Lecture5-6

J concentration net flux number of molecules that move

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Unformatted text preview: Fick’s laws (1855) 1. J … concentration (net) flux, number of molecules that move across an area A per unit time (units: #/area/time) c … concentration, here: number of molecules per volume (units: #/volume) x … average distance traveled by each molecule average distance traveled by each molecule in x-direction (positive or negative) in the time interval t c x, t 2 c x, t D t x 2 diffusion equation 2. where D x 2 2t one particular solution: x2 C1 c x, t exp C2 4 Dt t J … concentration (net) flux, number of molecules that move across an area A per unit time (units: #/area/time) Diffusion + Convection c x, t 2 c x, t D t x 2 c … concentration, here: number of molecules per volume (units: #/volume) x … average distance traveled by each molecule average distance traveled by each molecule in x-direction (positive or negative) in the time interval t diffusion equation Adding drift (at velocity v(x)) to Fick’s first law: drift (at velocity to Fick law: J x D dc x dx v xc x Drift is caused by force f acting on molecules, where c x, t t D 2 c x, t x 2 f x v x f x c x, t x At equilibrium, c is stationary (doesn’t change with time), and is given by the Boltzmann distribution: distribution: Concentration Probability number of molecules per volume c x, t … number of molecules per volume at position x at time t p x, t … probability of finding a molecule at position at position x at time t time c p, so we may replace the “concentration flux” J by the “probability flux” j p x, t 2 p x, t f x D p x, t t x x 2...
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This note was uploaded on 07/12/2011 for the course BIM 162 taught by Professor Heinrich during the Spring '11 term at UC Davis.

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