Data-Driven Surrogate Modeling for Micromixing of Non-Newtonian Fluids in Sinusoidal Converging-Diverging Microchannels
Micromixing of non-Newtonian fluids remains challenging because laminar flow at microscales restricts transverse transport primarily to molecular diffusion. In this study, we investigate the transport mechanisms governing passive micromixing of a Carreau--Yasuda fluid in two-dimensional sinusoidal converging--diverging microchannels and develop a surrogate-assisted framework for their multi-objective design. We perform high-fidelity finite-volume simulations by systematically varying the wall-amplitude ratio, phase offset, and wave count under creeping-flow conditions. The results show that successive contraction--expansion units enhance mixing through the combined effects of interface stretching, elevated shear rates, and shear-thinning-induced viscosity reduction. These mechanisms improve scalar transport but simultaneously increase pressure drop, creating an inherent trade-off between mixing performance and hydraulic resistance. To efficiently explore the multidimensional design space, we construct surrogate models from high-fidelity numerical simulations and identify Gaussian Process Regression (GPR) as the most accurate predictor of both the mixing index and pressure drop. Coupling the validated GPR surrogate with Non-dominated Sorting Genetic Algorithm II (NSGA-II) accurately reproduces the Pareto front obtained from the high-fidelity simulations and identifies optimal microchannel geometries that balance mixing enhancement against pressure loss. The proposed machine learning framework provides a fast, accurate, and physically consistent strategy for the multi-objective design of passive micromixers for non-Newtonian fluids.