Motion of a sphere and the suspending low-Reynolds-number fluid confined in a cubic cavity

Abstract

Dynamics of a spherical particle and the suspending low-Reynolds-number fluid confined by a cubic cavity were studied numerically. We calculated the particle’s hydrodynamic mobilities along $x$-, $y$-, and $z$-directions at various locations in the cavity. The mobility is largest in the cavity center and decays as the particle becomes closer to no-slip walls. It was found that mobilities in the entire cubic cavity can be determined by a minimal set in a unit tetrahedron therein. Fluid vortices in the cavity induced by the particle motion were observed and analyzed. We also found that the particle can exhibit a drift motion perpendicular to the external force. Magnitude of the drift velocity normalized by the velocity along the direction of the external force depends on particle location and particle-to-cavity sizes ratio. This work forms the basis to understand more complex dynamics in microfluidic applications such as intracellular transport and encapsulation technologies.