ネルンストプランクの式
WordNet
- the act of regarding as equal (同)equating
- a mathematical statement that two expressions are equal
- German physicist whose explanation of blackbody radiation in the context of quantized energy emissions initiated quantum theory (1858-1947) (同)Max Planck, Max Karl Ernst Ludwig Planck
- German physicist and chemist who formulated the third law of thermodynamics (1864-1941) (同)Walther Hermann Nernst
PrepTutorEJDIC
- 等式; 方程式
Wikipedia preview
出典(authority):フリー百科事典『ウィキペディア(Wikipedia)』「2014/01/18 15:11:12」(JST)
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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]
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[edit]
- Goldman-Hodgkin-Katz equation
- Bioelectrochemistry
Notes[edit]
- ^ Kirby BJ. (2010). Micro- and Nanoscale Fluid Mechanics: Transport in Microfluidic Devices: Chapter 11: Species and Charge Transport.
- ^ Probstein R (1994). Physicochemical Hydrodynamics.
- ^ Sparks, D.L. (1988). Kinetics of Soil Chemical Processes. Academic Press, New York. pp. 101ff
UpToDate Contents
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English Journal
- A New Poisson-Nernst-Planck Model with Ion-Water Interactions for Charge Transport in Ion Channels.
- Chen D1.
- Bulletin of mathematical biology.Bull Math Biol.2016 Aug 1. [Epub ahead of print]
- In this work, we propose a new Poisson-Nernst-Planck (PNP) model with ion-water interactions for biological charge transport in ion channels. Due to narrow geometries of these membrane proteins, ion-water interaction is critical for both dielectric property of water molecules in channel pore and tra
- PMID 27480225
- Coupled metal partitioning dynamics and toxicodynamics at biointerfaces: a theory beyond the biotic ligand model framework.
- Duval JF1.
- Physical chemistry chemical physics : PCCP.Phys Chem Chem Phys.2016 Apr 14;18(14):9453-69. doi: 10.1039/c5cp07780j. Epub 2016 Mar 16.
- A mechanistic understanding of the processes governing metal toxicity to microorganisms (bacteria, algae) calls for an adequate formulation of metal partitioning at biointerfaces during cell exposure. This includes the account of metal transport dynamics from bulk solution to biomembrane and the kin
- PMID 26980542
- Modeling pH variation in reverse osmosis.
- Nir O1, Bishop NF2, Lahav O1, Freger V3.
- Water research.Water Res.2015 Dec 15;87:328-35. doi: 10.1016/j.watres.2015.09.038. Epub 2015 Sep 28.
- The transport of hydronium and hydroxide ions through reverse osmosis membranes constitutes a unique case of ionic species characterized by uncommonly high permeabilities. Combined with electromigration, this leads to complex behavior of permeate pH, e.g., negative rejection, as often observed for m
- PMID 26447944
Japanese Journal
- 谷岡 明彦
- 日本海水学会誌 = Bulletin of the Society of Sea Water Science, Japan 65(5), 294-300, 2011-10-01
- NAID 10029481836
- Asymptotic Expansion of Solution to the Nernst-Planck Drift-Diffusion Equation (Mathematical analysis on the self-organization and self-similarity)
- 1101 ナノ流路内のイオン輸送における電気二重層と界面電荷の影響(2)(OS11-1 ナノ・マイクロフルイディクス(ナノ・マイクロチャンネル),OS11 ナノ・マイクロフルイディクス,オーガナイズドセッション)
- 新宅 博文,川野 聡恭
- 流体工学部門講演会講演論文集 2007, "1101-1"-"1101-4", 2007-11-17
- … The numerical code which can calculates the electric field and ionic distribution in nanochannel is developed based on the Poisson-Nernst-Planck equation using finite difference method. … At lower ionic concentrations, the numerical result deviates from the Graham equation due to the overlapped electric double layer. …
- NAID 110008617740
Related Links
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- Next: Cubic Nonlinear ODE Up: Derivations For the Curious Previous: Derivations For the Curious Index Click for printer friendely version of this HowTo Nernst-Planck Equation When ions are in solution, there are three mechanisms ...
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