Streamlines around single spheres and trajectories of pairs of spheres in two-dimensional creeping flows

Abstract

A general two-dimensional linear flow having pure shear (or two-dimensional extensional) flow as one limit and pure rotation as the other, with simple shear flow as an intermediate case is discussed. Calculations of the streamlines around a rigid, neutrally buoyant sphere in creeping flow indicate that there are both closed and open streamlines in the flow regimes between pure and simple shear, whereas only closed streamlines exist between simple shear and pure rotation. The only flow in which closed streamlines do not exist is pure shear. The trajectories of two neutral spheres of equal size in this family of flows have also been calculated. Closed trajectories do not exist in a large regime of flows near pure shear. The significance of these findings with particular reference to hydrodynamic dispersion is discussed.