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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 Mason–Weaver equation ： ウィキペディア英語版 Mason–Weaver equation The Mason–Weaver equation (named after Max Mason and Warren Weaver) describes the sedimentation and diffusion of solutes under a uniform force, usually a gravitational field. Assuming that the gravitational field is aligned in the ''z'' direction (Fig. 1), the Mason–Weaver equation may be written :$$ \frac = D \frac where ''t'' is the time, ''c'' is the solute concentration (moles per unit length in the ''z''-direction), and the parameters ''D'', ''s'', and ''g'' represent the solute diffusion constant, sedimentation coefficient and the (presumed constant) acceleration of gravity, respectively. The Mason–Weaver equation is complemented by the boundary conditions :$$ D \frac + s g c = 0 at the top and bottom of the cell, denoted as $z\_$ and $z\_$, respectively (Fig. 1). These boundary conditions correspond to the physical requirement that no solute pass through the top and bottom of the cell, i.e., that the flux there be zero. The cell is assumed to be rectangular and aligned with the Cartesian axes (Fig. 1), so that the net flux through the side walls is likewise zero. Hence, the total amount of solute in the cell :$$ N_ = \int_} dz \ c(z, t) is conserved, i.e., $dN\_/dt\; =\; 0$. ==Derivation of the Mason–Weaver equation== A typical particle of mass ''m'' moving with vertical velocity ''v'' is acted upon by three forces (Fig. 1): the drag force $f\; v$, the force of gravity $m\; g$ and the buoyant force $\backslash rho\; V\; g$, where ''g'' is the acceleration of gravity, ''V'' is the solute particle volume and $\backslash rho$ is the solvent density. At equilibrium (typically reached in roughly 10 ns for molecular solutes), the particle attains a terminal velocity $v\_$ where the three forces are balanced. Since ''V'' equals the particle mass ''m'' times its partial specific volume $\backslash bar$, the equilibrium condition may be written as :$$ f v_ = m (1 - \bar \rho) g \ \stackrel\ m_ g where $m\_$ is the buoyant mass. We define the Mason–Weaver sedimentation coefficient $s\; \backslash \; \backslash stackrel\backslash \; m\_\; /\; f\; =\; v\_/g$. Since the drag coefficient ''f'' is related to the diffusion constant ''D'' by the Einstein relation :$$ D = \frac , the ratio of ''s'' and ''D'' equals :$$ \frac = \frac T} where $k\_$ is the Boltzmann constant and ''T'' is the temperature in kelvins. The flux ''J'' at any point is given by :$$ J = -D \frac - v_ c = -D \frac - s g c. The first term describes the flux due to diffusion down a concentration gradient, whereas the second term describes the convective flux due to the average velocity $v\_$ of the particles. A positive net flux out of a small volume produces a negative change in the local concentration within that volume :$$ \frac = -\frac. Substituting the equation for the flux ''J'' produces the Mason–Weaver equation :$$ \frac = D \frac. 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「Mason–Weaver 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.