Abstract

A semi-analytical study for the Stokes flow approximation caused by two solid spheres of different sizes with slip surfaces, immersed in a porous medium in the presence of a transverse magnetic field, is investigated. The two spheres are translating with different velocities along the line joining their centers. A general solution is developed from the superposition of the essential solutions in two spherical frameworks with origins located at the centers of the two spheres. Numerical results for the normalized hydrodynamic drag force acting on each sphere are obtained with good convergence for various values of the Hartmann number which characterizes the presence of magnetic field, the permeability parameter which characterizes the porous medium, separation parameter, and velocity and size ratios of the spheres. Our drag results are in good agreement with the available solutions in the literature in the cases of no-slip surfaces and when the porous medium turns into a pure fluid.

Graphic abstract

中文翻译：

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磁场对嵌入具有滑动表面的多孔介质中的两个刚性球运动的影响

摘要

对由两个不同大小的带滑动表面的固体球体引起的斯托克斯流近似进行了半分析研究，该固体球体在存在横向磁场的情况下浸入多孔介质中。两个球体沿着连接其中心的直线以不同的速度平移。从基本解在两个球体框架中的叠加中得出了一个通用解，其原点位于两个球体的中心。对于在表征磁场存在的哈特曼数，表征多孔介质的磁导率参数，分离参数以及速度和尺寸比的各种值的哈特曼数的各种值，具有良好的收敛性，获得了作用在每个球体上的归一化水动力阻力的数值结果，具有很好的收敛性。领域。

图形摘要