Capillary Surface Tension

8/3/2019 Capillary Surface Tension

1/30

Colloidal Dispersions 2005

Surface and Interfacial Tensions

Lecture 1


2/30

Surfaces and Interfaces 1Colloidal Dispersions 2005

Surface tension is a pull


3/30


Thermodynamics for Interfacial Systems

F A =

Work must be done to increase surface area just as work must be done

to compress a gas.

At constant temperature (T), volume (V) and composition (n), the

energy, F, necessary to increase the surface area by an amount, A,is:

Where is the surface tension.

When Fis negative, the process is spontaneous.When Fis positive, the process reverses.


4/30


Coalescence of Droplets

The change in energy is:

+

( )

0

final initial

final initial

F F F

A A

A

=

=

=

+

This is not the common assertion.


7/30


Works of Cohesion and Adhesion

12 1

2

11

1 2 12

adhW = +

12

coh

W =

The work of adhesion is the

separation to create two new

surfaces from one interface:

The work of cohesion is theseparation to create two new

surfaces.


8/30


Liquids have different contact angles on different solids


9/30


Contact angles: Liquids on solids

The contact angle of 140o is the same for each drop, independent of

drop size.

The observation is that the contact angle depends on the materials but

not the particular geometry.

Mercury drops on glass.*

Drops vary in size from 4 to 24grains (1 grain = 64.8 mg)

* Bashforth and Adams, 1883.


10/30


The interaction of a liquid and a solid

= +cossv lv sl

The Young-Dupr introduces the idea of a solid surface/vapor surface

tension, sv and a solid/liquid interfacial tension, sl.

sv

lv

sl

The idea is that the three

tensions are balanced:

A sessile liquid drop on a

solid:

The contact angle is and is assumed to be independent of the geometry.


11/30


The Molecular Origin of Surface Tension

The molecules at the

liquid surface are pulled

towards the bulk liquid.

To expand the surface

requires work. The workis the surface tension

times the change in

area.


12/30


The Molecular Origin of Interfacial Tension

= + 1 2 12adhW

The stronger the interfacial

interactions, the lower the

interfacial tension!

But the greater the work of

adhesion:


13/30


A theory for interfacial tensions

Liquid 1

Liquid 2

1

2

1 2

d d

1 2

d d

12 1 2 1 22d d = +

Fowkes, in Ross, ed. 1965, p. x

The adhesion between the

liquids is approximated by the

root-mean-square of the

surface tensions:

1 22adh d d

W =

hence

The superscript d refers to the dispersion or van der Waals types of attraction.


14/30


Large surface heterogeneities - contact angle

hysteresis

Advancing liquids are held up by low energy spots and

show high contact angles.

Receding liquids are held by high energy spots and

show low contact angles.

High energy spots

low contact angles.

Low energy spots

high contact angles.


15/30


Small heterogeneities - contact angle changes

Coverage

0.0 0.2 0.4 0.6 0.8 1.0

cos

w

0.0

0.2

0.4

0.6

0.8

1.0

The cosine of the static contact angle of water on varioussubsaturated monolayers plotted versus the surface coverage

measured directly using the atomic force microscope.

Text, p. 220.


16/30


Motion of liquids due to surface energies

Capillary flow

Motion as a consequence of shape.

Key idea: pressure drop across a curved

surface

Marangoni flow

Motion as a consequence of variation insurface tension.


17/30


Pressure drops across a curved surface

R1

R2

x x+dx

dz

y

y+dy

1 2

1 1Lp

R R

= +

The pressure is larger on the concave (inside) of the curved surface.

The Laplace equation:

R1 and R2 are the radii of curvature.


18/30


Bubbles are difficult to nucleate


19/30


Ostwald Ripening

The pressure inside > pressure outside

2p

r

=

This equation implies that in an emulsion with a range of drop sizes or

a foam with a range of bubble sizes, material diffuses from small

drops to large drops.

Also, this equation implies that bubbles are difficult to nucleate.


20/30


The Kelvin Equation

2ln m

o

P V

P rRT

=

0

2ln m

c V

c rRT

=

Similarly for small particles in suspension. If the particles have any

solubility, the small particles become smaller and the large particles

become larger. The effect is described by the Kelvin equation.

All these processes are called Ostwald ripening.


21/30


Capillary rise is another example of Laplace pressure


22/30


Capillary rise

The final position is determined by 2 principles:

(1) The pressure drops across curved interfaces.

(2) The pressure in the liquid must be the sameat the same depth.

In the final state the pressure drop across the ACinterface equals the hydrostatic pressure from C to B.

2 co sLg hR

=


23/30


Marangoni Flow

Marangoni flow

flow resulting from local differences in

surface tension.

Causes of Variation in Surface Tension

Local temperature differences.

Local differences in composition due to

differential evaporation.

Electric charges at surfaces.

Local compression or dilatation of

adsorbed films.


24/30


Liquid will flow away from a low surface tension region


25/30


Liquid flows to the higher surface tension


26/30


Tears of Wine

+

EthOH/H O2


27/30


Flow due to surface tension differences


28/30


Liquid flows away from a hot spot


29/30


Liquid flows to a cold spot


30/30


Equations of Capillarity

, , iT V n

F

A

=

= +cosSV LV SL

1 2

1 1pR R

= +

( )grad = +

Surface Free Energy

Young-Dupr Equation

LaPlace Equation

Marangoni Flow

Capillary Surface Tension

Documents

Transcript of Capillary Surface Tension