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  • Letter
  • Open Access

Mutual information as a measure of mixing efficiency in viscous fluids

Yihong Shi1, Ramin Golestanian1,2,3,*, and Andrej Vilfan1,4,†

  • *ramin.golestanian@ds.mpg.de
  • †andrej.vilfan@ds.mpg.de
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Phys. Rev. Research 6, L022050 – Published 3 June, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L022050

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 nonuniform 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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Phys. Rev. Research 6, L022050– Published 3 June, 2024
  • Received 19 October 2023
  • Accepted 18 May 2024
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by Max Planck Society.

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