Transport of material in stagnant fluids or across the streamlines of a fluid in laminar flow occurs by molecular diffusion.

**MOLECULAR DIFFUSION IN GASES**

Transport of material in stagnant fluids or across the streamlines of a fluid in laminar flow occurs by molecular diffusion. In Figure 4.1, two adjacent compartments, separated by a partition, are drawn. Each compartment contains a pure gas, A or B. Random movement of all molecules occurs so that after a period of time molecules are found quite remote from their original positions. If the partition is removed, some molecules of A will move toward the region occupied by B, their number depending on the number of molecules at the point considered. Concurrently, molecules of B diffuse toward regions formerly occupied by pure A.

**FIGURE 4.1 ***Molecular diffusion of gases A and B.*

Ultimately,
complete mixing will occur. Before this point in time, a gradual variation in
the concentration of A will exist along an axis, designated *x*, which joins the original
compartments. This variation, expressed mathematically, is -*d*C_{A}/d*x*, where C_{A} is the concentration of A. The negative sign
arises because the concentration of A decreases as the distance x increases.
Similarly, the variation in the concentration of gas B is -*d*C_{B}/d*x*. These
expressions, which describe the change in the number of molecules of A or B
over some small distance in the direction indicated, are concentration
gradients. The rate of diffusion of A, N_{A}, depends on the
concentration gradient and on the average velocity with which the molecules of
A move in the *x* direction. Fick’s law
expresses this relationship.

where
D is the diffusivity of A in B. It is a property proportional to the average
molecular velocity and is, therefore, dependent on the temperature and pressure
of the gases. The rate of diffusion, N_{A}, is usually expressed as the
number of moles diffusing across unit area in unit time. In the SI system,
which is used frequently for mass transfer, N_{A} would be expressed as
moles per square meter per second. The unit of diffusivity then becomes m^{2}/sec.
As with the basic equations of heat transfer, equation (4.1) indicates that the
rate of a process is directly proportional to a driving force, which, in this
context, is a concentration gradient.

This
basic equation can be applied to a number of situations. Restricting discussion
exclusively to steady-state conditions, in which neither dC_{A}/d*x* nor dC_{B}/d*x* changes with time, equimolecular
counterdiffusion is considered first.

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