Capillarity

ESS5855 LectureFall 2010

Capillarity: the tendency of a liquid in a narrow tube or pore to rise or fall as a result of surface tension (The concise Oxford Dictionary)

Surface tension: the tension of the surface film of a liquid, which tends to minimize surface area(The concise Oxford Dictionary)

Surface tension (γ) results from inter-molecular forces:a molecule in the interior of a liquid experiences interactions with other molecules equally from all sides, while a molecule at the surface is only affected by molecules below it in the liquid

Surface Tension

• As a result, the interfacial molecules are pulled into the bulk (to the extent allowed by their finite size and repulsive interactions) and the net density of molecules in the surface region is decreased

• There is more space between surface molecules and the springs acting between them are therefore stretchedbeyond their equilibrium length, creating a tension pulling along the surface working to keep the molecules together

• The force of the springs pulling along the surface, then, is the surface tension or surface free energy

Interfaces

• In order for two phases to exist in contact, there must be a region through which the intensive properties of the system change from those of one phase to those of the other

• In order for such a boundary to be stable, it must possess an interfacial free energy such that workmust be done to extend or enlarge the boundary or interface

• If not and if no other external forces act to separate the phases, then no energy will be required to increase the interfacial area and random forces will distort, fold, and convolute the interface until the phases become mixed

Surface Free Energy

• Free energy: the total amount of energy in a physical system that can be converted to do work

• Quantity derived from the relationships studied in thermodynamics and used as a measure of the relative stability of a physical system, i.e., the tendency of the system to change

• Atoms and molecules at interfaces, because of their special environment, often possess energies significantly different from those of the same species in a bulk situation

Interfaces

• Nature will always act so as to attain a situation of minimum total free energy

• In the case of a two-phase system, if the presence of the interface results in a higher (positive) free energy, the interface will spontaneously be reducedto a minimum - the two phases will tend to separateto the greatest extent possible within the imposed constraints

Capillarity

• The macroscopic motion of a fluid system under the influence of its own surface and interfacial forces

• Such flow is similar to other types of hydraulic flow in that it results from the presence of a pressuredifferential between two hydraulically connected regions of the liquid mass

• The direction of flow is such as to decrease the pressure difference

• When the difference vanishes, or when there is no longer a mechanism to reduce the difference, flow ceases

Capillarity

• The topic of capillarity concerns interfaces that are sufficiently mobile to assume an equilibrium shape– The common examples are meniscuses, thin

films, and drops formed by liquids in air or in another liquid

• Capillarity deals with macroscopic and statisticalbehavior of interfaces rather than the details of their molecular structure

Surface Tension/Free Energy

• Although referred to as a force per unit length, surface tension may equally well be thought of as a free energyper unit area

A soap film stretched across a wire frame with one movable side

Fl

dx

Capillary rise

θ

R

r

Pb

Pb

Important functions of capillary forces in practical situations. (a) As two emulsion drops approach, the pressure at the nearest surfaces increases, deforming the drops and enlarging the radius of curvature in the immediate area. That deformation causes the capillary pressure in the regions outside that area to decrease in a relative sense, suctioning continuous phase from between the drops and increasing the likelihood of contact and film rupture or coalescence. (b) In capillary displacement, the liquid that preferentially

wets the solid will displace the less wetting liquid.

Contact angle:1. surface tension and contact angle are two different but closely related things2. surface tension is a property of the interface between two phases, whereas the contact angle describes the edge of the two-phase boundarywhere it ends at a third phase3. two phases must be specified to describe surface tension; three are needed to describe contact angle

γ γ γ

Wenzel’s Model

Metastable states

Cassie-Baxter Model

=

c

c

c

c

A

B

(σ=γ: surface tension)

AABBA dA)(G σ+σ−σ=Δ

)2( BBABBA σ−σ−σ+σ=

BABAB dA)(G σ+σ−σ=Δ

SB/A

-

P3

Bashforth-Adams Equation

( )

( )

Drop in Motion

2

V3

dx

dP

ςη

−=