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 arbitrary viscosity moving in a low-Reynolds-number linear shear flow is derived through a matched asymptotic expansion procedure. This solution extends the result established by Saffman in the particular case of 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 vorticity present at the surface of the drop. As a consequence the lift force decreases with the viscosity of the drop and the ratio of the forces experienced by an inviscid bubble and a solid sphere is equal to (2/3)2.