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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 Stokes flow ： ウィキペディア英語版 Stokes flow Stokes flow (named after George Gabriel Stokes), also named creeping flow or creeping motion,〔Kim, S. & Karrila, S. J. (2005) ''Microhydrodynamics: Principles and Selected Applications'', Dover. ISBN 0-486-44219-5.〕 is a type of fluid flow where advective inertial forces are small compared with viscous forces. The Reynolds number is low, i.e. $\backslash textit\; \backslash ll\; 1$. This is a typical situation in flows where the fluid velocities are very slow, the viscosities are very large, or the length-scales of the flow are very small. Creeping flow was first studied to understand lubrication. In nature this type of flow occurs in the swimming of microorganisms and sperm〔Dusenbery, David B. (2009). ''Living at Micro Scale''. Harvard University Press, Cambridge, Mass. ISBN 978-0-674-03116-6.〕 and the flow of lava. In technology, it occurs in paint, MEMS devices, and in the flow of viscous polymers generally. The equations of motion for Stokes flow, called the Stokes Equations, are a linearization of the Navier-Stokes Equations, and thus can be solved by a number of well-known methods for linear differential equations. The primary Green's function of Stokes flow is the Stokeslet, which is associated with a singular point force embedded in a Stokes flow. From its derivatives other fundamental solutions can be obtained.〔Chwang, A. and Wu, T. (1974). ("Hydromechanics of low-Reynolds-number flow. Part 2. Singularity method for Stokes flows" ). ''J. Fluid Mech. 62''(6), part 4, 787–815.〕 The fundamental solution due to a point force in a steady Stokes flow was first derived by the Nobel Laureate, Lorentz, as far back as 1896. This solution is now known by the name Stokeslet, although Stokes never knew about it. The name Stokeslet was coined by Hancock in 1953. The closed-form fundamental solutions for generalized unsteady Stokes and Oseen flows associated with arbitrary time-dependent translational and rotational motions have been derived for Newtonian and micropolar fluids. == Stokes equations == The equation of motion for Stokes flow can be obtained by linearizing the steady state Navier-Stokes Equations. The inertial forces are assumed to be negligible in comparison to the viscous forces, and eliminating the inertial terms of the momentum balance in the Navier–Stokes equations reduces it to the momentum balance in the Stokes equations:〔 :$\backslash boldsymbol\; \backslash cdot\; \backslash mathbb\; +\; \backslash mathbf\; =\; 0$ where $\backslash scriptstyle\; \backslash mathbb$ is the Cauchy stress tensor representing viscous and pressure stresses,〔Happel, J. & Brenner, H. (1981) ''Low Reynolds Number Hydrodynamics'', Springer. ISBN 90-01-37115-9.〕 and $\backslash scriptstyle\; \backslash mathbf$ an applied body force. The full Stokes equations also includes an equation for the conservation of mass, commonly written in the form: :$\backslash frac\; +\; \backslash rho\backslash nabla\backslash cdot\backslash mathbf\; =\; 0$ where $\backslash scriptstyle\; \backslash rho$ is the fluid density and $\backslash scriptstyle\; \backslash mathbf$ the fluid velocity. To obtain the equations of motion for incompressible flow, it is assumed that the density, $\backslash scriptstyle\; \backslash rho$, is a constant. Furthermore, occasionally one might consider the unsteady Stokes equations, in which the term $\backslash scriptstyle\; \backslash rho\; \backslash frac$ is added to the left hand side of the momentum balance equation.〔 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「Stokes flow」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.