The molecules exert an attraction on each other, and therefore when a liquid surface such as a soap film is stretched the surface gains potential energy since the molecules are being separated from each other. All free liquid surfaces are said to possess energy.
Consider a soap film (Figure 1). If the film is bounded by a movable wire
at the right-hand edge, then the molecules along that edge will experience a surface tension
force acting only towards the left. To prevent the film from contracting an equal and opposite
force must be applied.
Figure 2
If the wire has a length L,
then this force is 2LT where T is the surface tension of the liquid. Notice the 2 in this formula.
This must he included because the film has two sides, and therefore the surface tension acts
on both sides of it and we have to maintain equilibrium on both these two sides.
If
the wire is moved a distance dx to the right then the work done is 2lTdx, and this is equal to
the energy gained by the surface. However, 2Ldx is the increase in the surface area of the
film and therefore the energy gained is equal to the surface tension multiplied by the
increase in surface area.
This provides an alternative definition for the surface tension:
One important
difference between the behaviour of a liquid surface or soap film and that of an elastic sheet
is that the tension of the film is constant while that of the elastic sheet increases with
increasing area – the more you stretch the elastic sheet the bigger the tension in it becomes.
This does not happen with a liquid surface.
Any liquid surface will try to exist in the
lowest state of potential energy that it can; this explains the spherical shape of liquid drops,
the sphere having the minimum surface area for a given volume. It also explains the way in
which soap films can be used to solve such mathematical problems as finding the shortest
series of roads that could connect a number of towns.
The energy of a liquid surface can
be explained in terms of the forces of attraction between the molecules. The molecules in
the liquid surface are attracted only to molecules beside them and below, while molecules
within the body of the liquid are attracted to liquid molecules all around them. To bring a
molecule from the body of the liquid to the surface requires a force to overcome these
attractive forces between the molecules and therefore net work must be done on the
molecule. Consequently the molecules at the surface have a greater potential energy than
those beneath it. A molecule in the surface would need further energy to remove it to infinity
against the attraction of the liquid - this is provided in evaporation.
Gravitational
effects often distort the theoretical spherical shape of droplets; in practice droplets show a
flattened shape. However drops of oil in an alcohol-water mixture of the same density show
true spherical shapes.