Inertial Particle Migration in Contraction–Expansion Microchannels: Effects of Rectangular and Hook-Shaped Microstructures on Secondary Flow and Inertial Lift Competition

Inertial microfluidics offers significant advantages for bioparticle manipulation, including structural simplicity, label-free and external-field-free operation, and high throughput. In this study, numerical simulations and polydimethylsiloxane (PDMS)-based microfluidic experiments were combined to systematically investigate the effects of embedding depth (H) and expansion segment length (L) on particle inertial migration in contraction–expansion array (CEA) channels incorporating embedded rectangular and hook-shaped microstructures. The results demonstrate that particle equilibrium positions are governed by the competition among inertial lift, secondary flow drag, and the effective range over which the secondary flow acts. For both channel configurations, increasing H simultaneously enhances the peak secondary flow intensity and enlarges its effective range, thereby driving particles toward the sidewalls. In contrast, for the two microstructures studied here, the secondary flow intensity is only weakly sensitive to L. In rectangular microstructures, however, the secondary flow is already fully developed within short expansion cavities; further increasing L does not enlarge the effective range but instead weakens the modulation effect of the secondary flow on particles, allowing inertial lift to become more prominent. In hook-shaped microstructures, the secondary flow is not fully developed in short cavities, and increasing L promotes its development and markedly enlarges its effective range, thereby strengthening lateral particle regulation. It can be anticipated that, once the secondary flow is fully developed, its effective range will saturate, and further increasing L will weaken the modulation effect of the secondary flow on particles, allowing inertial lift to dominate again. Using the experimental structure, particle separation experiments were performed, achieving efficient label-free inertial separation of 7 μm and 15 µm particles, with a recovery rate of 99.3% for 15 μm particles and both purity and recovery exceeding 98%. This work elucidates the key role of the effective range of secondary flow in inertial particle migration and provides theoretical guidance for the rational design of CEA-based microfluidic devices.