Mutual information as a measure of mixing efficiency in active microfluidic systems

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 firstly 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. Later, we extend the system to active microswimmers and apply mutual information to optimise fluid mixing induced by different types of microswimmers. Our results show that mutual information provides a universal and assumption-free measure of mixing efficiency in microscale flows.

Y. Shi, R. Golestanian and A. Vilfan, Phys. Rev. Research (2024).
L. Cocconi, Y. Shi, and A. Vilfan, Phys. Rev. Lett. (2025).
Y. Shi, Y. Hosaka, A. Vilfan, and R. Golestanian, (being drafted).