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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 ffi ciently small that the particles di ff use 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 di ff usivity, 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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