Settling dynamics of two spheres in a suspension of Brownian rods

Abstract

We investigate via numerical simulations the settling dynamics of two non-Brownian rigid spheres in a dilute suspension of Brownian rods at low Reynolds numbers. Specifically, this work focuses on how the overall settling dynamics is affected by the coupling between the flow field around the spheres and the orientation of the rods. The Brownian motion introduces a finite relaxation time in the suspending medium which is modeled as a continuum. When the spheres fall along their centerline, the spheres experience two contributions: one Newtonian and a non-Newtonian contribution due to the presence of the Brownian rods. The interactions between the two settling spheres are evaluated as a function of Péclet number (Pe) and the distance between the centers of the spheres. Repulsive interactions are found, and these interactions are affected by Pe and the distance between the centers of the spheres. An analysis of the flow fields highlights the origin of these repulsive interactions in non-Newtonian elongational effects.