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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