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 solutions2,3,8,9. 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 (θ) functions:
Similar content being viewed by others
Article PDF
References
Hartley, G. S., Trans. Faraday Soc., 42, B, 6 (1946).
Crank, J., and Henry, M. E., Trans. Faraday Soc., 45, 636 (1949).
Crank, J., and Henry, M. E., Trans. Faraday Soc., 45, 1119 (1949).
Klute, A., Soil Science, 73, 105 (1952).
Philip, J. R., J. Inst. Eng. Aust., 26, 255 (1954).
Philip, J. R., Proc. Nat. Acad. Sci. (India), Allahabad, 24 A, 93 (1955).
Philip, J. R., Soil Science, 83, 345, 435, 84, 163, 257, 329 (1957); 85, 278, 333 (1958).
Philip, J. R., Trans. Faraday Soc., 51, 885 (1955).
Philip, J. R., Aust. J. Physics, 10, 29 (1957).
Crank, J., “Mathematics of Diffusion”, 166, (Oxford 1956).
Fujita, H., Text Res. J., 22, 757 (1952).
Fujita, H., Text. Res. J., 22, 823 (1952).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
PHILIP, J. A Very General Class of Exact Solutions in Concentration-dependent Diffusion. Nature 185, 233 (1960). https://doi.org/10.1038/185233a0
Issue Date:
DOI: https://doi.org/10.1038/185233a0
This article is cited by
-
Partial analysis applied to scale problems in surface moisture fluxes
Surveys in Geophysics (1991)
-
Diffusion Studies of Bovine Serum Albumin with Jamin Interference Optics and Micro-Diffusion Cell
Nature (1962)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.