Asymmetric hydrodynamics for inertialess deterministic particle deflection

In Stokes flow, a neutrally buoyant, force-free particle can be displaced across streamlines by hydrodynamic interactions with an interface, and net displacement is possible if the fore–aft symmetry of this interaction is broken (while time-reversal symmetry remains intact). Having developed a rigorous hydrodynamic model for particle motion in Stokes flow incorporating recent results on wall-interaction velocity corrections, we apply the formalism to the encounter of a spherical particle with a cylindrical obstacle of given 2D cross-section. Numerically solving for the particle trajectories, we confirm net displacements across streamlines after the encounter if the flow symmetry is doubly broken: the obstacle cross section is elliptical and the flow has a non-trivial angle of attack. This geometry mimics characteristics of Deterministic Lateral Displacement (DLD) devices relevant to microfluidic particle sorting. We further develop an analytical understanding of the magnitude of deflection and its scaling with the ellipse eccentricity and angle of attack, as well as its quadratic dependence on the particle size. The theory shows that a particular impact parameter leads to maximum deflection and predicts this optimum in good agreement with our numerical results. As these effects necessitate very close approach of particles to the obstacle, the deflections are in practice superimposed with filtering effects of particle sticking by short-range attraction. The combination of both processes suggests strategies for designing microfluidic particle manipulators, such as DLD arrays and porous-media filters, without inertia and using hydrodynamic forces only.