Full numerical simulations of two- and three-dimensional bubbles in a shear flow, by a finite difference front tracking method, are presented. The effects of inertial, viscous, gravitational, and surface forces on the lift of a deformable bubble rising due to buoyancy in a vertical shear flow, are examined. Bubbles with a large surface tension coefficient migrate toward the downward moving fluid, as predicted analytically for a cylinder or a sphere in a shear flow. Bubbles with smaller surface tension deform, and generally migrate in the opposite direction. The combined effects of the shear flow and the buoyancy deform the bubble in such a way that the circulation around the deformed bubbles is opposite to that of undeformed bubbles.

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