On the deformation of two droplets in a quasisteady stokes flow

A theoretical method is given for the determination of the shape of two drops (bubbles) moving with constant velocities parallel to their line of centres in a quiescent viscous fluid. The Reynolds numbers for the motions within the fluids are assumed to be sufficiently small that the equations governing these motions are quasisteady Stokes' equations. It is also assumed that the maximum deviation of the interfaces from spherical form is small when compared with the radius of the “equivalent” spherical drop. The paper deduces the first-order pressure distribution exterior and interior to the droplets. Effects of fluid viscosities, capillary numbers and distances between the droplets are taken into account. Special attention is paid to the influence of a solid plane or solid sphere on the shape of a drop (bubble) approaching or receding away from the solid boundary. The obtained solutions may serve as a first iteration of an iterative procedure for determining more accurate flow fields, taking into account the deviation from sphericity of the deformed particles.