Department of Mathematics, Faculty of Sciences, Princess Nourah bint Abdulrahman University, Riyadh, Kingdom of Saudi Arabia.
Department of Mathematics, Faculty of Science, Damanhour University, Damanhour, Egypt.
Eur Phys J E Soft Matter. 2021 May 15;44(5):68. doi: 10.1140/epje/s10189-021-00073-2.
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.
研究了在横向磁场存在下，两个具有滑移面的不同大小固体球在多孔介质中引起的 Stokes 流近似的半分析解。这两个球体沿着它们的中心连线以不同的速度平移。通过将原点位于两个球体中心的两个球形框架中的基本解进行叠加，得到了一个通用解。对于各种哈特曼数（表征磁场的存在）、渗透率参数（表征多孔介质）、分离参数以及球体的速度和大小比，获得了作用于每个球体的归一化流体阻力的数值结果，收敛性良好。在无滑移表面的情况下以及当多孔介质变成纯流体时，我们的阻力结果与文献中可用的解非常吻合。
