Universal correlation for the critical diameter of deterministic lateral displacement devices with polygonal posts

Deterministic lateral displacement (DLD) is a microfluidic technique that utilizes a specific array of micro-posts to separate cells or particles larger and smaller than a critical diameter. The critical diameter depends on the shape of the posts, the gap between the posts, and the relative shift between the adjacent rows of posts. Here, we present an experimental and numerical investigation to elucidate the functional dependence of the critical diameter of DLD arrays with polygonal posts on the geometric parameters. Based on simulations of fluid flow through DLD devices with varying geometric parameters, we first derived a correlation to predict the critical diameter of DLD arrays with polygonal post shapes having an arbitrary number of sides. We then used a novel experimental approach, wherein we coupled different DLD arrays with an upstream droplet generator to flow droplets of varying sizes and estimate the critical diameter. The critical diameter predicted by the correlation based on simulations compares well with our experimental data and with data available in the literature. The universal correlation for a critical diameter presented here can help design and optimize DLD devices with polygonal posts.