The role of inertia in coalescence of drops in liquid-liquid emulsions

The collision and coalescence of liquid drops immersed in a second liquid play a critical role in deciding the fate of liquid-liquid emulsions which are ubiquitous in nature, e.g. oil water emulsions and food products. We simulate the approach, collision, and eventual coalescence of two equal-sized drops of radius R immersed in an ambient liquid where both liquids are incompressible Newtonian fluids, using a Galerkin finite element based algorithm. The governing continuity and Navier Stokes equations are augmented to account for long range van der Waals interactions that become significant as the separation between the drops falls below the order of a few hundred nanometers. For ambient fluids with low capillary numbers Ca = μGR/σ, where μ is the viscosity of the ambient liquid, G is the strain rate of the compressional flow imposed on the ambient liquid, and σ is the interfacial tension, the drops are seen to rebound on first approach before coalescing on approaching each other again, leading to a departure from existing scaling theories for drainage times. We examine the significance of inertia in causing the drops to rebound, resulting in increased drainage times.