the situations where one of the two fluids is air or where the two fluids
meet at a solid as well (i.e. capillarity).
The molecules in a fluid feel forces, generally electrical, from
nearby molecules. Of course, some molecules are polar, that is, their
bonding structure creates a geometry in which one side of the mole-
cule contains a plus electrical charge while the other side contains a
minus charge.
Example 1.2.1. Water molecules H2O have a geometry which places
the two hydrogen molecules (+ charge) on one side of the molecule
and the oxygen molecule ( charge) on the other. Thus, water is
highly polar.
Polar molecules attract each other in the usual fashion; plus
charges attract minus charges and repel other plus charges. There-
fore, a polar molecule in the interior of a fluid will surrpund itself
with attracted molecules oriented to match electrical charges in this
way. The molecules near the surface of a fluid have a different envi-
ronment, however, and this is what creates surface tension. Molecules
near the surface of a fluid feel forces from inside the fluid, but do not
feel the same forces from outside the fluid. Therefore, on the interface
between a liquid and air, say, the fluid molecules will (on average) be
pulled into the fluid, decreasing both the surface area of the interface
and the density of the fluid in the region of the interface. Water,
because it is highly polar, has a strong tendency to minimize area.
A soap solution (see Figure 1) consists of water molecules and
soap molecules. A soap molecule is formed from a metal salt of a long
chain fatty acid molecule and becomes ionized in solution [Ise92].
Ordinary soap is a sodium salt of a fatty acid. A standard example
is sodium stearate C^H^COO'Na+. In solution, the ATa+'s are
free ions, while the geometry of
CIJH^COO'
is such that COO~
forms a negatively charged head with a long hydrocarbon chain tail
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