Chaotic advection of finite-size bodies in a cavity flow

Abstract

We considered advection of neutrally buoyant discs in two-dimensional chaotic Stokes flow. The goal of the study is to explore a possibility to enhance laminar mixing in batch-flow mixers. Addition of freely moving bodies to periodically driven chaotic flow renders the flowfield nonperiodic [D. F. Zhang and D. A. Zumbrunnen, AIChE J. 42, 3301 (1996)], i.e., the Lagrangian chaos of the bodies motion induces Eulerian chaos of the flow that makes mixing more intensive. The presence of three bodies creates new topological features that do not exist in “pure” fluid. The trajectories of the discs in the augmented phase space tangle and form a braid that leads to so-called topological chaos [P. L. Boyland, H. Aref, and M. A. Stremler, J. Fluid Mech. 403, 277 (2000)]. Simulations were performed using a new variant of the immersed boundaries method that allows the direct numerical simulation of fluid–solid flows on a regular rectangular grid without explicit calculation of the forces that the particles exert on the fluid.