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DY: Fachverband Dynamik und Statistische Physik
DY 50: Wetting, Droplets, and Microfluidics (joint session DY/CPP)
DY 50.6: Talk
Thursday, March 21, 2024, 16:30–16:45, BH-N 334
Mutual information as a measure of mixing efficiency in viscous fluids — •Yihong Shi1, Ramin Golestanian1,2,3, and Andrej Vilfan1,4 — 1Max Planck Institute for Dynamics and Self-Organization, Goettingen, Germany — 2Rudolf Peierls Centre for Theoretical Physics, University of Oxford, UK — 3Institute for the Dynamics of Complex Systems, University of Göttingen, Germany — 4Jozef Stefan Institute, Lublijana, Slovenia
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 the mixing efficiency depends in a non-trivial way on the time sequence of rotation. We also determine mutual information from Brownian dynamics simulations using data compression algorithms and demonstrate that advanced neural network based compression algorithms can be applied to estimate mutual information to a high accuracy. Our results show that mutual information provides a universal and assumption-free measure of mixing efficiency in microscale flows.
Keywords: mixing enhancement; entropy production; mutual information; viscous fluids; data compression algorithm