Quantification and optimization of mixing efficiency in active microfluidic systems

Mixing at the microscale is a fundamental process in biological systems and microfluidic technologies, yet it remains challenging due to the kinematic reversibility of low–Reynolds-number flows, where viscous forces dominate and inertial effects are negligible. Efficient mixing in such systems relies on a subtle interplay between advection and diffusion, and its quantification depends sensitively on the choice of mixing metric. In this thesis, a universal and assumption-free framework for quantifying mixing efficiency in viscous fluids is developed based on mutual information between the initial and final positions of fluid particles. Interpreting mixing as a process of information loss, mutual information provides a global measure of mixing that is independent of imposed solute distributions and applicable to general advection–diffusion systems. The approach is first validated in a two-dimensional Taylor–Couette flow, where the advection–diffusion equation is solved using spectral methods and Brownian dynamics simulations. The decay of mutual information is used to compare different mixing protocols and to identify optimal strategies. It is shown that non-uniform rotation sequences can significantly enhance mixing efficiency compared to uniform protocols at fixed rotation or dissipation. Mutual information is further compared with conventional measures such as concentration variance, highlighting its robustness and universality. Complementary techniques, including data-compression-based estimators and Taylor-dispersion analysis, are introduced to provide alternative routes for estimating mutual information in complex flows. The framework is then extended to active microfluidic systems driven by micro-swimmers. Using multipole expansions for swimmer-induced Stokes flows in free space and confined geometries, the mixing efficiency generated by different swimmer configurations is quantified. For a fixed rate of viscous dissipation, the results identify optimal swimmer types and spatial arrangements that maximize mixing. Overall, this thesis demonstrates that mutual information provides a natural and universal framework for quantifying and optimizing mixing in viscous and active fluid systems. By recasting mixing as an irreversible process of information loss, the approach transcends traditional pattern-dependent measures and unifies passive and active mixing within a single theoretical perspective rooted in information theory. Beyond its immediate applications to microfluidic and swimmer-driven flows, this framework opens new avenues for the systematic design and control of nonequilibrium transport processes in soft and biological matter.