Limits of Parabolic Flow Theory in Microfluidic Particle Separation: A Computational Study

Microfluidic particle separation technologies are useful for enriching rare cell populations for academic and clinical purposes. In order to separate particles based on size, deterministic lateral displacement (DLD) arrays are designed assuming that the flow profile between posts is parabolic or shifted parabolic (depending on post geometry). The design process also assumes the shape of the normalized flow profile is speed-invariant. The work presented here shows flow profile shapes vary, in arrays with circular and triangular posts, from this assumption at practical flow rates (10 < Re < 100). The root-mean-square error (RMSE) of this assumption in the circular post arrays peaked at 0.144. The RMSE in the triangular post array peaked at 0.136. Flow development occurred more rapidly in circular post arrays when compared to triangular post arrays. Additionally, the changes in critical bumping diameter (D_CB) the DLD design metric used to calculate the size-based separation threshold were examined for 10 different row shift fractions (F_RS). These errors correspond to a D_CB that varies as much as 11.7% in the circular post arrays and 15.1% in the triangular post arrays.