Regime mapping of multiple breakup of droplets in shear flow by phase-field lattice Boltzmann simulation

Abstract

Multiple breakup refers to a sequence of events through which a single droplet eventually produces multiple daughter droplets in a shear flow. It is a more common phenomenon than binary breakup. Using a phase-field lattice Boltzmann method, this work investigates the effects of Reynolds number, capillary number and soluble surfactant on multiple breakup in shear flow. We find that the regime map for a droplet in a surfactant-free shear flow can be segmented into the non-breakup, elementary breakup, multiple breakup, filament and coalescence regimes. By contrast, the multiple-breakup regime widens and the coalescence regime narrows in the system of surfactant. This difference on macroscale regimes originates from the mesoscale behaviour caused by the interaction of surfactant and shear flow. While surfactant hinders droplet breakup at lower Re, it promotes breakup at higher Re. The interfaces around the breaking points are stretched by the opposite reaction of Marangoni stress. While the regime map gives the number of daughter droplets in a given shear flow, a correlation is proposed to calculate the composition of breakup events, viz. the number of binary breakup and of ternary breakup events.