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Unformatted text preview: Transport Properties: Diffusion, Ficks Laws, Random Walks 13th February 2011 1 Introduction In this discusison, we explore aspects of describing how systems change in time from an initial state to a final state. Effectively, we are interested in that non-equilibrium regime during which system properties change. System properties change in response to perturbations from equilibrium (external forces) System properties that can change include: 1). matter(diffusion), 2). energy (temperature), 3). momentum (viscosity) 2 Fluxes Quantity transferred through a given area per unit time Flux occurs because of a spatial and time-varying gradient of an associated system property. Flux occurs in opposition to spatial gradient Flux continues until the gradient is nullified and equilibrium is reached. Flux continues until external force stop The most general relation for a flux in the x-direction is: J x =- d ( property ) dx J x = 1 Surface Area d ( property ) dt 1 This relates a flux to a gradient of a property (not specifically defined to be anyting at this point) Flux is a linear response ; this treatment assumes a perturbative dis- placement from equilibrium. It can be shown (Engel and Reid, Section 34.2) that the total flux in the x-direction (considering one-dimensional diffusion) across a surface is: J =- D d N d x ! F ick s F irst Law where the diffusion constant , D , is the proportionality constant (or con- ductance of mass) given in the earlier general expression. The diffusion constant is related to microsopic properties of matter, namely the particles comprising the fluid, through the relation: D = 1 3 h...
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