Multi-objective optimization of low-Reynolds number micromixers: a data-driven framework integrating CFD and evolutionary algorithms

Efficient mixing is a critical requirement for microfluidic biochemical analysis, yet achieving high uniformity under low Reynolds number ( R e ) conditions often necessitates complex geometries that incur high Pressure Drop ( Δ p ). This study proposes a Z-shaped centerline-baffle passive micromixer (ZCB-PMM) and establishes an automated optimization framework integrating Computational Fluid Dynamics (CFD) and Machine Learning (ML). A dataset of 750 design points was generated using Latin Hypercube Sampling (LHS) to capture the relationship between geometric variables and flow characteristics. Six regression models, including Backpropagation (BP), CNN, and LSTM were benchmarked as surrogates. The BP neural network achieved the best performance, yielding test-set R 2 values of 0.9954 for the Mixing Index ( M I ) and 0.9996 for Δ p . After offline training, the surrogate evaluated a new design in approximately 0.2 s, compared with about 30 min for a single high-fidelity CFD simulation, while maintaining a mean relative error of 1.47% on unseen data. Using the BP-driven NSGA-II algorithm, Pareto-optimal designs were identified. At Re = 0.1 the optimized geometry increased M I from 54.1% (reference design) to 86.0% with a negligible pressure increase. At R e = 100, M I reached 99.5%, though with a significantly higher pressure cost. Experimental validation confirmed the numerical predictions with an average relative error of approximately 7%. The proposed closed-loop simulation, learning, then optimization framework enables the rapid, intelligent design of high-performance microfluidic devices.