The fluidic resistance of an array of obstacles and a method for improving boundaries in deterministic lateral displacement arrays

Deterministic lateral displacement (DLD) is a microfluidic method of separating particles by size. DLD relies on precise flow patterns to deliver high-resolution particle separation. These patterns determine which particles are displaced laterally, and which follow the flow direction. Prior research has demonstrated that the lateral array boundaries can be designed to improve the uniformity of the critical size and hence separation performance. A DLD device with an invariant critical size throughout is yet unknown. In this work, we propose a 3D design approach. We first represent the flow through the DLD as a 2D lattice of resistors. This is used to determine the relative flow resistances at the boundaries that will deliver the correct flux patterns. We then use the lattice Boltzmann method to simulate fluid flow in a 3D unit cell of the DLD and measure the fluidic resistance for a range or typical dimensions. The results of this work are used to create a new equation for fluidic resistance as a function of post size, post height, and post spacing. We use this equation to determine array geometries that should have the appropriate resistances. We then design and simulate (in COMSOL) complete devices and measure fluid fluxes and first flow-lane widths along the boundaries. We find that the first flow-lane widths are much more uniform than in any devices described previously. This work provides the best method for designing periodic boundaries, and enables narrower, shorter, and higher throughput DLD devices.