It has been shown in our previous publication(Blawzdziewicz,Cristini,Loewenberg,2003) that high-viscosity drops in twodimensional linear creeping flows with a nonzero vorticity component may havetwo stable stationary states. One state corresponds to a nearly spherical,compact drop stabilized primarily by rotation, and the other to an elongateddrop stabilized primarily by capillary forces. Here we explore consequences ofthe drop bistability for the dynamics of highly viscous drops. Using bothboundary-integral simulations and small-deformation theory we show that aquasi-static change of the flow vorticity gives rise to a hysteretic responseof the drop shape, with rapid changes between the compact and elongatedsolutions at critical values of the vorticity. In flows with sinusoidaltemporal variation of the vorticity we find chaotic drop dynamics in responseto the periodic forcing. A cascade of period-doubling bifurcations is found tobe directly responsible for the transition to chaos. In random flows we obtaina bimodal drop-length distribution. Some analogies with the dynamics ofmacromolecules and vesicles are pointed out.
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