PARTICLE MOTIONS IN SHEARED SUSPENSIONS: XVI. ORIENTATIONS OF RODS AND DISKS IN HYPERBOLIC AND OTHER FLOWS

Abstract

The angular velocity of a body of revolution suspended in a viscous fluid undergoing slow arbitrary shear flow is given. Integrated equations are derived for the orientation of its axis, directly in terms of the vorticity and dilatation components, for any flow in which the vorticity is parallel to a principal axis of dilatation; these are analogous to the equations for motion of a spheroid in Couette flow with an electric field parallel or perpendicular to the vorticity. The flows considered include examples of hyperbolic–parabolic, elliptic–spiral, and hyperbolic–logarithmic flows in three dimensions, as well as all two-dimensional shear flows.The behavior of certain bodies of revolution that remain stationary in Couette flow is discussed. Translational orbits of asymmetric bodies of revolution in Couette flow are calculated.The behavior of particles in some important shear flows is described, the theory of rotation in hyperbolic flow being developed in detail and confirmed experimentally with rods and disks. Comparison of equivalent ellipsoidal axis ratios obtained from Couette-flow and hyperbolic-flow measurements shows that the former are more accurate if the particle deviates greatly from the spherical shape.