A Very General Class of Exact Solutions in Concentration-dependent Diffusion

Abstract

THE mathematics of concentration-dependent diffusion has been found in recent years to be important in problems of diffusion in polymers1-3 and in the problems of the transport of water in its various phases in soils and other porous materials4-7. Almost without exception, it has been necessary to use numerical methods to secure the necessary solutions 2,3,8,9. According to Crank10, the only known 'formal solutions' are due to Fujita11,12. They provide solutions of the equation: subject to the conditions: and are for the following D () functions: © 1960 Nature Publishing Group.