The axisymmetric motion of a spherical particle in the presence of a porous interface is considered in the limit of small Reynolds and capillary numbers where the interface is of negligible deformation. We consider the translation along and the rotation about an axis perpendicular to the interface. The flow through the porous medium is modeled by Brinkman equation with a tangential stress jump condition applied at the interface and a slip boundary condition is used at the surface of the particle. A semi-analytical approach based on a collocation technique is used. Due to the linearity of the present problem, the flow variables for the two flow regions are constructed by superposing basic solutions in both cylindrical and spherical coordinate systems. The collocation solutions for the normalized hydrodynamic drag force and torque acted on the particle are calculated with good convergence for various values of the separation parameter, the stress jump coefficient, viscosity ratio and the permeability parameter. The results for the normalized drag and torque coefficients are in good agreement with the available solutions in the literature for the limiting cases.

在存在多孔界面的情况下，球形粒子的轴对称运动被认为是在小雷诺数和毛细管数的限制下，其中界面的变形可以忽略不计。我们考虑沿垂直于界面的轴的平移和旋转。通过多孔介质的流动由 Brinkman 方程建模，在界面处应用切向应力跳跃条件，在颗粒表面使用滑动边界条件。使用基于搭配技术的半分析方法。由于当前问题的线性，两个流动区域的流动变量是通过在圆柱坐标系和球坐标系中叠加基本解来构造的。对作用在颗粒上的归一化流体动力拖曳力和扭矩的配置解进行了计算，对于分离参数、应力跳跃系数、粘度比和渗透率参数的各种值具有良好的收敛性。归一化阻力和扭矩系数的结果与文献中针对极限情况的可用解决方案非常一致。