Editing Molecular diffusion (section)

== Molecular diffusion of gases ==
Transport of material in stagnant fluid or across streamlines of a fluid in a laminar flow occurs by molecular diffusion. Two adjacent compartments separated by a partition, containing pure gases A or B may be envisaged. Random movement of all molecules occurs so that after a period molecules are found remote from their original positions. If the partition is removed, some molecules of A move towards the region occupied by B, their number depends on the number of molecules at the region considered. Concurrently, molecules of B diffuse toward regimens formerly occupied by pure A.
Finally, complete mixing occurs. Before this point in time, a gradual variation in the concentration of A occurs along an axis, designated x, which joins the original compartments. This variation, expressed mathematically as −dC<sub>A</sub>/dx, where C<sub>A</sub> 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 −dC<sub>B</sub>/dx. The rate of diffusion of A, N<sub>A</sub>, depend on concentration gradient and the average velocity with which the molecules of A moves in the x direction. This relationship is expressed by [[Fick's law]]

:                <math>N_{A}= -D_{AB} \frac{dC_{A}}{dx}</math> (only applicable for no bulk motion)

where D is the diffusivity of A through B, proportional to the average molecular velocity and, therefore dependent on the temperature and pressure of gases. The rate of diffusion N<sub>A</sub> is usually expressed as the number of moles diffusing across unit area in unit time. As with the basic equation of heat transfer, this indicates that the rate of force is directly proportional to the driving force, which is the concentration gradient.
 
This basic equation applies to a number of situations. Restricting discussion exclusively to steady state conditions, in which neither dC<sub>A</sub>/dx or dC<sub>B</sub>/dx change with time, equimolecular counterdiffusion is considered first.