2007/12/21 by Y.-N. YOUNG, Yuan N. Young, Jerzy Blawzdziewicz +5 · 17 citations
Chemical Engineering · Engineering · Physics and Astronomy · #Bistability #Chaotic #Drop (telecommunication) #Dynamics (music) #Fluid Dynamics and Heat Transfer #Micro and Nano Robotics #Rheology and Fluid Dynamics Studies #Viscous liquid #Vortex #Vorticity #cond-mat.mtrl-sci #cond-mat.soft
paper · pdf · doi:10.1017/s0022112008002036
published in Journal of Fluid Mechanics 607, 209-234 (Cambridge University Press) · 22 pages, 13 figures. submitted to Journal of Fluid Mechanics
arxiv created 2007/12/21 · openalex publication_date 2008/06/30 · arxiv updated 2015/05/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We have shown that high-viscosity drops in two-dimensional linear creeping flows with a non-zero vorticity component may have two stable stationary states. One state corresponds to a nearly spherical, compact drop stabilized primarily by rotation, and the other to an elongated drop stabilized primarily by capillary forces. Here we explore consequences of the drop bistability for the dynamics of highly viscous drops. Using both boundary-integral simulations and small-deformation theory we show that a quasi-static change of the flow vorticity gives rise to a hysteretic response of the drop shape, with rapid changes between the compact and elongated solutions at critical values of the vorticity. In flows with sinusoidal temporal variation of the vorticity we find chaotic drop dynamics in response to the periodic forcing. A cascade of period-doubling bifurcations is found to be directly responsible for the transition to chaos. In random flows we obtain a bimodal drop-length distribution. Some analogies with the dynamics of macromolecules and vesicles are pointed out.