Residence time distributions for in-line chaotic mixers

TL;DR

This paper analyzes residence time distributions in in-line chaotic mixers, revealing a universal power-law tail, and evaluates how different mixer designs influence mixing efficiency and residence time characteristics.

Contribution

It introduces a synthetic model for exact calculations and demonstrates the universal $t^{-3}$ tail in residence time distributions across various mixers.

Findings

Residence time distributions have a universal $t^{-3}$ tail.

Standard deviation is invalid for heavy-tailed distributions, but mean absolute deviation converges.

Mixer performance varies with the number of elements and cross-sectional shape.

Abstract

We investigate the distributions of residence time for in-line chaotic mixers; in particular, we consider the Kenics, the F-mixer and the Multi-level laminating mixer, and also a synthetic model that mimics their behavior and allows exact mathematical calculations. We show that whatever the number of elements of mixer involved, the distribution possesses a $t^{-3}$ tail, so that its shape is always far from Gaussian. This $t^{-3}$ tail also invalidates the use of second-order moment and variance. As a measure for the width of the distribution, we consider the mean absolute deviation and show that, unlike the standard deviation, it converges in the limit of large sample size. Finally, we analyze the performances of the different in-line mixers from the residence-time point of view when varying the number of elements and the shape of the cross-section.