Hysteretic and chaotic dynamics of viscous drops in creeping flows with rotation

TL;DR

This paper investigates the complex behavior of viscous drops in creeping flows, revealing hysteresis, chaos, and bimodal distributions due to flow-induced bistability and dynamic forcing, with implications for understanding drop and vesicle dynamics.

Contribution

It demonstrates how flow vorticity variations induce hysteresis and chaos in viscous drops, extending previous bistability findings with new dynamic and stochastic insights.

Findings

Hysteretic shape transitions at critical vorticity values

Chaotic drop dynamics under sinusoidal vorticity variation

Bimodal length distribution in random flows

Abstract

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.