Topological Optimization of a 2D Microfluidic Channel for Particle Separation

This study presents an advanced computational framework that integrates a finite-difference Navier--Stokes solver, a SIMP-based topology optimization engine, and a Lagrangian particle advection module into a unified, iteratively coupled pipeline for physics-driven geometric design. The framework autonomously evolves the internal material distribution of a 2D microchannel by minimizing an objective function that directly quantifies particle mis-sorting, eliminating reliance on manual heuristic design and external actuation forces. Applied to the problem of passive microfluidic particle separation, the computational approach generated manufacturable, binary-material topologies across five optimization iterations, achieving a peak sorting efficiency of $\Phi = 0.6667$ (66.67%) at iteration~2 and stabilizing at $\Phi = 0.6111$ (61.11%) in subsequent iterations. The results demonstrate that physics-based iterative optimization can autonomously discover non-intuitive channel geometries that outperform conventional heuristic designs in adaptability and separation robustness. This work contributes a modular, extensible computing methodology applicable to a broad class of constrained geometric optimization problems in engineering systems.