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The Mechanical Basis for Fick’s Law and Its Generalizations

  • E. L. Roetman
  • R. E. Barr
Part of the Advances in Experimental Medicine and Biology book series (AEMB, volume 75)

Abstract

In 1855 Fick [1] wrote about the problem of diffusion of one fluid species through another. After a rather long discussion of the basis for such diffusion in terms of molecular motion and the difficulties of careful analysis based on molecular theory, Fick proposed, by analogy to heat flow, that the concentration satisfies the differential equation
$$\frac{{\partial c}} {{\partial t}} = D{\nabla ^2}c$$
.

Keywords

Momentum Balance Molecular Theory Fluid Mixture Logarithmic Decrement Momentum Balance Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    A. Fick. Ueber Diffusion. Ann. Physik 94(1855) 59–86.CrossRefGoogle Scholar
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    C. Eckart. The thermodynamics of irreversible Processes II. Fluid Mixtures. Phys. Rev. 58(1940) 269–275.CrossRefGoogle Scholar
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    M. Gurtin. On the thermodynamics of chemically reacting fluid mixtures. Arch. Rational Mech. Anal. 43(1971) 198–212.Google Scholar
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    V. Smirnov. A course of Higher Analysis, vol. II. Pergamon: Oxford, 1964.Google Scholar
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    W. Fulks and R. Guenther. Damped wave equations and the heat equation. Czech. Math. 21(96) (1971) 683–695.Google Scholar
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    P. Altman and D. Dittmer, editors. Respiration and Circulation. Federation of American Societies for Experimental Biology: Bethesda, Maryland, 1971.Google Scholar
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    Standard Methods for Examination of Water by American Public Health Association. Reported in: Beckman Instructions 1223-B, June 1964, Beckman Instruments Inc.Google Scholar

Copyright information

© Plenum Press, New York 1976

Authors and Affiliations

  • E. L. Roetman
    • 1
  • R. E. Barr
    • 2
  1. 1.Department of MathematicsUniversity of MissouriColumbiaUSA
  2. 2.Department of OpthalmologyUniversity of MissouriColumbiaUSA

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