Surface Tension
1.1. Introduction
All of us have had the experience of filling a glass with water which
crests above the rim of the glass, but doesn't spill over. How can
this happen? Think of a liquid as a collection of (polar) molecules
which exert attractive forces of equal strength on each other. Deep
inside the liquid a molecule feels equal forces from all directions, but
near the surface of the liquid a molecule feels more of a force from
inside the liquid than it does from the small number of molecules
between it and the surface. Hence, those molecules near the surface
are drawn into the liquid and the surface of the liquid displays a
'curvature'. This property of pulling the surface of a liquid taut is
called surface tension. Thus we see liquids form into drops or bubbles
because surface tension acts as a skin holding the liquid together. But
a soap bubble doesn't shrink away to nothing, so at some point surface
tension must be balanced by an internal pressure. In the case of the
soap bubble, of course, the air pressure inside the bubble is larger than
that outside, so an eventual equilibrium is attained. Nature often tells
us when an equilibrium has been reached by making the geometry
of the equilibrium state very special and so it is with geometry
constrained by surface tension. Excellent references for what follows
are [Ise92], [Lov94] and [Fin86].
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