Witches' Brew and Bloodcraft An Examination of Inertial Behaviors In Laminar Flow Environments

Abstract

Deterministic Lateral Displacement arrays (DLDs) utilize the properties of laminar or viscous flow to separate biological material by characteristic size. DLDs are comprised of a long, at chip through which a solution is forced. A grid of laterally offset rows of pillars determines a flow pattern throughout the length of the chip. Due to laminar behavior, particles are expected to closely follow flow patterns, separating them based on their flow mode. As the size scale of DLDs decreases in an effort to boost the resolution of separation, experimentalists find that the efficiencies are decreasing: Polymer chains that otherwise traverse the length of the array unscathed break apart in the smaller scale, and particles do not separate as expected from laminar properties. Using low Reynolds and Stokes number approximations, this paper solves the laminar case in 2 1/2 dimensions for a scalar stream function. The scalar stream function allows us to translate boundary conditions from cartesian to polar, which allows us to de fine a critical radius and characteristic displacement vector to locate regions of inertial particle behavior in an otherwise completely laminar fluid. Finally, the scalar stream function and critical radius are applied to simulated flow environments to investigate if inertial behaviors may be occurring. We find clear patterns which are compliant with experimental observations, and make claims regarding theoretical models.