Drag force of a particle moving axisymmetrically in open or closed cavities

Hydrodynamic resistance to particle transport arising from the solid mass in porous media is of fundamental importance. We investigate an axisymmetric creeping flow caused by a spherical particle migrating in a spherical cavity or connected cavities of equal size by a boundary element method. Each cavity has either one or two circular apertures, through which a sufficiently small particle can pass. Drag force on the particle is calculated to determine the correction factor to the Stokes law. It is found that when passing through an aperture, the particle experiences a local maximum drag force larger than that located in the cavity center. This force is also greater than that for the particle near the closed end at the same smallest surface-to-surface distance. For connected cavities open to the exterior fluid, the drag force is smaller than that in the corresponding closed system.