A numerical study on the coalescence of emulsion droplets in a constricted capillary tube

Abstract

Using a new computational model, we have studied the dynamics and coalescence of a pair of two-dimensional droplets in pressure-driven flow through a constricted capillary tube, which is a prototype problem for the analysis of the interaction of emulsion droplets in porous media. We present simulations that quantify the effects of various system parameters on the droplet stability. These include the capillary number, the interfacial tension, the suspended-to-suspending-phase viscosity ratio, the valence and concentration of added electrolytes, the droplet-to-pore-size ratio, the pore-body-to-throat-size ratio, and the type of pore geometry. Our simulations show that the capillary number Ca plays an important role in determining whether the drops coalesce. At low Ca, drops deform only slightly and coalescence occurs at the entrance of the pore throat, whereas significant deformation enables the drops move through the pore without coalescence at high Ca. Coalescence is favored at intermediate values of the viscosity ratio. The destabilizing effect of added electrolytes is found to be insignificant for 10-μm drops, but significant for micron-size drops. Among the geometric-related parameters, the drop-to-pore-size ratio is the most significant.