Chaotic mixing using micro-rotors in a confined domain

TL;DR

This paper investigates chaotic mixing in a bounded 2D Stokes flow induced by micro-rotors modeled as rotlets, revealing how their initial positions influence fluid mixing efficiency and demonstrating a realistic, smooth velocity field suitable for microfluidic applications.

Contribution

It introduces a novel model of micro-rotor induced chaotic mixing with realistic boundary conditions and analyzes the impact of rotor positions on mixing quality using entropy measures.

Findings

Chaotic advection occurs due to non-Hamiltonian rotor dynamics in bounded domains.

Regions of good and poor mixing are identified via locational entropy analysis.

The model's smooth velocity field is more realistic for microfluidic device applications.

Abstract

In this work we study chaotic mixing induced by point micro-rotors in a bounded two dimensional Stokes flow. The dynamics of the pair of rotors, modeled as rotlets, are non Hamiltonian in the bounded domain and produce chaotic advection of fluid tracers in subsets of the domain. A complete parametric investigation of the fluid mixing as a function of the initial locations of the rotlets is performed based on pseudo phase portraits. The mixing of fluid tracers as a function of relative positions of micro-rotors is studied using finite time entropy and locational entropy. The finite time locational entropy is used to identify regions of the fluid that produce good vs poor mixing and this is visualized by the stretching and folding of blobs of tracer particles. Unlike the case of the classic blinking vortex dynamics, the velocity field of the flow modeled using rotlets inside a circular boundary is smooth in time and satisfies the no slip boundary condition. This makes the considered model a more realistic case for studies of mixing in microfluidic devices using magnetic actuated microspheres.