Quantification of mixing in vesicle suspensions using numerical simulations in two dimensions

TL;DR

This study uses numerical simulations to analyze how vesicle suspensions affect mixing in a two-dimensional Couette flow, revealing conditions under which vesicles either hinder or enhance mixing.

Contribution

The paper introduces a numerical framework combining boundary integral and spectral methods to quantify mixing effects of vesicles in 2D flows, identifying conditions that promote mixing.

Findings

Vesicles generally slightly suppress mixing due to limited advection across interfaces.

In some configurations, vesicles enable mixing where pure flow fails.

A simple criterion relates velocity and solute distribution to predict mixing enhancement.

Abstract

We study mixing in Stokesian vesicle suspensions in two dimensions on a cylindrical Couette apparatus using numerical simulations. The vesicle flow simulation is done using a boundary integral method and the advection-diffusion equation for the mixing of the solute is solved using a pseudo-spectral scheme. We study the effect of the area fraction, the viscosity contrast between the inside (the vesicles) and the outside (the bulk) fluid, the initial condition of the solute, and the mixing metric. We compare mixing in the suspension with mixing in the Couette apparatus without vesicles. On the one hand, the presence of vesicles in most cases, slightly suppresses mixing. This is because the solute can be only diffused across the vesicle interface and not advected. On the other hand, there exist spatial distributions of the solute for which the unperturbed Couette flow completely fails to mix whereas the presence of vesicles enables mixing. We derive a simple condition that relates the velocity and solute and can be used to characterize the cases in which the presence of vesicles promotes mixing.