Chapter

Einstein's theory of diffusion

Daniel T. Gillespie and Effrosyni Seitaridou

in Simple Brownian Diffusion

Published in print October 2012 | ISBN: 9780199664504
Published online January 2013 | e-ISBN: 9780191748516 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199664504.003.0003
Einstein's theory of diffusion

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Before it was universally accepted that a fluid consists of many moving molecules, Fick's Law and the diffusion equation were widely regarded as statements in continuum mechanics. With the molecular theory in mind, Einstein derived the diffusion equation from a model of random molecular motion instead of from a continuity equation and Fick's Law. This chapter presents Einstein's derivation and examine its strengths and weaknesses. The chapter then deduces some of the implications of Einstein's model of diffusion: its novel probabilistic perspective on the classical diffusion equation; its predictions for the mean of the square of the displacement of a single solute molecule in a given time, and the consequent single-molecule interpretation of the diffusion coefficient; its formulas for the covariance and the correlation of the displacement; its implied formula for the diffusion coefficient of one solute molecule relative to another; and its implied notion of single-molecule probability flux. Finally, The chapter takes the first step toward deriving a formula for the stochastic rate of a diffusion-controlled bimolecular chemical reaction, a derivation which will be will completed in Chapter 4.

Keywords: Einstein; probability density function; diffusion coefficient; relative diffusion stochastic bimolecular reaction; rate; diffusion-controlled reactions; Smoluchowski formula; Collins-Kimball theory

Chapter.  10635 words.  Illustrated.

Subjects: Physics

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