Hindered and enhanced coalescence of drops in Stokes flows

We analyze axisymmetric near-contact motion of two drops under the action of an external force or imposed flow. It is shown that hydrodynamic stresses in the near-contact region that are associated with the outer (drop-scale) flow can qualitatively affect the drainage of the thin fluid film separating the drops. If this far-field stress acts radially inward, film drainage is arrested at long times; exponential film drainage occurs if this stress acts outward. An asymptotic analysis of the stationary long-time film profile is presented for small-deformation conditions, and the critical strength of van der Waals attraction for film rupture is calculated. The effect of an insoluble surfactant is also considered. Hindered and enhanced drop coalescence are not predicted by the current theories, because the influence of the outer flow on film drainage is ignored.