A two-dimensional numerical study on the coalescence of viscous double emulsion droplets in a constricted capillary tube

In this paper, we study numerically the motion of a pair of double-emulsion (DE) droplets in a two-dimensionally singly constricted capillary tube. The momentum and continuity equations are solved using the finite element method, and the interface is tracked via the level set method. The influence of interfacial tension, viscosity and density ratios, droplet size, pore throat size, and geometrical shape on the droplets' local extra pressure drop and instantaneous velocities are calculated. It is found that at higher interfacial tension, DE droplets are difficult to deform and lead to coalescence at the constriction throat. At low interfacial tension, droplets do not coalesce and can be easily deformed. Higher interfacial tension gives a larger pressure drop and reduces fluid flow mobility. More viscous oil drops pass through the constriction without coalescence and create larger pressure drops. Changing the inner drop size does not result in oil drop coalescence. However, the local pressure drop elevates as the inner water drop size decreases and vice versa. Small pores reduce the droplet and fluid flow mobility. Among the geometrical shape effects, the rectangular shape is more responsible for larger local pressure drop.