5 - Diffusion: Basic theory

Abstract

This chapter discusses the development of the basic equation of molecular diffusion and simple application. The basic diffusion of matter, also called molecular diffusion, is described by Fick's law. The continuity equation for the contaminant states that spatial rate of change of mass flow rate per unit area equals minus the time rate of change of mass. Considering an initial mass slug, the analytical solution of the diffusion equations is presented. The solution is based on the assumption that the mass slugs diffuse independently because of the fundamental premise that the motion of individual particles is independent of the concentration of other particles. It is found that the step function is a limiting of the sudden increase in mass concentration at the origin with constant mass concentration at the origin. It is observed in the chapter that when the spreading is restricted by a solid boundary, the principle of superposition and the method of images are used. The spreading pattern resulting from a combination of two mass slugs of equal strength includes a line of zero concentration gradient midway between them.