Thus, we can interpret surface tension as a two-dimensional analog to a
spring—it is the measure of the resistance of a surface to increase its area.
Example 7.1 Determining the Work Done in Expanding
a Liquid Film
Consider a simple experiment in which a film is withdrawn from a
soap solution as shown in Figure 7.3. By noting that work done is
force times displacement and that this work is the surface free
energy given by Equation 7.1, show that surface tension is F/2L.
Prove that the units of surface tension are N m
–1
.
Solution Work must be done to pull up the frame and create a film
(Figure 7.3b).
Work done (dw = F dh) is equal to the surface free energy (γ dA),
where A is the area of the surface. The soap film has two sides or
surfaces, so in this example area A is actually 2A. Also, A is the
length L times the distance moved dh.
Therefore, F dh = γ 2dA = γ 2L dh.
(a)
L
F
(b)
dh
Figure 7.3 A film being
withdrawn from a soap solution to a height dh by a force F,
using a wire frame of length L.
(a) Apparatus prepared for
producing a film. (b) Film
created by moving the bar
above the solution surface.
FUNDAMENTALS OF SURFACE SCIENCE 221