Computations of bubbles and drops in shear flow.

Abstract

Full numerical simulations of two- and three-dimensional bubbles and drops in shear flows are presented. The method used is based on a finite difference approximation of the full Navier-Stokes equations and explicit tracking of the interface between the fluids. The effect of inertial, viscous, and gravitational forces on the lateral migration and lift force of a deformable bubble rising due to buoyancy in a vertical shear flow, is discussed. Lateral migration of particles in a shear flow is influenced by relative motion and rotation. When surface tension is sufficiently large, so that the bubble remains spherical, the bubble migrates in the direction of downward fluid motion. This is as predicted analytically for a cylinder or a sphere in an inviscid, uniform shear flow. However, when surface tension is smaller and the bubble deforms, the migration is generally in the opposite direction. The explanation can be found by looking at the circulation around the bubble. The flow field, as seen from a frame of reference moving with the bubble, reveals two vortices within its contour, caused by the balance of forces at its surface, that rotate in opposite directions. In the case of the spherical bubble, the larger of the two vortices rotates in the direction induced by the outer shear walls. However, the larger of the two vortices of the deformed bubble rotates in the opposite direction, and in turn, dominates the overall circulation and the resulting motion. Three-dimensional calculations confirm this result. The effect of inertia, surface tension, and gravity on deformation dependent life is explored. Increased inertia, buoyancy, and deformation, due to the decreased surface tension, all contribute to deformation induced lift. Neutrally buoyant drops have also been analyzed. The effect of both inertia and viscosity ratio on the breakup of three-dimensional drops is considered for the first time. Inertia generally enhances the breakup mechanism, however modest increases of inertia at low viscosity ratio suppress the breakup mechanism due to the countering role of inertial forces within the drop. Results of the neutrally buoyant drops compared favorably with the available Stokes flow results.