1.6 - Diffusion

Abstract

This chapter starts with a statement of Fick’s First Law of Diffusion, derived from analogy from Fourier’s Law of Heat Transfer. It then uses the continuity equation to derive Fick’s Second Law of Diffusion. Fick’s Second Law of Diffusion is then derived from the statistics of the random walk. This derivation clarifies the nature of the diffusion coefficient and the meaning of the variance of the Gaussian concentration distribution as a measure of the diffusion distance at any given time. This chapter then describes the Kushmerick and Podolsky experiment, in which cellular diffusion coefficients are shown to be smaller than free diffusion in water. Modification of Fick’s First Law is shown when solvent drag occurs or when another force acts on the diffusing particle such as electrical forces. This chapter then describes the drag or frictional coefficient for diffusing particles as described by Einstein and the frictional coefficient of a sphere derived by Stokes. The two together result in the Stokes–Einstein equation for the diffusion coefficient.