A NOTE ON THE LIFT FORCE ON A SPHERICAL BUBBLE OR DROP IN A LOW-REYNOLDS-NUMBER SHEAR-FLOW

The analytical solution giving the lift force on a spherical drop of a rbitrary viscosity moving in a low-Reynolds-number linear shear flow i s derived through a matched asymptotic expansion procedure. This solut ion extends the result established by Saffman in the particular case o f a solid sphere [J. Fluid Mech. 22, 385 (1965)]. It appears that, to leading order, the lift force is proportional to the square of the vor ticity present at the surface of the drop. As a consequence the lift f orce decreases with the viscosity of the drop and the ratio of the for ces experienced by an inviscid bubble and a solid sphere is equal to ( 2/3)(2). (C) 1997 American Institute of Physics.