Surface energy and surface tension

Oil and water do not mix; water wets people but not ducks; mercury does not wet glass while water clings to it; oil climbs a cotton wick; sap reaches the top of a tree; a paint brush forms a fine tip only when lifted out of water. All of these come from free liquid surfaces.

A liquid has a definite volume but no definite shape, so in a container it forms a free surface. That surface carries extra energy; the effect is surface tension. Gases have no free surface, so surface tension belongs to liquids.

A molecule deep inside a liquid is attracted by all its neighbours, giving it a negative potential energy. The large heat needed to evaporate a liquid shows how deep this is: for water about 40 kJ/mol.

A molecule at the surface has neighbours only on the liquid side, so its negative potential energy is roughly half that of an interior molecule. Surface molecules therefore have extra energy, and a liquid takes the least surface area its surroundings allow.

Bringing a molecule to the surface costs roughly half the energy needed to remove it from the liquid entirely, about half the heat of evaporation. The surface is not razor-sharp: density falls to zero over a few molecular sizes.

A horizontal film on a frame with a sliding bar of length l: moving the bar a distance d adds area 2dl, because the film has two surfaces. The work Fd becomes surface energy: S(2dl) = Fd, so S = F/2l.

Surface tension S is the surface energy per unit area of the interface, and equally the force per unit length acting in the plane of the interface. It is the extra energy of interface molecules compared with interior ones.

Across any line drawn on a liquid surface, equal and opposite forces S per unit length act perpendicular to the line and in the plane of the surface. At a true edge of the interface only the inward force S per unit length remains.

The surface energy belongs to the interface between two materials and depends on both: mutual attraction lowers it, repulsion raises it.

Surface tension (N/m) with heat of vaporisation (kJ/mol): helium 0.000239 at −270 °C (0.115); oxygen 0.0132 at −183 °C (7.1); ethanol 0.0227 at 20 °C (40.6); water 0.0727 at 20 °C (44.16); mercury 0.4355 at 20 °C (63.2).

Surface tension usually falls as temperature rises, as viscosity does for liquids.

Measuring it: a vertical glass plate hangs from one arm of a balance with its lower edge just above the liquid. The raised liquid touches and pulls the plate down; the extra weight W needed to just free it gives S_la = W/2l = mg/2l, with l the length of the plate edge.