Assessment of mixing in rotating microfluidic channels: A variational calculus approach

We present a theoretical investigation of the mixing dynamics of two constituent fluids within a soft rotating microfluidic channel. We solve a coupled system of transport equations, governing the mixing dynamics in this endeavor, with the associated symmetric and antisymmetric boundary conditions using the variational calculus approach. Our theoretical framework, developed in the context of centrifugal microfluidics, demonstrates strong agreement with full-scale simulated data and analytical solutions in the limiting case. Beginning with the characterization of flow velocity, including Coriolis force-induced secondary flows across different aspect ratios of the fluidic channel, we provide a comprehensive analysis of the underlying mixing phenomena. Through Poincaré map analysis, we qualitatively visualize fluid stream mixing, while mixing entropy analysis offers a quantitative evaluation of mixing performance. Our findings suggest that a lower aspect ratio in the rotating channel enhances mixing efficiency compared to higher aspect ratios. Additionally, our analysis highlights that the Coriolis force modulated emergence of vortex structures in the flow field significantly improves mixing in rotating channels, even at higher aspect ratios, relative to nonrotating channels of identical configuration. The insights from this study hold significant implications for the optimized design of rotational fluidic platforms, largely used in laboratory-on-a-chip applications, including point-of-care diagnostics.