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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Nernst–Planck equation ： ウィキペディア英語版 Nernst–Planck equation The time dependent form of the Nernst–Planck equation is a conservation of mass equation used to describe the motion of a charged chemical species in a fluid medium. It describes the flux of ions under the influence of both an ionic concentration gradient $\backslash nabla\; c$ and an electric field $E=-\backslash nabla\; \backslash phi\; -\; \backslash frac$. 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: $\backslash frac\; =\; \backslash nabla\; \backslash cdot\; \backslash left(D\; \backslash nabla\; c\; -\; u\; c\; +\; \backslash fracc(\backslash nabla\; \backslash phi+\backslash frac)\; \backslash right)$ 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, * $k\_B$ is the Boltzmann constant * ''T'' is the temperature. * u is relative velocity of the observer to the ionic system 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. In the context of Neuroscience, this equation is best known in its steady-state form, where there is a balance of diffusion and drift. Setting time derivatives to zero, and noting that the term $J\; =\; -uc$ represents a current flux $J$ $\backslash nabla\; \backslash cdot\; \backslash left(D\; \backslash nabla\; c\; +\; J\; +\; \backslash fracc(\backslash nabla\; \backslash phi)\; \backslash right)=\; 0$ Integrating the divergence over an arbitrary surface, one obtains the steady state Nernst-Planck equation $J\; =\; -\backslash left(D\; \backslash nabla\; c\; +\; \backslash fracc(\backslash nabla\; \backslash phi)\; \backslash right)$ Finally, in units of $\backslash frac$ and the gas constant R, one obtains the more familiar form (e.g. 〔B. Hille (1992) Ionic Channels of Excitable Media, 2nd Edition, Sinauer, Sunderland Mass. p.267〕 $J\; =\; -zFD\backslash left(\backslash nabla\; c\; +\; \backslash frac(\backslash nabla\; \backslash phi)\; \backslash right)$ ==See also== *Goldman-Hodgkin-Katz equation *Bioelectrochemistry 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Nernst–Planck equation」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.