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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 Herschel–Bulkley fluid ： ウィキペディア英語版 Herschel–Bulkley fluid The Herschel–Bulkley fluid is a generalized model of a non-Newtonian fluid, in which the strain experienced by the fluid is related to the stress in a complicated, non-linear way. Three parameters characterize this relationship: the consistency ''k'', the flow index ''n'', and the yield shear stress $\backslash tau\_0$. The consistency is a simple constant of proportionality, while the flow index measures the degree to which the fluid is shear-thinning or shear-thickening. Ordinary paint is one example of a shear-thinning fluid, while oobleck provides one realization of a shear-thickening fluid. Finally, the yield stress quantifies the amount of stress that the fluid may experience before it yields and begins to flow. This non-Newtonian fluid model was introduced by Winslow Herschel and Ronald Bulkley in 1926. ==Definition== The constitutive equation of the Herschel-Bulkley model is commonly written as :$\backslash tau\; =\; \backslash tau\_\; +\; k\; \backslash dot\; ^$ where $\backslash tau$ is the shear stress, $\backslash dot$ the shear rate, $\backslash tau\_$ the yield stress, $k$ the consistency index, and $n$ the flow index. If the Herschel-Bulkley fluid behaves as a solid, otherwise it behaves as a fluid. For the fluid is shear-thinning, whereas for $n>1$ the fluid is shear-thickening. If $n=1$ and $\backslash tau\_0=0$, this model reduces to the Newtonian fluid. As a generalized Newtonian fluid model, the effective viscosity is given as 〔K. C. Sahu, P. Valluri, P. D. M. Spelt, and O. K. Matar (2007) 'Linear instability of pressure-driven channel flow of a Newtonian and a Herschel–Bulkley fluid' Phys. Fluids 19, 122101〕 :$$ \mu_ \mu_0, & |\dot| \leq \dot_0 \\ k |\dot|^+\tau_0 |\dot|^ , & |\dot| \geq \dot_0 \end The limiting viscosity $\backslash mu\_0$ is chosen such that $\backslash mu\_0=k\; \backslash dot\_0^+\backslash tau\_0\; \backslash dot\_0^$. A large limiting viscosity means that the fluid will only flow in response to a large applied force. This feature captures the Bingham-type behaviour of the fluid. The viscous stress tensor is given, in the usual way, as a viscosity, multiplied by the rate-of-strain tensor :$\backslash tau\_\; =\; 2\; \backslash mu\_|)\; E\_\; =\; \backslash mu\_|)\; \backslash left(\backslash frac+\backslash frac\backslash right),$ where the magnitude of the shear rate is given by :$|\backslash dot|=\backslash sqrt\}$. The magnitude of the shear rate is an isotropic approximation, and it is coupled with the second invariant of the rate-of-strain tensor :$II\_E\; =\; tr(E\_\; E^)\; =\; E\_E^$. 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「Herschel–Bulkley fluid」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.