Deformation and breakup of a compound droplet in three-dimensional oscillatory shear flow

Abstract

A compound droplet subject to three-dimensional oscillatory shear flow is studied using a three-phase lattice Boltzmann model. Firstly, focusing on low values of capillary number (Ca) where the compound droplet eventually reaches steady-state oscillatory condition, we study the effect of oscillatory period, viscosities of inner and outer fluids of the compound droplet, wall confinement and Ca on the droplet behavior. As the oscillatory period increases, the maximum deformation parameters gradually approach the steady-state values in the corresponding simple shear flow for both inner and outer droplets, and the compound droplet is more synchronous with applied shear. We demonstrate for the first time that due to high pressure near two tips inside the outer droplet the inner droplet may rotate counterintuitively in a direction opposite to the outer one. The compound droplet undergoes larger deformation when either droplet is less viscous, which also decreases the synchronization between inner and outer droplets. Increasing confinement ratio not only promotes the deformations of both constituent droplets, but also makes them more synchronous with applied shear. It is also found that the maximum deformation parameters of both droplets increase linearly with Ca up to Ca=0.35 but deviate from the linearity at higher Ca, where multipeaked oscillations are observed for the deformation of the inner droplet, which can be due to the extensional flow resulting from the rapid contraction of the outer droplet. We then analyze the breakup behavior of compound droplet in the oscillatory shear flow for varying confinement ratios, and compare the findings with those in simple shear flow. The critical capillary number for droplet breakup exhibits a non-monotonic behavior with the confinement ratio in both shear flows, but its value is always higher in oscillatory shear flow than in simple shear flow. As the confinement ratio increases, in the case of oscillatory shear flow, the droplet undergoes a transition from inner ternary breakup to inner binary breakup, distinct from the one observed in the case of simple shear flow. Finally, increasing oscillatory period is found to not only decrease the critical capillary number but also change the mode of droplet breakup.