Numerical simulation-driven pearson guided ant colony optimization of a three-dimensional serpentine passive micromixer for progressive axial homogenization

Rapid and efficient water-dye homogenization in microfluidic systems is a progressive area in passive micromixing process under laminar flow conditions without external recirculation. In this study, micromixer variants configurations such as simple T-shape micromixer (STM), vortex-T micromixer with ridges (VTMR) and three-dimensional serpentine Micromixer (TDSM) were numerically compared. The flow and species transport behavior are solved based on the Navier–Stokes framework while mixing performance is quantified based on mixing index under varying Reynolds numbers (5-165). A quantitative grid-convergence analysis based on successive-grid relative error confirmed that the final mesh produced less than 2% variation in mixing index across the investigated Reynolds-number range. Pearson analysis identified Reynolds number as the strongest mixing-related driver, with Re–mixing index correlation of r = 0.48437 and Adj. R² = 0.21393, followed by axial distance–mixing index with r = 0.4072 and Adj. R² = 0.14327. The STM showed limited improvement, increasing from η = 0.10 to 0.36, while VTMR increased from η = 0.28 to a peak of 0.65 at Re = 75 In contrast, TDSM produced near-uniform scalar homogenization, with η increasing to 0.985–0.9975 from Re = 75–165. Ant colony optimization (ACO) further identified Path-3 as the optimal route, reaching a fitness of 0.96 at iteration 20, followed by Path-8 at 0.95. The maximum computed mixing index was obtained for Case 39, corresponding to TDSM with five serpentine units at Re = 165 and P9/3000 µm, where η = 0.9975 was supported by an outlet concentration standard deviation of 0.00125 and variance of 1.56 × 10 − 6 .