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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 | | |||
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 | | |||
year=1994}}</ref> | |||
<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> | |||
Where | |||
* t is time, | |||
* D is the [[Mass diffusivity|diffusivity]] of the chemical species, | |||
* c is the concentration of the species, and u is the velocity of the fluid, | |||
* ''z'' is the valence of ionic species, | |||
* ''e'' is the [[elementary charge]], | |||
* <math>k_B</math> is the [[Boltzmann constant]] | |||
* ''T'' is the temperature. | |||
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. --> | |||
}}</ref> | |||
==See also== | |||
*[[Goldman-Hodgkin-Katz equation]] | |||
*[[Bioelectrochemistry]] | |||
==Notes== | |||
{{reflist}} | |||
{{DEFAULTSORT:Nernst-Planck equation}} | |||
[[Category:Articles with inconsistent citation formats]] | |||
[[Category:Diffusion]] | |||
[[Category:Physical chemistry]] | |||
[[Category:Electrochemical equations]] | |||
[[Category:Statistical mechanics]] | |||
Revision as of 16:31, 24 November 2013
The Nernst–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 ions under the influence of both an ionic concentration gradient and an electric field . 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:[1][2]
![{\displaystyle {\frac {\partial c}{\partial t}}=\nabla \cdot \left[D\nabla c-uc+{\frac {Dze}{k_{B}T}}c(\nabla \phi +{\frac {\partial \mathbf {A} }{\partial t}})\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fb3d07caafab14ab57b17a095e937cfb0fa641fd)
Where
- t is time,
- D is the diffusivity of the chemical species,
- c is the concentration of the species, and u is the velocity of the fluid,
- z is the valence of ionic species,
- e is the elementary charge,
- is the Boltzmann constant
- T is the temperature.
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 kinetics in soils.[3]
See also
Notes
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- ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ Template:Cite document