Abstract
This chapter, in which the primary aim is to obtain solutions to Fick’s laws of diffusion, is similar to Chapter 9 where we presented solutions to heat conduction problems. Therefore, much of the groundwork laid in Chapter 9 reappears in the following discussions. We begin by presenting some classical approaches used for determining diffusion coefficients in solids, and then consider some applied problems involving diffusion in solids as the rate-limiting step.
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Notes
S. Pauly, “Permeability and Diffusion Data,” in J. Brandrup and E. H. Immergut, editors, Polymer Handbook, third edition, John Wiley & Sons, New York, NY, 1989, pages VI/435 to VI/449.
Extensive compilations of solutions are presented in J. Crank, The Mathematics of Diffusion, Oxford University Press, London, 1956
and W. Jost, Diffusion in Solids, Liquids, and Gases, Academic Press, 1960.
With appropriate change of variables, one can also refer to H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, second edition, Oxford University Press, 1959.
W. Jost, Diffusion in Solids, Liquids, and Gases, Academic Press, New York, 1960, page 76, and also
W. Jost, Z Physik 127, 163 (1950).
M. C. Flemings, Solidification Processing, McGraw-Hill, New York, NY, 1974, pages 34–36, 142.
J. Crank, The Mathematics of Diffusion, Oxford University Press, London, 1957, page 58.
T. F. Kattamis and M. C. Flemings, Trans. TMS-AIME 233, 992 (1965).
S. N. Singh and M. C. Flemings, Trans. TMS-AIME 245, 1803 (1969).
G. Tammann, Z. Anorg. u. Allgem. Chem. 111, 78 (1920).
N. B. Pilling and R. E. Bedworth, J. Inst. Metals 29, 529 (1923).
C. Wagner, Atom Movements, Amer. Soc. for Metals, Cleveland, OH, 1951, page 153.
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Poirier, D.R., Geiger, G.H. (2016). Diffusion in Solids. In: Transport Phenomena in Materials Processing. Springer, Cham. https://doi.org/10.1007/978-3-319-48090-9_13
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DOI: https://doi.org/10.1007/978-3-319-48090-9_13
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