Abstract This study introduces a Flexible Physics-Informed Neural Network (FlexPINN) to overcome the limitations of standard PINNs in modeling fully three-dimensional, geometrically complex micromixers with internal baffles. The mesh-free framework integrates parallel-network architecture, first-order dimensionless governing equations, adaptive loss weighting, and a novel global conservation penalty to prevent trivial solutions and ensure robust convergence. Employing transfer learning reduces the training time for new baffle shapes by ~ 35%, requiring approximately 3.5 h versus 5.5 h for a base case on a single GPU. Validated against conventional Computational Fluid Dynamics, FlexPINN achieves high-fidelity predictions, with maximum relative errors of 3.25% for the pressure drop coefficient and 2.86% for the mixing index. A comprehensive parametric study evaluates three baffle shapes (rectangular, elliptical, triangular) across four configurations and Reynolds numbers (Re = 5, 20, 40, 80). Results demonstrate that rectangular baffles in a double-unit, staggered configuration (C) at Re = 40 yield the peak mixing efficiency of 1.63, significantly outperforming other designs. This work successfully bridges a critical gap in PINN applications by providing a validated, efficient tool for the analysis and optimization of intricate 3D passive micromixers.
Hassanzadeh et al. (Sat,) studied this question.