Transport in porous media 3MT130 · Transport in porous media 3MT130 Cap I part A: surface tension....

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Transport in Permeable Media

Transport in porous media3MT130

Cap I part A: surface tension

How is the moisture distributed??

SURFACETENSION

What’s going onat the surfaceof a liquid?

Let’s takea look!

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

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

= intermolecularattractionsCOHESION

But how do intermolecular forces

influence the surface?

Under the surface,

intermolecular attractions pull onindividual molecules in all directions

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.

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

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

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

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

Surface tension = N/m

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

Zero gravity

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

Surface Tension

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

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

Separation of liquid to create a new surface requires

work to overcome cohesion forces

Formation of a Surface

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.

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

(N/m) (J/m2)

Units of measurement

Surface Tension Surface Energy

1 Joule = 1 Nm

(Nm/m2)

• For Liquid/Liquid Interface, usually termed Interfacial Tension

• For Gas/Liquid interface usually termed Surface Tension

𝛾 =𝐹

Release of a Liquid drop from a capillary

Surface Tension Measurement-- Drop--

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--

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.

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)

Floating paperclip DEMO

Mass: F=m 10

Surface tension F= 2 0.073 0.01

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

Water strider

Nature: all sizes

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).

Surface tension ships DEMO

Walking over water ?

Pressure in droplet /soap bubble

rPP oi

rrPP oi 2)( 2 =−

droplet

bubble

rPP oi

Balloons: what will happen?

Pressure buble:

Transport in porous media 3MT130 · Transport in porous media 3MT130 Cap I part A: surface tension....

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