Diffusion of non-electrolytes in solution

In Chapter 2 we discussed the movement of ions in solution under the influence of an electric field. In this chapter we will first consider the movement of non-electrolytes down concentration gradients and then the movements of electrolytes subject to the joint effect of an electric field and a concentration gradient.

Figure 3.1a shows a slab of a solid non-electrolyte, interfaced to a cuboid of solvent of length l and of unit cross-sectional area (1 cm2).

The solid non-electrolyte might, for example, be sugar and sugar molecules can be imagined to be dissolving from the face of the sugar slab into the solvent. The solvent is unstirred and assumed not to react with the non-electrolyte. At time t, after the sugar slab has come into contact with the solvent, we obtain a concentration profile of the type shown in Figure 3.1b (t). This profile is due to solute molecules which move from a high concentration (the face of the sugar slab) to the lower concentration in the solvent. At different times (t1, t2, …, t) different concentration profiles will be obtained.

Fick's First Law

A quantitative treatment of these concentration profiles was first carried out by Fick (who adapted the problem previously solved by Fourier for the conduction of heat through a slab) and assumed that the rate at which a solute flows through a plane of area A at right angles to the flow, is proportional to this area A.