Two-dimensional numerical modelling of viscous emulsion drops coalescence in a constricted capillary channel

Abstract

We study numerically the coalescence of viscous emulsion drops in a two-dimensional semi-elliptical shape constricted channel. The Navier-Stokes equations are solved using the finite element method and the oil-water interface is tracked using the level-set techniques. Effects of interfacial tension, inertia, viscosity ratio, droplet size, and constriction shape on the droplet coalescence and average viscous pressure drop along the channel are investigated. It is found that at high interfacial tension, droplets are circular, approach each other more quickly, coalesce at the constriction entrance, and give higher pressure drops. At intermediate interfacial tension, the onset of coalescence occurs downstream of the constriction entrance while at very low interfacial tension, no coalescence of the droplets was observed. Inertia is found to be negligible effects on the coalescence of the droplets. High inertia gives less viscous pressure drop. Less viscous droplets are more likely to quickly coalesce compared to high viscous drops. Higher viscous drops create more resistance to flow. Moreover, larger size drops are responsible for more quick coalescence and tend to create more viscous pressure drops. In addition, we found that circular constriction offers less resistance to fluid flow. We hope that these numerical results would be beneficial while displacing oil from the underground reservoirs.