Mutual information as a measure of mixing efficiency in viscous fluids

Yihong Shi; Ramin Golestanian; Andrej Vilfan

doi:10.1103/physrevresearch.6.l022050

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arXiv · 2311.09840

Mutual information as a measure of mixing efficiency in viscous fluids

Yihong Shi·Ramin Golestanian·Andrej Vilfan

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Abstract

Because of the kinematic reversibility of the Stokes equation, fluid mixing at the microscale requires an interplay between advection and diffusion. Here we introduce mutual information between particle positions before and after mixing as a measure of mixing efficiency. We demonstrate its application in a Couette flow in an annulus and show that non-uniform rotation sequences can lead to more efficient mixing. We also determine mutual information from Brownian dynamics simulations using data compression algorithms. Our results show that mutual information provides a universal and assumption-free measure of mixing efficiency in microscale flows.

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Yihong Shi, Ramin Golestanian, Andrej Vilfan. 2023-11-16. Mutual information as a measure of mixing efficiency in viscous fluids. https://doi.org/10.1103/physrevresearch.6.l022050

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