Liquid surfaces

Question

The surface between a liquid and a vapour distinguishes these fluids.

The surface tension of liquids can be looked upon as that the property which draws a liquid together and forms a liquid vapour interface, therefore, distinguishing liquids from gases.

The molecular basis for this property is suggested, where the unbalanced attractions experienced by the surface molecules are shown to lead to the amount of free liquid will pull it together to form a less spherical drop. The surface layer can be expected to have properties that differ from those of the bulk of the liquid.

The surface tension of the liquid can be defined with reference to where it is most easily pictured is a wire frame, arranged as a piston, used to expand a soap film. The definition also applies to the mechanically more difficult systems where the film is replaced by a layer of liquid of appreciable thickness. The force required stretching the film or liquid vapour is proportional to the length l of the piston. Since there are two surfaces of the film, the total length of the film is 2l, and the proportionality equation:

ƒ = γ(2l) can be written.

The proportionality constant γ is known as the surface tension, and according to the above equation it can be looked upon as the force by a surface of unit length.
Of more general use is the relation between surface tension and surface energy. The mechanical energy required to expand the surfaces by moving the piston a distance dx is f dx, or 2l dx. Since the area of new surface is 2l dx, the result:

Mechanical energy/change of surface area = 2lγ dx/ 2l dx = γ, can be obtained. This expression shows that the surface tension can be interpreted as the energy per unit surface area and that it is a mechanical rather than thermal energy. In these terms, the tendency of a surface to reduce its area is just another example of a system tending toward an arrangement of low free energy.

Surface tension of some liquids, N m^-1:

Liquid	20°C	60°C	100°C	Liquid	t, °C	Surface tension
H2O	0.07275	0.06618	0.05885	Hg	0	0.480
C2H5OH	0.0223	0.0223	0.0190	Ag	970	0.800
C6H6	0.0289	0.0237		NaCl	1080	0.094
(C2H5)2O	0.0170		0.0080	AgCl	452	0.125

Example: compare the heights to which water and carbon tetrachloride will rise as a result of capillary action in a tube with an internal diameter of 0.1 mm. at 20°C the surface tensions of water and carbon tetrachloride, respectively, are 0.0727 and 0.0268 N m^-1, and their densities are 0.998 and 1.595 g mL^-1.

Solution: we use to obtain:

L = 2 γ/rpg

The radius of the cube is 0.5 mm = 0.5 × 10^-4 m, and the densities are 9.98 × 10³ and 1.598 × 10³ kg m^-3.

For water: l = 2 (0.0727 N m^-1)/(0.5 × 10^-4 m) (9.98 × 10³ kg m^-3) (9.81 m s^-1)

= 0.0297 m = 29.7 mm

For CCl₄: l = 2 (0.0268 N m^-1)/(0.5 × 10^-4 m) (1.595 × 10³ kg m^-3) (9.81 m s^-2)

= 0.00685 m = 6.85 mm.