The problem of the boundary condition setting is considered for creeping flows over cylindrical and spherical obstacles. The interaction of Newtonian and micropolar liquid with the solid surface is discussed in the context of the Stokes paradox and the cell model technique. Mathematical and mechanical aspects of various types of boundary conditions at the hypothetical liquid surface are considered in the framework of the spherical cell model used for the simulation of membrane flows. New properties of the flow pattern in a spherical cell are found, and their independence of the boundary conditions is rigorously proved. The criteria of the boundary conditions equivalence are derived in terms of the membrane porosity and hydrodynamic permeability.

中文翻译：

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关于斯托克斯流中的边界条件

边界条件设置的问题考虑了圆柱和球形障碍物上的蠕动流。牛顿和微极性液体与固体表面的相互作用在斯托克斯悖论和细胞模型技术的背景下进行了讨论。在用于模拟膜流动的球形单元模型的框架中考虑了假设液体表面处各种类型边界条件的数学和机械方面。发现了球形单元中流动模式的新特性，并严格证明了它们与边界条件的独立性。边界条件等效的标准是根据膜孔隙率和水动力渗透率推导出来的。