On the three-dimensional structure of the flow through deterministic lateral displacement devices and Its effects on particle separation

Experiments have shown that a suspension of particles of different dimensions pushed through a periodic lattice of micrometric obstacles can be sorted based on particle size. This label-free separation mechanism, referred to as Deterministic Lateral Displacement (DLD), has been explained hinging on the structure of the 2D solution of the Stokes flow through the patterned geometry, thus neglecting the influence of the no-slip conditions at the top and bottom walls of the channel hosting the obstacle lattice. We show that the no-slip conditions at these surfaces trigger the onset of off-plane velocity components, which impart full three-dimensional character to the flow. The impact of the 3D flow structure on particle transport is investigated by enforcing an excluded volume approach for modelling the interaction between the finite-sized particles and the solid surfaces. We find that the combined action of particle diffusion and of the off-plane velocity component causes the suspended particles to migrate towards the top and bottom walls of the channel. Preliminary results suggest that this effect makes the migration angle of the particles significantly different from that obtained by assuming a strictly two-dimensional structure for the flow of the suspending fluid.