Topology Optimization for Microfluidic Mixers by a Phase Field Method

ABSTRACT We investigate multi‐physical topology optimization for microfluidic mixers. Starting from the Ising model, we derive a thermodynamically consistent Ginzburg–Landau free energy functional that incorporates the objective functional as an effective external field, providing a physically interpretable framework for phase‐field topology optimization. To eliminate fluid blockage in microfluidic mixers, we incorporate the coupled Navier–Stokes, convection–diffusion, and Poisson–Boltzmann equations. An Allen–Cahn type gradient flow method is proposed based on sensitivity analysis. The algorithm is validated for its computational effectiveness through numerical simulations of benchmark problems in 2D and 3D.