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 opti... More >