Deterministic separation of suspended particles in a reconfigurable obstacle array

We use a macromodel of a flow-driven deterministic lateral displacement microfluidic system to investigate conditions leading to size-separation of suspended particles. This model system can be easily reconfigured to establish an arbitrary forcing angle, i.e. the orientation between the average flow field and the square array of cylindrical posts that constitutes the stationary phase. We also consider posts of different diameters, while maintaining a constant gap between them, to investigate the effect of obstacle size on particle separation. In all cases, we observe the presence of a locked mode at small forcing angles, in which particles move along a principal direction in the lattice. A locked-to-zigzag mode transition takes place when the orientation of the driving force reaches a critical angle. We show that the transition occurs at increasing angles for larger particles, thus enabling particle separation. Moreover, we observe a linear regression between the critical angle and the size of the particles, which allows us to estimate size-resolution in these systems. The presence of such a linear relation would guide the selection of the forcing angle in microfluidic systems, in which the direction of the flow field with respect to the array of obstacles is fixed. Finally, we present a simple model based on the presence of irreversible interactions between the suspended particles and the obstacles, which describes the observed dependence of the migration angle on the orientation of the average flow.