Numerical study on the engulfing behavior between immiscible droplets in a confined shear flow

[Display omitted] •Extensive numerical analysis is carried out regarding droplet engulfing behavior.•A global picture of the droplet engulfing in a confined shear flow is derived.•The effect of shear rate, surface tension, and confinement is investi- gated. This study investigates the engulfing behavior between two equal-sized immiscible droplets suspended in a confined shear flow. The finite element analysis is carried out, where a ternary diffuse-interface model and the Stokes equation are coupled. The numerical results of nearly 60 cases are studied to systematically examine the effect of shear rate, surface tension, and confinement on the engulfing behavior. In general, the partial and complete engulfing result in Janus and compound droplets, respectively, when the shear rate is low. It is found that the partial engulfing regime is significantly affected by the shear rate such that a proper condition for the Janus formation becomes narrower as the shear rate increases. We also note that the shell of a compound droplet can be broken by increasing the initial separation or confinement.