Separation mechanisms underlying vector chromatography in microlithographic arrays

Micropatterned chips possessing an asymmetric, spatially periodic array of obstacles enable the vector (directional) chromatographic separation of charged particles animated by an external electric field. We apply a network theory to analyze the chip-scale (L-scale) transport of finite-size Brownian particles in such devices and identify those factors that break the symmetry of the chip-scale particle mobility tensor, most importantly the hydrodynamic wall effects between the particles and the obstacle surfaces. Our analysis contrasts with prevailing separation theories, which are limited to effectively point-size particles, for which wall effects are negligible. These theories require a biasing of obstacle-scale (l-scale; l≪L) bifurcation branches within the network. Such bifurcations are shown to constitute but one factor in modeling the vector chromatography of finite-size particles, and not necessarily the dominant factor.