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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 Fick's law of diffusion ： ウィキペディア英語版 Fick's laws of diffusion Fick's laws of diffusion describe diffusion and were derived by Adolf Fick in 1855. They can be used to solve for the diffusion coefficient, ''D''. Fick's first law can be used to derive his second law which in turn is identical to the diffusion equation. == Fick's first law == Fick's first law relates the diffusive flux to the concentration under the assumption of steady state. It postulates that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient (spatial derivative), or in simplistic terms the concept that a solute will move from a region of high concentration to a region of low concentration across a concentration gradient. In one (spatial) dimension, the law is: :$\backslash bigg.\; J\; =\; -D\; \backslash frac\; \backslash bigg.$ where * $J$ is the "diffusion flux," of which the dimension is amount of substance per unit area per unit time, so it is expressed in such units as $(\backslash tfrac)$. $J$ measures the amount of substance that will flow through a small area during a small time interval. * $\backslash ,\; D$ is the diffusion coefficient or diffusivity. Its dimension is area per unit time, so typical units for expressing it would be $(\backslash tfrac)$. * $\backslash ,\; \backslash phi$ (for ideal mixtures) is the concentration, of which the dimension is amount of substance per unit volume. It might be expressed in units of $(\backslash tfrac)$. * $\backslash ,\; x$ is position, the dimension of which is length. It might thus be expressed in the unit $\backslash ,\backslash mathrm\; m$. $\backslash ,\; D$ is proportional to the squared velocity of the diffusing particles, which depends on the temperature, viscosity of the fluid and the size of the particles according to the Stokes-Einstein relation. In dilute aqueous solutions the diffusion coefficients of most ions are similar and have values that at room temperature are in the range of 0.6x10−9 to 2x10−9 m2/s. For biological molecules the diffusion coefficients normally range from 10−11 to 10−10 m2/s. In two or more dimensions we must use $\backslash nabla$, the del or gradient operator, which generalises the first derivative, obtaining :$\backslash mathbf=-\; D\backslash nabla\; \backslash phi$ where J denotes the diffusion flux vector. The driving force for the one-dimensional diffusion is the quantity $-\; \backslash frac$ which for ideal mixtures is the concentration gradient. In chemical systems other than ideal solutions or mixtures, the driving force for diffusion of each species is the gradient of chemical potential of this species. Then Fick's first law (one-dimensional case) can be written as: :$J\_i\; =\; -\; \backslash frac\; \backslash frac$ where the index i denotes the ith species, c is the concentration (mol/m3), R is the universal gas constant (J/(K mol)), T is the absolute temperature (K), and μ is the chemical potential (J/mol). If the primary variable is mass fraction ($y\_i$, given, for example, in $\backslash tfrac$), then the equation changes to: :$J\_i=-\; \backslash rho\; D\backslash nabla\; y\_i$ where $\backslash rho$ is the fluid density (for example, in $\backslash tfrac$). Note that the density is outside the gradient operator. 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「Fick's laws of diffusion」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.