We study droplet dynamics and breakup in generic time-dependent flows via a multicomponent lattice Boltzmann algorithm, with emphasis on flow startup conditions. We first study droplet breakup in a confined oscillatory shear flow via two different protocols. In one setup, we start from an initially spherical droplet and turn on the flow abruptly (“shock method”); in the other protocol, we start from an initially spherical droplet as well, but we progressively increase the amplitude of the flow, by allowing the droplet to relax to the steady state for each increase in amplitude, before increasing the flow amplitude again (“relaxation method”). The two protocols are shown to produce substantially different breakup scenarios. The mismatch between these two protocols is also studied for variations in the flow topology, the degree of confinement, and the inertia of the fluid. All results point to the fact that under extreme conditions of confinement the relaxation protocols can drive the droplets into metastable states, which break only for very intense flow amplitudes, but their stability is prone to external perturbations, such as an oscillatory driving force.

中文翻译：

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有限和时间相关流中液滴破裂的格子Boltzmann模拟

我们通过多组分晶格玻尔兹曼算法研究通用时间相关流中的液滴动力学和破裂，重点是流启动条件。我们首先通过两种不同的方案研究有限振荡振荡流中的液滴破裂。在一种设置中，我们从最初的球形液滴开始，然后突然打开流（“冲击法”）；在另一个协议中，我们也从最初的球形液滴开始，但是通过使液滴在每次增大幅度时都松弛到稳态，然后再次增大流动幅度（“松弛”），从而逐渐增加流的振幅。方法”）。显示这两种协议会产生实质上不同的分解方案。还研究了这两种协议之间的不匹配情况，以了解流动拓扑，限制程度，和流体的惯性 所有结果都表明这样一个事实，即在极端的限制条件下，松弛协议可以将液滴驱动为亚稳态，这种状态仅在非常强的流动幅度下才破裂，但其稳定性易于受到外部干扰，例如振荡驱动力。