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We study droplet dynamics and breakup in generic time-dependent flows via amulticomponent Lattice Boltzmann algorithm, with emphasis on flow start upconditions. We first study droplet breakup in a confined oscillatory shear flowvia two different protocols. In one set up, we start from an initiallyspherical droplet and turn on the flow abruptly ("shock method"); in the otherprotocol, we start from an initially spherical droplet as well, but weprogressively increase the amplitude of the flow, by allowing the droplet torelax to the steady state for each increase in amplitude, before increasing theflow amplitude again ("relaxation method"). The two protocols are shown toproduce substantially different breakup scenarios. The mismatch between thesetwo protocols is also studied for variations in the flow topology, the degreeof confinement and the inertia of the fluid. All results point to the fact thatunder extreme conditions of confinement the relaxation protocols can drive thedroplets into metastable states, which break only for very intense flowamplitudes, but their stability is prone to external perturbations, such as anoscillatory driving force.

Lattice Boltzmann simulations of droplet breakup in confined and time-dependent flows