Abstract

Analytical solutions of the non-steady-state Brinkman equation that describes the flow of a fluid inside a porous spherical shell with a solid impermeable core immersed into it, which makes translational oscillatory motions, and of the Navier–Stokes equation in the Stokes approximation outside the shell are obtained. The fields of the filtration rates in the porous medium and velocities of the free fluid outside the porous shell are determined. The force acting on the control spherical surface around the porous shell is determined. An analysis of the solutions is presented. Different particular cases, including the case of uniform motion of the porous shell in the viscous fluid, are considered.

中文翻译：

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具有固体不渗透核心的多孔球壳在粘性流体中的平移振荡运动

摘要

非稳态 Brinkman 方程的解析解，该方程描述了多孔球壳内的流体流动，其中浸入了一个固体不可渗透的核心，这会产生平移振荡运动，以及外部 Stokes 近似中的 Navier-Stokes 方程的解析解得到外壳。确定了多孔介质中的过滤速率和多孔壳外自由流体的速度场。确定作用在多孔壳周围的控制球面上的力。提出了解决方案的分析。考虑了不同的特殊情况，包括多孔壳在粘性流体中匀速运动的情况。