Dynamics of two unequal micron-sized viscous emulsion drops flowing in a two-dimensional constricted microcapillary channel: A numerical study

Abstract

Emulsions containing unequal-sized droplets are ubiquitous. Compared to the equal-sized emulsion droplet coalescence process in porous media, unequal-sized emulsion droplets show distinctly different dynamics and features when flowing through the capillary channel. In this paper, we numerically studied the flow of two unequal small micron-size emulsion drops flowing in a two-dimensional (2D) half-sine pulse shape constricted tube. The finite element method solves the momentum, continuity, and level set equations. The oil–water interface is tracked using the level set method. Effects of drop size, capillary number (interfacial tension), viscosity ratio, and geometrical shape constriction effects on the droplets' flow behavior across the throat, its flow velocities, and average viscous pressure across the tube were investigated. It is found when there is a significant difference in diameters of the two un-equalized droplets, they will flow separately through the throat, whereas when the two un-equalized droplets’ size is close to each other, they coalescence with each other after passing through the constriction. Higher interfacial tension leads unequal-sized droplets to coalescence more readily while droplets pass without coalescence at low interfacial tension cases. The highest pressure drop is recorded at the critical point where the two unequal-sized droplets begin to merge in the constriction throat. Increasing droplet viscosity reduces the chances of coalescence and increases the average viscous pressure drop hence leading to mobility reduction. In the case of geometrical constrictions, circular-shaped contracted tubes offer the least resistance to fluid flow and are more appropriate for enhanced oil recovery processes. We hope our numerical findings will provide more information to facilitate the enhanced oil recovery process.