MIT10_626S11_lec22

MIT10_626S11_lec22 - IV. Transport Phenomena Lecture 22:...

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IV. Transport Phenomena Lecture 22: Transport in Bulk Electrolytes MIT Student 1 Nernst-Planck Equations The continuity equation for a species i is an expression of conservation of that species under conditions where the concentration can be assumed to be a continuous field. The continuity equation can be expressed in vectorial form as Dc i = Dt -∇· F i For a dilute solute, that is, for a solute whose concentration is su±ciently small that the particles di²use independently and are not coupled by the motion of the surrounding fluid (or any other interaction), the flux F i is given by Fick’s law as F i = - D i c i . However, in the case of a charged solute subject to an electric field, the solute flux has a contribution of the form F i , E =c i M i (z i e E ), where M i is the mobility of the solute in solution. Using the Einstein relation between the mobility and the di²usivity, and writing the electric field in terms of the scalar potential, the total flux is ± ez F i = - D i c - i i c i k B T
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This note was uploaded on 11/27/2011 for the course CHEMICAL E 20.410j taught by Professor Rogerd.kamm during the Spring '03 term at MIT.

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MIT10_626S11_lec22 - IV. Transport Phenomena Lecture 22:...

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