transport in porous media 3mt130 · transport in porous media 3mt130 cap i part a: surface tension....

Transport in Permeable Media

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Transport in porous media3MT130

Cap I part A: surface tension


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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?


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What’s going onat the surfaceof 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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= intermolecularattractionsCOHESION

But how do intermolecular forces

influence 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 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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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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Separation of liquid to create a new surface requires

work to overcome cohesion forces

Formation of a Surface


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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

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.

Aw =


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

(N/m) (J/m2)

Units of measurement

Surface Tension Surface Energy

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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𝛾 =𝐹

2𝑙


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movie

DEMO


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Release of a Liquid drop from a capillary

Surface 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.

• 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 determined by the mass of the drop is no longer balanced by the surface tension

mg = 2rc


TPMSurface Tension Measurement-- Ring--


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Wtot = Wring + 4R

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.

F

2R


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Surface tension (10-3 Nm-1)

alcohol 23

benzene 29

glycerol 62

mercury 500

milk 45

water 73

influence surfactants (soap)

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


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Floating paperclip DEMO


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mass

Mass: F=m 10

Surface tension F= 2 0.073 0.01

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

Water strider


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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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movie


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Surface tension ships DEMO


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Walking over water ?

movie


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Pressure in droplet /soap bubble

rPP oi

2=−

Pi

Po

rrPP oi 2)( 2 =−

droplet

bubble

rPP oi

4=−


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Balloons: what will happen?


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Pressure buble:

r

Pin

Pout

rP

4=


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transport in porous media 3mt130 · transport in porous media 3mt130 cap i part a: surface tension....

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