A level set analysis of oil droplet division dynamics in an oil-in-water emulsion flow through a constricted splitting channel

The rheology properties accompanying the oil droplet division process lack in-depth discussions so far. In this paper, we numerically studied the oil droplet division dynamics in a two-dimensional O/W flow in a constricted splitting channel. The Navier–Stokes equations are solved numerically using the finite element method while the oil–water interface is tracked using the level set method. After validating the numerical scheme, the dynamic behavior of the oil droplet division is studied and the flow rheology properties are scrutinized. It is observed the droplet interface morphology variations lead to much higher average pressure drops in the droplet division process, which underlies the applicability of O/W emulsion in EOR practices. Then, systematic parameter investigations are performed on the effects of gravity, surface tension, and contact angle on the droplet flow dynamics. Gravity and surface tension are characterized in terms of Bond (Bo) and capillary (Ca) numbers, respectively, while the contact angle is denoted by $$\theta$$ . It is found that the droplet splits asymmetrically and tends to push larger droplet volume to the upper branch under the high Bo number. And lower Ca lead to a drastic increase in the pressure drop and decay in the velocity. While a larger $$\theta$$ gives the convex shape of the droplet's rear and front, decreasing the average pressure drop and increasing the average fluid velocity. This work is expected to help understand porous media's O/W emulsion flow characteristics.