (dipole-dipole interaction and H bonding) that must be overcome

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Floating paperclip DEMO


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Water strider

mass


Mass: F=m 10

Surface tension F= 2 0.073 0.01

mass,max~ 0.15 gram=150 mgr (~10 mgr)

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Nature: all sizes


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The relation between the maximum curvature force Fs = P and body weight Fg = Mg for 342 species of water striders. P = 2(L1+L2+L3) is the combined lengths of the tarsal segments.

Hu, Chan & Bush (Nature, 424, 2003).

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42: above 38: feet slightly lower42: above 38: feet slightly lower

35: feet lower 33: feet broken through surface,head & body still dry


31: feet & body even lower 30: feet & body under water

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Surface tension ships DEMO


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Walking over water ?


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Pressure in droplet /soap bubble

droplet

rPP oi

2

Pi

Po

rrPP oi 2)( 2

bubble


bubble

rPP oi

4

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Balloons: what will happen?


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Pressure in balloon versus time

burst


Valid model system

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Pout

Pressure buble:

r

Pin

rP

4


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•The interfacial tension between two fluids is a measure of how much energy is needed to enlarge the surface by one unit area. That is, the dimension is J/m2, or N/m.

•( intermolecular) attractions, the interfacial tension may have different "signs"different "signs".

– A "positive" interfacial tension ( > 0) means that the molecules of each fluid are most strongly attracted to the molecules of their own kind. Whereby the two fluids are immiscible, and their contact surface is minimized

– A ”neutral” interfacial tension ( = 0) means that the molecules of each fluid are attracted equally to the molecules of their own kind as to those of the other kind, and the two fluids are ”truly”miscible.


– A ”negative” surface tension ( < 0) means that the molecules of one fluid are more strongly attracted to the molecules of the other fluid. This kind of miscibility is called dissolution, wich usually means a chemical reaction between the two fluids, leading to a stable new fluid. Alcohol i water is an example of dissolution.

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• Porous material – porosity• Porous material – porosity• Surface tension• Contact angle


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Droplets on materials


• One fluid wets the surfaces of the formation rock (wetting phase) in preference to the other (non-wetting phase).

• Gas is always the non-wetting phase in both oil-gas and water-gas systems.

• Oil is often the non-wetting phase in water-oil systems.

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Cohesive and Adhesive ForcesWater on: Water is said to “wet” glass

Teflon GlassAdhesive attraction between water and teflon is low and the cohesive forces among the water molecules pull the water molecules into spheresAdh i tt ti b t t d l i hi h d


Adhesive attraction between water and glass is high and water is “pulled onto” the glass

TiO2-Silicone film before UV irradiation

TiO2-Silicone film after UV irradiation

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Liquid surface

border


equilibrium GSSLLG cosLG

SLGS

cos

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LG

SLGS

cos

Contact angle


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Contact angle: 0° 90° 180°

cos 1 0 -1

Spreading Complete wett. Partial wetting SL= SV Negligible wett. Non-wett.(a) (b)


(a) is the case of a liquid which wets a solid surface well, e.g. water on a very clean copper. Perfect wetting.(b) is the case of no wetting, contact angle =180o. This represents water on teflon or mercury on clean glass.

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Extremes


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The lotus effect(~150o)

Water droplet on lotus leaf,with adhering particles

Contaminating stain powderremoved by rinsing with water


The Lotus Effect is based on surface roughnesscaused by different microstructures togetherwith the hydrophobic properties of the epicuticularwax (~150o)

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Cassie–Baxter model


1coscos * ffr yf

Apparent contact angle

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A droplet on an inclined superhydrophobic surface does not slide off; it rolls off. When the droplet rolls over a contamination, the particle is removed from the surface if the force of absorption of


particle is removed from the surface if the force of absorption of the particle is higher than the static friction force between the particle and the surface. Usually the force needed to remove a particle is very low due to the minimized contact area between the particle and the surface. As a result, the droplet cleans the leaf by rolling off the surface.

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Oil

WATER-WET ROCK

• 0 < < 90

Solid

Water

Oil

os ws

ow

os


• Adhesive tension between water and the rock surface exceeds that between oil and the rock surface.

0 < < 90

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OIL-WET ROCK

Waterow

Solid

Oil

os ws

os

Reservoir rock is oil-wet if oil preferentially wets the k f


• 90 < < 180

• The adhesion tension between water and the rock surface is less than that between oil and the rock surface.

rock surfaces.

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Experimental setup for measuring contact angles


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Contact angle hysteresisYoung eq. predicts single value for intrinsic c. a. but

Range of stable apparent an be measured experimentally: => hysteresisi d i i i dimaximum - advancing minimum – receding

Advancing contact angle (θA < θR) is always larger than or equal to thereceding contact angle

Roughness

Ch i l t i ti

r

ahysteresis

raindrop


Chemical contaminationor heterogeneity of solid surface

Solutes in the liquid(surfactants, polymers)may deposit a film on solid surface

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Oil drop in water : lens


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Oil drop in water

Oil

WA OA

Air

13 Oil

WaterOW

•Force balance for both horizontal and vertical direction

1

2

3


213 coscoscos owoawa

owoawa lens

owoawa spreading

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TPMBenzene-Water system

Air

WaterOil

S = WA – (OW - OA)

S > 0 the oil spreads into a thin film (complete wetting)S < 0 lens with finite size (partial wetting)

Example: adding a drop of Benzene tothe surface of water

WA = 72.8 mN/mBA = 28.9 mN/m 35 0 N/

Sinit > 0 WA = 62 4 mN/mSfinal < 0


BW = 35.0 mN/m WA = 62,4 mN/m

TimeBenzene dissolves

in water

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• Porous material – porosity• Porous material – porosity• Surface tension• Contact angle• Capillary pressure +


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ds

Pressure ????

r1

dn


Small curved surface element

r2r2

r1r1

r2

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Forces: small curved surface element

dnds

r1r1


r2r2

r2

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Forces: small curved surface element

dndswnds wndn

r1r1

wndswndn


r2r2

r2

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Pressure difference

dndswnds wndn

pwdsdn

r1r1

wndswndn

pndsdn


r2r2

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dsd

pwdsdn

r1 r1

wndswnds pndsdn


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wnds

pwdsdn

½d ?

r1 r1

wndspndsdn

½dn ?


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wnds

pwdsdn12

1sin

r

dn

2

r1 r1

wndspndsdn

½dn F? wndsdnr

12

2

wndsdn

dsdn

rA

Fp

1

1

11


wntot rrp

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Capillary Pressure ?Water in a fine glass capillary tube

Water wets the surface of the glass, and is pulled upwards to form a curved surface or meniscussurface, or meniscus.

rP

2

Capillary tube

R

r


r

R=r1=r2=rNegative pressure : suction

DEMO

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EXAMPLE: Water in a fine glass capillary tube

Water wets the surface of the glass, and is pulled upwards to form a curved surface, or meniscus.

The pressure difference across the meniscus can be expressed as:The pressure difference across the meniscus can be expressed as:

and:

cos

ar

rP

2

r


therefore we get:

aP

cos2

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BetterCapillary tube

R

r


R=r1=r2=R/cos

rppp wn

wnc

cos2

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Rubber Membrane

• Rubber membrane at the end of cylindrical tube. An


yinner pressure Pi can be applied, which is different than the outside pressure Pa

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Capillary tubeR

r

Short cut

r

Work: dSdV

dSppp wnc )(


dVpp wn )( dV

sphere

rpc

2

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Because the pressure on the concave side is lower than that on the convex side (Pin < Pout), water rises within the capillary tube.

Fluid rises in the capillary until the pressure due to the weight of the column of fluid in the capillary is equal to the pressure difference across the meniscus:

Where:

ghPP watermeniscus


h = height of capillary riseg = force due to gravityρ = density of water

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isince:

we get:

ghr

Pmeniscus

2

2


Washburn equation

rgh

2

max

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Liquids in Contact with a Solid SurfaceLiquids in Contact with a Solid Surface

• The adhesive forces (liquid-glass) are greater than the cohesive forces (liquid-liquid)forces (liquid liquid)

• The liquid clings to the walls of the container

• The liquid “wets” the surface

• Cohesive forces (liquid-glass) are


greater than the adhesive forces

• The liquid curves downward

• The liquid does not “wet” the surface

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NOTE:

The contact angle between the fluidThe contact angle between the fluid

and the capillary wall

determines whether:

(a) capillary rise

(b) capillary depression

02

r

P


(b) capillary depression

02

r

P

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Hydrophillic Hydrophobic

Definition water contact surface


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example

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Maximum height ???

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Soil Type Capillary Rise (m)Clay >10Fine Silt 7.5C Silt 3 0Coarse Silt 3.0Very Fine Sand 1.0Fine Sand 0.50Medium Sand 0.25Coarse Sand 0.15

d


Very Coarse Sand 0.04Fine Gravel 0.015

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Cellular concrete

Capillary rise

Water level


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Rising damp city of Venice


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Capillary suction

Capillary suction


suction

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Related phenomena


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Sugar cube in coffee

movie

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Lungs

It takes some effort to breathe in because these tiny balloons must be inflated but the elastic recoil of the tiny balloons assists


must be inflated, but the elastic recoil of the tiny balloons assists us in the process of exhalation

Baby: The alveoli of the lungs are collapsed in the fetus and must be inflated in the process of inhalation

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Wet DryMoist


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Water in porous material


Underpressure => shrinkage

soil, glass beads, dijken, beach

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10 x 10 cm 0.1 μm


Hyundai Pony 1.5 924 kg

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2

Force of plates

Sr

F2

NNF 9240146001.01.0101.0

073.026


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Crystallization pressure

limestone

airflow


Movie of Eric Doehne

Getty Science

Na2SO4 solution

1 month in 52 secs

www.getty.edu/conservation/science movie

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Gypsum crystals growing in a ‘pore space’


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Crystallization pressure

pressure

rp

crystal Pc


p

clc r

P cos2

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Surface tensione.g. fired-clay brick :3 MPa

Damage crystal

crystal

Na2CO3 =0.09 Nm-1

Na2SO4 7H20 very low

m][Par

0.04P

damage

< 12 nm

nonm][Par

0.0P


Na2SO4 10H20 =0.10 Nm-1 m][Par

0.06P < 20 nm

r

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MIP: Mercury Intrusion PorosimetryNon-wetting fluid


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

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Assumes pores in porous material shaped like cylindrical tubes

MIP: Mercury Intrusion Porosimetry

Working principleAssuming a cylindrical pore model, the relation between the pressure applied and the pore size is described by the Washburn equation:

r Hg cos2

THIS IS A MODEL


Where:r = radius of the pore intruded by the mercury, = surface tension of the mercury, = contact angle between the mercury and the material testedp= pressure applied

Pr

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• Inject mercury into pores to measure pore size and pore size pdistribution.

• MIP cylindrical pores


MODEL OF MATERIAL

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r

drrfV )(

cumulative

o

f )(

pore size


distribution

dr

dVrf )(

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r

o

drrfV )(dr

dVrf )(

cumulative pore size distribution

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• Advantages– Results obtained quickly (minutes,hours)– Method is reasonably accuratey

– Very high range of capillary pressures

• Disadvantages– Ruins core / mercury disposal– Hazardous testing material (mercury)

Con e sion eq i ed bet een


– Conversion required between mercury/air capillary data to reservoir fluid systems

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Capillary instabilitySelf study

The force g = r forces fluid from the throat, decreasing rleading to collapse.


Joseph Plateau, in 1873, observed experimentally that a falling stream of water of length greater than approximately 3.13 times its diameter will form droplets while falling.

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TPMSurface Tension with Temperature

low T high T

• Weaker intermolecular forces• Increase of surface area

Water molecule representative

• Lower Surface Tension

Surface tension decreases


Su ace te s o dec easesat approximately one percent per 4oC

TPMTemperature gradient


T1 < T2

Water moves to lower temp

course + lectures notesporousmedia.nl/nfcmr/college/college-week2a-2016.pdf · tu19‐4‐2016...

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