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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 Faxén's law ： ウィキペディア英語版 Faxén's law In fluid dynamics, Faxén's laws relate a sphere's velocity $\backslash mathbf$ and angular velocity $\backslash mathbf$ to the forces, torque, stresslet and flow it experiences under low Reynolds number (creeping flow) conditions. ==First law== Faxen's first law was introduced in 1922 by Swedish physicist Hilding Faxén, who at the time was active at Uppsala University, and is given by〔Durlofsky, Louis, John F. Brady, and Georges Bossis. "Dynamic simulation of hydrodynamically interacting particles." Journal of fluid mechanics 180.1 (1987): 21-49 , equations (2.15a, b, c). Note sign change.〕 :$$ \mathbf = 6 \pi \mu a \left(\left( 1 + \frac \nabla^2\right) \mathbf' - (\mathbf - \mathbf^\infty) \right ), where * $\backslash mathbf$ is the force exerted by the fluid on the sphere * $\backslash mu$ is the Newtonian viscosity of the solvent in which the sphere is placed * $a$ is the sphere's radius * $\backslash mathbf$ is the (translational) velocity of the sphere * $\backslash mathbf\text{'}$ is the disturbance velocity caused by the other spheres in suspension (not by the background impressed flow), evaluated at the sphere centre * $\backslash mathbf^\backslash infty$ is the background impressed flow, evaluated at the sphere centre (set to zero in some references). It can also be written in the form :$$ \mathbf - \mathbf^\infty = \mathbf' + b_0 \mathbf + \frac \nabla^2 \mathbf', where $b\_0\; =\; -\backslash frac$ is the mobility. In the case that the pressure gradient is small compared with the length scale of the sphere's diameter, and when there is no external force, the last two terms of this form may be neglected. In this case the external fluid flow simply advects the sphere. 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「Faxén's law」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.