Chapter

The Fickian 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/9780199664504.003.0001
The Fickian theory of diffusion

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The classical macroscopic theory of simple Brownian diffusion focuses on two physical entities: the solute molecular density and the solute molecular flux. This chapter reviews the traditional way in which two relations involving those two entities, the exact continuity equation and the purely empirical Fick's Law, are combined to obtain a partial differential equation for the molecular density called the diffusion equation, which is the centerpiece of the classical Fickian model of diffusion. The chapter solves the diffusion equation for several different initial and boundary conditions to illustrate the variety of physical systems that it can describe. The chapters that follow refine our physical understanding of the diffusion equation, and then go beyond that equation to develop a more comprehensive theory of simple Brownian diffusion.

Keywords: continuity equation; diffusion equation; Fick's Law; molecular density; molecular flux

Chapter.  7110 words.  Illustrated.

Subjects: Physics

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