Role of interfacial viscosity on droplet coalescence

In this work, we perform boundary-integral simulations to explore the role of surface viscosity on the early stages of coalescence of two equal-sized droplets in an axisymmetric extensional flow under the Stokes flow limit. We model the surface rheology of the droplet using the Boussinesq–Scriven constitutive relationship for a Newtonian interface. Previous studies have shown that colliding droplets at low capillary numbers (i.e., low impact velocities) remain almost spherical up to the point of film rupture, while droplets at large values of capillary number form dimples during the early stages of coalescence that significantly slows down the drainage time. We present how the interfacial viscosity affects the dimple formation during a head-on collision and the scaling of the film drainage time with capillary number values in the range 10^-4 - 10^-2. We observe that the surface viscosity significantly arrests the thinning of the film between the coalescing droplets compared to a clean interface. We find that the film drainage time at a given capillary number increases upon increasing the Boussinesq parameter for total surface viscosity and is independent of the ratio of surface dilational viscosity to the surface shear viscosity. We also explore the coupled influence of surface viscosity and Marangoni stresses on droplet coalescence. We incorporate the effect of surfactant transport by solving the time-dependent convection-diffusion equation and consider a nonlinear equation of state (Langmuir adsorption isotherm) to correlate the interfacial tension with the changes in surfactant concentration.