The mathematics of diffusion

J. CRANK

A MORE precise title for this book would be ‘Mathematical solutions of the diffusion equation’, for it is with this aspect of the mathematics of diffusion that the book is mainly concerned. It deals with the description of diffusion processes in terms of solutions of the differential equation for diffusion. Little mention is made of the alternative, but less well developed, description in terms of what is commonly called ‘the random walk’, nor are theories of the mechanism of diffusion in particular systems included.

1. The diffusion equations 1

2. Methods of solution when the diffusion coefficient is constant 11

3. Infinite and sem-infinite media 28

4. Diffusion in a plane sheet 44

5. Diffusion in a cylinder 69

6. Diffusion in a sphere 89

7. Concentration-dependent diffusion: methods of solution 104

8. Numerical methods 137

9. Some calculated results for variable diffusion coefficients 160

10. The definition and measurement of diffusion coefficients 203

11. Non-Fickian diffusion 254

12. Diffusion in heterogeneous media 266

13. Moving boundaries 286

14. Diffusion and chemical reaction 326

15. Simultaneous diffusion of heat and moisture 352

Tables 375

References 399

Author index 407

Subject index 411

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