Deterministic Lateral Displacement: Are contact interactions necessary?

One of the simplest microfluidic separation techniques, Deterministic Lateral Displacement (DLD), involves flowing particles of different size across a grid of cylindrical obstacles. Particles of different sizes follow different paths, even at very small Reynolds number, a fact traditionally explained by invoking contact interactions with the obstacles that force particles off streamlines. However, in true Stokes flow of force-free particles, contact in finite time is impossible. We investigate here whether hydrodynamic interactions alone can explain permanent particle deflections at vanishing Re. Using recent analytical results for corrections of tangential and normal particle velocity near a wall, we model displacement of a neutrally buoyant spherical particle encountering a single obstacle in a uniform flow. By changing the obstacle and flow geometry in order to break both the fore-aft symmetry and the cross-flow symmetry, we find permanent displacement without invoking contact or other short-range forces. While the magnitude of the effect is small, it is predictable and can be enhanced for different particle shapes or by using multiple obstacles, as in DLD. For a range of initial conditions, hydrodynamic effects force the particle to approach the interface so closely as to engage short-range interaction (e.g. sticking) in realistic scenarios. These results serve as fundamental building blocks for the understanding of hydrodynamic particle manipulation at zero Reynolds number.