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Diffusion in Inhomogeneous Media
1.C. J. F. Böttcher, Theory of Electric Polarization (Elsevier Publishing Company, New York, 1952), p. 415.
2.W. F. Brown, J. Chem. Phys. 23, 1514 (1955).
3.The summation convention is used throughout this paper. Indices appearing after the comma indicate differentiation with respect to the corresponding position coordinate (for example the components of are and ).
4.Equation (2) assumes that the distribution coefficient κ of the penetrant is constant throughout the medium. If, as is to be expected, κ is also a function of position, then, at equilibrium, and not c. will be the position independent quantity. In this case Eq. (2) must be replaced by , which is formally identical with (2), and can be treated by the same methods. To correct for variable κ, D should be replaced by in all calculations of described in this paper, and the so obtained should be divided by the average value of κ.
5.J. H. Wang, J. Am. Chem. Soc. 76, 4755 (1954).
6.The approach of this section bears some similarity to Brown’s calculation2 of dielectric constants in inhomogeneous media. The two treatments are not directly comparable, however, because of a difference in the choice of the source term in Eq. (18). This strongly affects the nature of the series obtained, and it is only in the limit of very small fluctuations (Eq. 28) that our results are equivalent to Brown’s.
7.G. K. Batchelor, The Theory of Homogeneous Turbulence (Cambridge University Press, New York, 1953), p. 79.
8.H. S. Green, The Molecular Theory of Fluids (North‐Holland Publishing Company, Amsterdam, 1952), p. 71.
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