In this chapter we start by giving Fick's law of
diffusion, which describes the movement of one
chemical species A through a binary mixture of A
and B because of a concentration gradient of A.
The movement of a chemical species from a region of
high concentration to a region of low concentration can
be observed by dropping a small crystal of potassium
permanganate into a beaker of water.
The KMnO, begins to dissolve in the water, and very
near the crystal there is a dark purple, concentrated
solution of KMnO,. Because of the concentration
gradient that is established, the KMnO, diffuses away
from the crystal. The progress of the diffusion can then
be followed by observing the growth of the dark purple
Consider a thin, horizontal, fused-silica plate of
area A and thickness Y. Suppose that initially (for
time t < 0) both horizontal surfaces of the plate are
in contact with air, which we regard as completely
insoluble in silica.
In this system, we will call helium “species A” and
silica “species B”. The concentrations will be given
by the "mass fractions" wA and wB.
The mass fraction wA is the mass of helium divided
by the mass of helium plus silica in a given
microscopic volume element. The mass fraction
wB is defined analogously.
The mass fraction of helium, wA
is everywhere equal to
The air below the plate is suddenly
replaced by pure helium. At the
lower surface, y = 0, the mass
fraction of helium is equal to wA0.
Helium slowly penetrates into
the plate by virtue of its
molecular motion - DIFFUSION
As time proceeds the mass
fraction profile develops, with
wA = wA0 at the bottom surface of
the plate and wA = 0 at the top
surface of the plate.
The profile tends toward a
straight line with increasing t
At time t = 0, the air below the plate is suddenly replaced
by pure helium, which is appreciably soluble in silica.
The helium slowly penetrates into the plate by virtue of
its molecular motion and ultimately appears in the gas
This molecular transport of one substance relative to
another is known as diffusion.
The air above the plate is being replaced rapidly, so that
there is no significant buildup of helium there.
In this section we discuss the prediction of the
diffusivity DAB for binary systems by