Solutions of the Radial Diffusion Equation

We may restrict ourselves to considerations of diffusions such that the spherical surfaces of constant concentration are concentric in this case the equation of diffusion is (12)  

Examples of diffusion in spheres may then be treated in a very simple manner by making the substitution 

The methods used in the previous pages for all the linear cases may then be employed, and analogous solutions obtained. Some examples of these solutions of the diffusion equation will now be given. 

Suppose one has a sphere of radius a, and containing solute at an initial concentration (7 = /(r). The surface of the sphere is kept at a constant concentration Cg. The substitution 

Case 1. The amount of absorption or desorption in spheres can easily be derived from (51 a) for some important examples. For instance, when /(r) = Cq throughout the sphere at = 0, equation (51a) becomes 

---