Abstract

Flow around a Reiner–Rivlin non-Newtonian liquid particle, which is surrounded with a Newtonian liquid shell and placed into a permeable medium, is studied. This formulation of the problem is typical for, e.g., studying the motion of an oil droplet surrounded with an aqueous medium (oil-in-water emulsion) in a porous collector under the action of an external pressure drop. An analogous problem is encountered when lymph penetrates into human or animal tissues. The flows inside of the permeable layer, in the region between the Reiner–Rivlin liquid and a porous medium, and inside of the spherical region are described by the Brinkman, Stokes, and Reiner–Rivlin equations, respectively. The general solution for the stream function in the external porous region is written in terms of the modified Bessel function and Gegenbauer polynomials. For the Reiner–Rivlin liquid sphere, the solution is found by expanding the stream function into a power series in terms of small dimensionless parameter S. The boundary problem is solved by conjugating the boundary conditions for all regions. The drag force applied to the Reiner–Rivlin liquid particle placed into the permeable medium is determined. The effects of permeability parameter α, viscosity ratio λ, and dimensionless parameter S on the drag coefficient are studied. Corresponding dependences are represented graphically and discussed. Known particular cases are described using passages to the limits.

中文翻译：

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在充满非牛顿液体并置于多孔介质中的液体球周围流动

摘要

研究了一个围绕着Reiner-Rivlin非牛顿液体粒子的流动，该粒子被牛顿液体壳包围并置于可渗透介质中。该问题的表述对于例如在外部压力降的作用下研究多孔收集器中被水性介质（水包油乳液）包围的油滴的运动是典型的。当淋巴渗透到人或动物组织中时，会遇到类似的问题。渗透层内部，在Reiner-Rivlin液体和多孔介质之间的区域以及球形区域内部的流动分别由Brinkman，Stokes和Reiner-Rivlin方程描述。外部多孔区域中流函数的一般解是根据修正的贝塞尔函数和Gegenbauer多项式编写的。小号。通过共轭所有区域的边界条件可以解决边界问题。确定施加到放置在渗透性介质中的Reiner-Rivlin液体颗粒上的阻力。研究了渗透率参数α，粘度比λ和无因次参数S对阻力系数的影响。相应的依赖关系以图形方式表示和讨论。已知的特定情况使用限制的段落进行描述。