Particle motions in sheared suspensions: V. Rigid rods and collision doublets of spheres

Abstract

The rotations executed by rigid rods, fused doublets of equal-sized spheres, and the transitory doublets formed by collision of equal-sized spheres suspended in a liquid subjected to laminar shear, have been studied by making observations along the planes of shear. In all cases there is excellent agreement with Jeffery's theoretical equations for rigid prolate spheroids when the equivalent axis ratio r e is used. For fused and collision doublets, including those in which there is visible separation at all times, r e = 2 except for nearly head-on collisions, when r e is greater. Unlike the earlier observations made across the shear planes, the collisions are not sharply defined. The paths of approach and recession are curvilinear and are mirror images of one another. The relative velocities of the two spheres vary continuously and the disturbance occurs well in advance of apparent particle contact. It is concluded that the spheres of the doublet do not touch. Doublets resulting from the rare occurrence of nearly head-on collisions show distinctive behavior with the two particles forming a doublet which executes a number of complete rotations. The collision doublet behavior differs in several respects from that found in the earlier observations from which it was inferred that the two spheres approach one another on a rectilinear path until they make apparent contact and then rotate with r e = 1 to the mirror-image position of separation. Equations are derived for the mean, maximum, and distribution of doublet lives corresponding to r e = 2. It is concluded, however, that for many calculations involving doublet life and collision frequency it is preferable to use the doublet equations based upon rectilinear approach and r e = 1. Finally, the distribution of orbit constants of collision doublets is calculated.