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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 Washburn's equation ： ウィキペディア英語版 Washburn's equation In physics, Washburn's equation describes capillary flow in a bundle of parallel cylindrical tubes; it is extended with some issues also to imbibition into porous materials. The equation is named after Edward Wight Washburn; also known as Lucas–Washburn equation, considering that Richard Lucas wrote a similar paper three years earlier, or the Bell-Cameron-Lucas-Washburn equation, considering J.M. Bell and F.K. Cameron's discovery of the form of the equation fifteen years earlier. ==Derivation== In case of a fully wettable capillary, it is :$$ L^2=\frac where $t$ is the time for a liquid of dynamic viscosity $\backslash eta$ and surface tension $\backslash gamma$ to penetrate a distance $L$ into the capillary whose pore diameter is $D$. In case of a porous materials many issues have been raised both about the physical meaning of the calculated pore diameter $D$ and the real possibility to use this equation for the calculation of the contact angle of the solid. The equation is derived for capillary flow in a cylindrical tube in the absence of a gravitational field, but is sufficiently accurate in many cases when the capillary force is still significantly greater than the gravitational force. In his (paper ) from 1921 Washburn applies Poiseuille's Law for fluid motion in a circular tube. Inserting the expression for the differential volume in terms of the length $l$ of fluid in the tube $dV=\backslash pi\; r^2\; dl$, one obtains :$\backslash frac=\backslash frac(r^4\; +4\; \backslash epsilon\; r^3)$ where $\backslash sum\; P$ is the sum over the participating pressures, such as the atmospheric pressure $P\_A$, the hydrostatic pressure $P\_h$ and the equivalent pressure due to capillary forces $P\_c$. $\backslash eta$ is the viscosity of the liquid, and $\backslash epsilon$ is the coefficient of slip, which is assumed to be 0 for wetting materials. $r$ is the radius of the capillary. The pressures in turn can be written as :$P\_h=h\; g\; \backslash rho\; -\; l\; g\; \backslash rho\backslash sin\backslash psi$ :$P\_c=\backslash frac\backslash cos\backslash phi$ where $\backslash rho$ is the density of the liquid and $\backslash gamma$ its surface tension. $\backslash psi$ is the angle of the tube with respect to the horizontal axis. $\backslash phi$ is the contact angle of the liquid on the capillary material. Substituting these expressions leads to the first-order differential equation for the distance the fluid penetrates into the tube $l$: :$\backslash frac=\backslash frac\backslash cos\backslash phi\; )(r^4\; +4\; \backslash epsilon\; r^3)\}$ 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「Washburn's 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.