Hydrodynamic drag force on porous sphere(s) moving in a Newtonian fluid: Two case studies

This paper is the first to evaluate numerically the hydrodynamic forces that apply in two case studies that involve a Newtonian fluid and three in-line spheres (case 1) and a sphere that moves in a circular cell (case 2). The hydrodynamic interactions between the spheres in case 1 or between the central sphere and the surrounding spherical wall in case 2 can be ignored at β (= d_f/2√k, where d_f and k are the diameter and permeability of the sphere, respectively) <0.5 (no-sphere limit), and the effects of interior flow in the sphere can be ignored at β>50 (solid sphere limit). At 0.5<β<50, the strength of the hydrodynamic interactions in the two studied cases increases with β. The porous spheres can move steadily with unchanged configurations at β<2. The incorporation of inertia weakens the effects of β in case 1 and both the effects of β and the suspension porosity in case 2 on the hydrodynamic interactions. At β>2, in neither case 1 nor case 2 can a steadily moving system form; in the former case, sweep coagulation-like behavior occurs, and in the latter, zone settling-like behavior occurs.