Effect of Droplet Viscosity Ratio and Surfactant Adsorption on the Coalescence of Droplets with Interfacial Viscosity

Surface rheology becomes important for droplets with adsorbed proteins, solid particulates, lipids, or polymers, and understanding how surface rheology alters basic droplet processes like coalescence provides insight into the processing of dispersions in industrial and biological systems. In this work, we model the approach of two equal-size deformable droplets under an axisymmetric, biaxial extensional flow in the Stokes flow limit. We explore how the viscosity contrast between the drop and suspending fluid alters the film drainage behaviour when interfacial viscosity is present. For a clean droplet at a fixed capillary number, the drainage time is observed to be independent of the viscosity ratio (lambda) for lambda <= O(1), while the drainage increases linearly with the viscosity ratio for lambda >= O(1). Surface viscosity increases the drainage time by causing the thin film between the droplets to flatten and widen, and shifts the viscosity ratio at which the aforementioned scaling behaviour changes to larger values. The drainage time is increased more significantly at lower viscosity ratio values than higher values. In the second half of the paper, we examine how surface viscosity alters film drainage when the surfactant can be soluble. We examine the kinetically controlled adsorption/desorption limit. We find that surfactant solubility abolishes surface tension gradients and increases the prominence of surface viscosity effects, the effects of which are quantified for Boussinesq numbers Bq similar to O(0.1).