The Hydrodynamic Deflection

In deterministic lateral displacement devices — microfluidic platforms used for cell sorting and particle filtering — particles passing arrays of obstacles are deflected from their initial streamlines. The standard explanation invokes contact: particles bump into obstacles, and the bump redirects them. This explanation requires short-range surface interactions and is difficult to predict quantitatively.

arXiv:2603.15695 demonstrates that net deflection of force-free particles in Stokes flow can arise purely from hydrodynamic interactions, provided that the flow-obstacle configuration breaks fore-aft symmetry. No contact is needed. The key ingredient is an inclined elliptic obstacle whose asymmetry generates wall-induced velocity corrections that systematically displace particles passing nearby.

The governing equations are time-reversible — Stokes flow has no memory. Yet the deflection is irreversible because the broken spatial symmetry converts the reversible dynamics into a net displacement. The particle’s trajectory after passing the obstacle does not retrace its approach. Time-reversibility of the equations does not imply spatial reversibility of the trajectory when the geometry breaks the symmetry.

Analytical scaling laws predict the maximum deflection as a function of particle size, obstacle geometry, and flow configuration. The predictions match direct numerical simulations across a broad parameter range. The magnitude of hydrodynamic deflection is comparable to what contact-based models predict, meaning hydrodynamics alone accounts for a substantial fraction of observed displacement in real devices.

The mechanism extends beyond deflection: the same asymmetric obstacles can maneuver particles close enough to surfaces for short-range attractive forces to capture them — enabling filtration in porous media microfluidics without requiring direct contact for the initial approach.