Theory and experiment on the three-dimensional motion of a freely suspended spherical particle at the entrance to a pore at low Reynolds number

This paper examines the three dimensional approach of a neutrally buoyant sphere of any size to a circular hole in a plane wall at very low Reynolds number. The analysis differs from previous studies, largely applied to the multipore filter, in that the authors investigate the three dimensional hydrodynamic interaction of the sphere with the entrance geometry of the pore in the limit of zero inertia. The problem is first exactly formulated as the linear superposition of fundamental Stokes flows for rotation and translation of the sphere and flow past a stationary sphere. Approximate solutions are then obtained for the deviation of sphere trajectories from fluid stream lines and the results compared with laboratory model experiments in a low Reynolds number settling tank. The theory and experiment show that because of the hydrodynamic interaction sphere trajectories and fluid streamlines deviate significantly as the opening is approached, that all spheres eventually enter the pore regardless of their initial position, but that a non-uniform concentration profile develops with large increases in concentration near the walls of the orifice in the vicinity of the opening. The results provide a basic mechanism to explain the onset of Fahraeus phenomenon for red cells entering small blood vessels and glass tubes.