Page 73 - 4498

In case of liquids, surface tension may be equivalently defined either
through force or through energy.
In terms of force: surface tension  of a liquid is one-half the force
per unit length required to keep still a movable side of a frame over which

the liquid is stretched (say, into a thin film). To visualize this, imagine a
rectangular frame which is composed of three unmovable sides that form a
"U" shape, and the fourth, movable side that can slide, along the two

parallel unmovable sides, either towards or away from the unmovable
"bottom" side of the "U." Now imagine that a liquid is stretched into a thin
film on this frame, much like soap water gets stretched over a bubble-
blowing ring after the ring is dunked into soapy water. Then it is
[5]
observed that the movable side will be pulled by the film towards the
"bottom" of the "U"; the force required to stop the movable side from
sliding turns out to be proportional to the length of the movable side.

Thus, the ratio depends only on the intrinsic properties of the liquid
(composition, temperature, etc.), but not on its geometry; for example, if
the frame has a more complicated shape, the ratio , with the length

of the movable side and the force required to stop it from sliding, is
found to be the same for all shapes. We therefore define the surface
tension as

1 F
.   (3.5.1)
2 L
The reason for the is that the film has two sides, each of which
contributes equally to the force; so the force contributed by each side is

 L  F , which adds up to a total force of .
2
In terms of energy: surface tension of a liquid is the ratio of 1. the

change in the energy of the liquid and 2. the change in the surface area of
the liquid (that led to the change in energy). This can be easily related to
the previous definition in terms of force: if is the force required to stop
the side from starting to slide, then this is also the force that would keep

the side in the state of sliding at a constant speed (by Newton's Second
Law). But if the side is moving, then 1. the surface area of the stretched
liquid is increasing while 2. the applied force is doing work on the liquid.

This means that increasing the surface area increases the energy of the
film. The work done by the force in moving the side by distancedx
is dA  Fdx; at the same time the total area of the film increases by
dS  2 Ldx(the factor of 2 is here because the liquid has two sides, two

73