旋转蠕动流中粘性液滴的滞回和混沌动力学
Hysteretic and chaotic dynamics of viscous drops in creeping flows with rotation
摘要：
在我们以前的出版物（Blawzdziewicz，Cristini，Loewenberg，2003）中已经表明，具有非零涡量分量的二维线性蠕动流中的高粘度液滴可能有两个稳定的定态。一种状态对应于主要通过旋转稳定的接近球形的紧凑液滴，而另一种状态对应于主要通过毛细力稳定的细长液滴。在这里，我们探讨的后果，高粘度液滴的动态的滴双稳态。使用边界积分模拟和小变形理论，我们表明，准静态变化的流动涡度引起的滞后响应的下降形状，与紧凑和细长的解决方案之间的快速变化在临界值的涡度。在流动的涡度的正弦时间变化，我们发现混沌滴动态响应的周期性强迫。级联倍周期分岔被发现是直接负责的过渡到混沌。在随机流中，我们得到一个双峰液滴长度分布。指出了与大分子和囊泡动力学的一些相似之处。
英文摘要：
It has been shown in our previous publication (Blawzdziewicz,Cristini,Loewenberg,2003) that high-viscosity drops in two dimensional linear creeping flows with a nonzero 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.
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