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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 Derjaguin approximation ： ウィキペディア英語版 Derjaguin approximation The Derjaguin approximation due to the Russian scientist Boris Derjaguin expresses the force profile acting between finite size bodies in terms of the force profile between two planar semi-infinite walls. This approximation is widely used to estimate forces between colloidal particles, as forces between two planar bodies are often much easier to calculate. The Derjaguin approximation expresses the force ''F''(''h'') between two bodies as a function of the surface separation as :$F(h)\; =\; 2\; \backslash pi\; R\_\; W(h),$ where ''W''(''h'') is the interaction energy per unit area between the two planar walls and ''R''eff the effective radius. When the two bodies are two spheres of radii ''R''1 and ''R''2, respectively, the effective radius is given by :$R\_^\; =\; R\_1^+R\_2^.$ Experimental force profiles between macroscopic bodies as measured with the surface forces apparatus (SFA)〔J. Israelachvili, ''Intermolecular and Surface Forces'', Academic Press, London, 1992.〕 or colloidal probe technique〔 〕 are often reported as the ratio ''F''(''h'')/''R''eff. ==Quantities involved and validity== The force ''F''(''h'') between two bodies is related to the interaction free energy ''U''(''h'') as :$F(h)\; =\; -\; ,$ where ''h'' is the surface-to-surface separation. Conversely, when the force profile is known, one can evaluate the interaction energy as :$U(h)\; =\; \backslash int\_h^\; F(h\text{'})\; \backslash ,\; dh\text{'}.$ When one considers two planar walls, the corresponding quantities are expressed per unit area. The disjoining pressure is the force per unit area and can be expressed by the derivative :$\backslash Pi(h)\; =\; -\; ,$ where ''W''(''h'') is the surface free energy per unit area. Conversely, one has :$W(h)\; =\; \backslash int\_h^\; \backslash Pi(h\text{'})\; \backslash ,\; dh\text{'}.$ The main restriction of the Derjaguin approximation is that it is only valid at distances much smaller than the size of the objects involved, namely ''h'' « ''R''1 and ''h'' « ''R''2. Furthermore, it is a continuum approximation and thus valid at distances larger than the molecular length scale. Even when rough surfaces are involved, this approximation has been shown to be valid in many situations. Its range of validity is restricted to distances larger than the characteristic size of the surface roughness features (e.g., root mean square roughness). 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「Derjaguin approximation」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.