Hindered and accelerated coalescence of drops in Stokes flow

We analyze axisymmetric near-contact motion of two drops under the action of an external force or imposed flow. It is shown that the far-field stress generated in the near-contact region by the outer flow qualitatively affects drainage of the thin fluid film separating the drops. If this stress acts radially outward, exponential film drainage occurs. For a radially inward far-field stress, film drainage is arrested at long times. An asymptotic analysis of the stationary long-time film profile is developed for small deformation conditions, and the critical strength of van der Waals attraction for film rupture is calculated. Hindered and accelerated drop coalescence have not been predicted by previous theories, because the far-field stress was neglected.