The effects of surface proximity and force orientation on the feeding flows of microorganisms on solid surfaces

Many aquatic microorganisms are attached to solid surfaces while creating feeding flows that bring prey particles to them. To explore the effects of surface proximity and orientation of the flow-generating force, we analyze the low-Reynolds-number flow due to a point force above a plane no-slip surface. The presence of the surface reduces the feeding flow relative to the unbounded situation. We show that the reduction of the flow rate through a circular clearance disk perpendicular to the force and centered at its position is twice as large when the force is perpendicular to the surface as when it is parallel. When the force is perpendicular to the surface, the flow forms a toroidal eddy with closed streamlines, and the resulting flow recirculation may lead to refiltration of water that has already been cleared for prey. We prove that due to the nature of the far-field flow, the shortest recirculation time along a streamline through a circular clearance disk is inversely proportional to the flow rate to the power four. Finally, we discuss the biological advantages and disadvantages of perpendicular and parallel force orientation and the effects of prey diffusion and ambient flow, and we argue that recirculation is irrelevant in the typical perpendicular feeding flow since the recirculation time is long compared to the biologically relevant timescales.