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| The '''[[Nernst]]–[[Max Planck|Planck]] equation''' is a conservation of mass equation used to describe the motion of chemical species in a fluid medium. It describes the flux of [[ion]]s under the influence of both an ionic [[concentration gradient]] <math>\nabla c</math> and an [[electric field]] <math>E=-\nabla \phi - \frac{\partial \mathbf A}{\partial t}</math>. It extends [[Fick's law of diffusion]] for the case where the diffusing particles are also moved with respect to the fluid by electrostatic forces:<ref name=Kirby>{{cite book | author=Kirby BJ. | title=Micro- and Nanoscale Fluid Mechanics: Transport in Microfluidic Devices: Chapter 11: Species and Charge Transport | | | The writer's title is Christy Brookins. One of the extremely very best things in the globe for him is doing ballet and he'll be beginning something else alongside with it. North Carolina is the place he loves most but now he is considering other choices. He is an purchase clerk and it's some thing he really appreciate.<br><br>my blog post: clairvoyant psychic ([http://Cartoonkorea.com/ce002/1093612 agree with this]) |
| url=http://www.kirbyresearch.com/index.cfm/wrap/textbook/microfluidicsnanofluidicsch11.html | year=2010}}</ref><ref name=Probstein>{{cite book | author=Probstein R | title=Physicochemical Hydrodynamics |
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| year=1994}}</ref>
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| <math>\frac{\partial c}{\partial t} = \nabla \cdot \left[ D \nabla c - u c + \frac{Dze}{k_B T}c(\nabla \phi+\frac{\partial \mathbf A}{\partial t}) \right]</math>
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| Where
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| * t is time,
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| * D is the [[Mass diffusivity|diffusivity]] of the chemical species,
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| * c is the concentration of the species, and u is the velocity of the fluid,
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| * ''z'' is the valence of ionic species,
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| * ''e'' is the [[elementary charge]],
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| * <math>k_B</math> is the [[Boltzmann constant]]
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| * ''T'' is the temperature.
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| If the diffusing particles are themselves charged they influence the electric field on moving. Hence the Nernst–Planck equation is applied in describing the [[ion-exchange]] [[chemical kinetics|kinetics]] in soils.<ref name=Sparks1988>{{Cite document | last = Sparks | first = D.L. | year = 1988 | title = Kinetics of Soil Chemical Processes. | publisher=Academic Press, New York | pages = 101ff | postscript = <!-- Bot inserted parameter. Either remove it; or change its value to "." for the cite to end in a ".", as necessary. -->
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| }}</ref>
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| ==See also==
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| *[[Goldman-Hodgkin-Katz equation]]
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| *[[Bioelectrochemistry]]
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| ==Notes==
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| {{reflist}}
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| {{DEFAULTSORT:Nernst-Planck equation}}
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| [[Category:Articles with inconsistent citation formats]] | |
| [[Category:Diffusion]]
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| [[Category:Physical chemistry]]
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| [[Category:Electrochemical equations]]
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| [[Category:Statistical mechanics]]
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