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Corrector Equations in Fluid Mechanics: Effective Viscosity of Colloidal Suspensions
Archive for Rational Mechanics and Analysis ( IF 2.6 ) Pub Date : 2020-11-22 , DOI: 10.1007/s00205-020-01589-1 Mitia Duerinckx , Antoine Gloria
Archive for Rational Mechanics and Analysis ( IF 2.6 ) Pub Date : 2020-11-22 , DOI: 10.1007/s00205-020-01589-1 Mitia Duerinckx , Antoine Gloria
Consider a colloidal suspension of rigid particles in a steady Stokes flow. In a celebrated work, Einstein argued that in the regime of dilute particles the system behaves at leading order like a Stokes fluid with some explicit effective viscosity. In the present contribution, we rigorously define a notion of effective viscosity, regardless of the dilute regime assumption. More precisely, we establish a homogenization result for when particles are distributed according to a given stationary and ergodic random point process. The main novelty is the introduction and analysis of suitable corrector equations.
中文翻译:
流体力学中的修正方程:胶体悬浮液的有效粘度
考虑在稳定的斯托克斯流中刚性粒子的胶体悬浮液。在一项著名的工作中,爱因斯坦认为,在稀粒子状态下,系统的行为就像斯托克斯流体一样,具有一定的显性有效粘度。在目前的贡献中,我们严格定义了有效粘度的概念,而不管稀释状态假设如何。更准确地说,我们建立了粒子根据给定的平稳遍历随机点过程分布时的均质化结果。主要新颖之处在于引入和分析了合适的校正方程。
更新日期:2020-11-22
中文翻译:
流体力学中的修正方程:胶体悬浮液的有效粘度
考虑在稳定的斯托克斯流中刚性粒子的胶体悬浮液。在一项著名的工作中,爱因斯坦认为,在稀粒子状态下,系统的行为就像斯托克斯流体一样,具有一定的显性有效粘度。在目前的贡献中,我们严格定义了有效粘度的概念,而不管稀释状态假设如何。更准确地说,我们建立了粒子根据给定的平稳遍历随机点过程分布时的均质化结果。主要新颖之处在于引入和分析了合适的校正方程。