翻訳と辞書 Words near each other ・ Capital Bars ・ Capital Beat ・ Capital Beltway (Amtrak station) ・ Capital Beltway (disambiguation) ・ Capital Beltway (Harrisburg) ・ Capital Beltway Hockey League ・ Capital Bikeshare ・ Capital Birmingham ・ Capital Bixi ・ Capital Bowl ・ Capital Breakfast (London) ・ Capillary length ・ Capillary number ・ Capillary pressure ・ Capillary refill ・ Capillary surface ・ Capillary Technologies ・ Capillary tube mat ・ Capillary wave ・ Capillas ・ Capillas District ・ Capillaster ・ Capillataspora ・ Capillipedium ・ Capillipes ・ Capillistichus ・ Capillitium ・ Capillovirus ・ Capim ・ Capim Branco Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Capillary surface ： ウィキペディア英語版 Capillary surface In fluid mechanics and mathematics, a capillary surface is a surface that represents the interface between two different fluids. As a consequence of being a surface, a capillary surface has no thickness in slight contrast with most real fluid interfaces. Capillary surfaces are of interest in mathematics because the problems involved are very nonlinear and have interesting properties, such as discontinuous dependence on boundary data at isolated points. In particular, static capillary surfaces with gravity absent have constant mean curvature, so that a minimal surface is a special case of static capillary surface. They are also of practical interest for fluid management in space (or other environments free of body forces), where both flow and static configuration are often dominated by capillary effects. ==The stress balance equation== The defining equation for a capillary surface is called the stress balance equation,〔(Surface Tension Module ), by John W. M. Bush, at MIT OCW〕 which can be derived by considering the forces and stresses acting on a small volume that is partly bounded by a capillary surface. For a fluid meeting another fluid (the "other" fluid notated with bars) at a surface $S$, the equation reads :$(\backslash sigma\_\; -\; \backslash bar\_)\; \backslash mathbf\}\; (\backslash nabla\_\; \backslash cdot\; \backslash mathbf\; \backslash gamma\; \backslash qquad\; ;\; \backslash quad\; \backslash nabla\_\; \backslash gamma\; =\; \backslash nabla\; \backslash gamma\; -\; \backslash mathbf\}\; \backslash cdot\; \backslash nabla\; \backslash gamma)$ where $\backslash scriptstyle\; \backslash mathbf$ is the stress tensor (note that on the left is a tensor-vector product), $\backslash scriptstyle\; \backslash gamma$ is the surface tension associated with the interface, and $\backslash scriptstyle\; \backslash nabla\_S$ is the surface gradient. Note that the quantity $\backslash scriptstyle\; -\backslash nabla\_\; \backslash cdot\; \backslash mathbf\; -\; \backslash bar\_)\; \backslash mathbf\}\; =\; -\backslash gamma\; \backslash nabla\_\; \backslash cdot\; \backslash mathbf\; -\; \backslash bar\_)\; \backslash mathbf\_1\}\; =\; \backslash nabla\_\; \backslash gamma\; \backslash cdot\; \backslash mathbf$ :$((\backslash sigma\_\; -\; \backslash bar\_)\; \backslash mathbf\_2\}\; =\; \backslash nabla\_\; \backslash gamma\; \backslash cdot\; \backslash mathbf$ Note that the products lacking dots are tensor products of tensors with vectors (resulting in vectors similar to a matrix-vector product), those with dots are dot products. The first equation is called the normal stress equation, or the normal stress boundary condition. The second two equations are called tangential stress equations. 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「Capillary surface」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.