13.1 Introduction

In an isotropic medium the diffusion coefficient D ⁱ of species i is defined through Fick's first law,

(13.1)

J ⁱ is the instantaneous net flux of species i, or diffusion current per unit area, and grad c ⁱ is the gradient of the concentration c ⁱ of i. If J and c are measured in terms of the same unit of quantity (e.g. J in g cm ^-2 s ^-1, c in g cm ^-3), D has the dimensions ( L ² T ^-1). It has usually been expressed as cm ² s ^-1, although the units m ² s ^-1 are becoming more common. Generally, D depends on the concentration.

That matter is to be conserved at each point leads to Fick's second law,

(13.2)

giving the rate of the change of concentration with time to which diffusion gives rise.

The fluxes J ⁱ are referred, at least for practical purposes, to axes fixed in the volume of the sample; but volume changes which take place as a result of diffusion lead to some ambiguity in the definition of such axes. Means have been proposed3 ^,6 for avoiding this by using axes scaled to the volume changes, but little use is made of these and it is more usual in accurate work to restrict the range of concentration employed so that volume changes...