Quantification of the performance of chaotic micromixers on the basis of finite time Lyapunov exponents

TL;DR

This paper introduces a computational method using finite-time Lyapunov exponents to quantitatively evaluate and optimize the chaotic mixing performance of micromixers, reducing reliance on trial-and-error experiments.

Contribution

The paper presents an algorithm that applies finite-time Lyapunov exponents to measure chaotic advection in micromixers, enabling more efficient design optimization.

Findings

The method accurately assesses chaotic mixing performance.

Simulation results align with literature data.

The approach facilitates geometric optimization of micromixers.

Abstract

Chaotic micromixers such as the staggered herringbone mixer developed by Stroock et al. allow efficient mixing of fluids even at low Reynolds number by repeated stretching and folding of the fluid interfaces. The ability of the fluid to mix well depends on the rate at which "chaotic advection" occurs in the mixer. An optimization of mixer geometries is a non trivial task which is often performed by time consuming and expensive trial and error experiments. In this paper an algorithm is presented that applies the concept of finite-time Lyapunov exponents to obtain a quantitative measure of the chaotic advection of the flow and hence the performance of micromixers. By performing lattice Boltzmann simulations of the flow inside a mixer geometry, introducing massless and non-interacting tracer particles and following their trajectories the finite time Lyapunov exponents can be calculated. The applicability of the method is demonstrated by a comparison of the improved geometrical structure of the staggered herringbone mixer with available literature data.