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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 Oldroyd-B model ： ウィキペディア英語版 Oldroyd-B model The Oldroyd-B model is a constitutive model used to describe the flow of viscoelastic fluids. This model can be regarded as an extension of the Upper Convected Maxwell model and is equivalent to a fluid filled with elastic bead and spring dumbbells. The model is named after its creator James G. Oldroyd.〔 The model can be written as: :$\backslash mathbf\; +\; \backslash lambda\_1\; \backslash stackrel\; +\; \backslash lambda\_2\; \backslash stackrel$ is the stress tensor; * $\backslash lambda\_1$ is the relaxation time; * $\backslash lambda\_2$ is the retardation time = $\backslash frac\backslash lambda\_1$; * $\backslash stackrel\; \backslash mathbf\; +\; \backslash mathbf\; \backslash cdot\; \backslash nabla\; \backslash mathbf\; -(\; (\backslash nabla\; \backslash mathbf)^T\; \backslash cdot\; \backslash mathbf\; +\; \backslash mathbf\; \backslash cdot\; (\backslash nabla\; \backslash mathbf))$; *$\backslash mathbf$ is the fluid velocity; *$\backslash eta\_0$ is the total viscosity composed of solvent and polymer components, $\backslash eta\_0=\; \backslash eta\_s\; +\; \backslash eta\_p$; *$\backslash mathbf$ is the deformation rate tensor or rate of strain tensor, $\backslash mathbf\; =\; \backslash frac\backslash left(\backslash mathbf\; +\; (\backslash boldsymbol\backslash nabla\; \backslash mathbf)^T\backslash right)$. The model can also be written split into polymeric (viscoelastic) part separately from the solvent part:〔 $\backslash mathbf\; =\; 2\backslash eta\_s\; \backslash mathbf\; +\; \backslash mathbf$. where :$\backslash mathbf\; +\; \backslash lambda\_1\; \backslash stackrel$ Whilst the model gives good approximations of viscoelastic fluids in shear flow, it has an unphysical singularity in extensional flow, where the dumbbells are infinitely stretched. This is, however, specific to idealised flow; in the case of a cross-slot geometry the extensional flow is not ideal, so the stress, although singular, remains integrable, i.e. the stress is infinite in a correspondingly infinitely small region.〔 If the solvent viscosity is zero, the Oldroyd-B becomes the Upper Convected Maxwell model. ==References== 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「Oldroyd-B model」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.