Multiscale modeling of polymer flow-induced migration and size separation in a microfluidic contraction flow

Abstract

We study polymer migration in a periodic pressure-driven sudden contraction-expansion flow with contraction dimension comparable to the polymer radius of gyration, for which several polymer migration mechanisms can be important: (1) sieving by the thin channel of polymers too large to easily enter them; (2) deformation-hydrodynamic coupling, including wall-hydrodynamic interaction, which causes polymers to drift away from the walls towards the center of the channel; (3) streamline-curvature-induced migration, in which polymers traveling along curved streamlines migrate towards the center of curvature; and (4) depletion-convection coupling, in which depletion layers in thin channels are convected across wide side chambers, creating a one-sided diffusion barrier that leads to depletion from the side chamber. We use both Stochastic Rotation Dynamics (SRD), which includes hydrodynamic interaction (HI), and simple Brownian dynamics (BD), with HI omitted and flow field given by finite element analysis. The similarity in results from SRD and BD at Weissenberg number Wi less than 10 (where Wi is based on the shear rate in the narrow region of the contraction channel) shows that HI (Mechanism 2) has only a weak effect on polymer migration in our tight geometry. At Wi>1, the polymer migrates towards the centerline in the wide region, due mainly to streamline-curvature-induced (SCI) migration (Mechanism 3), but also to depletion-convection-induced migration (Mechanism 4). And we demonstrate these two mechanisms more explicitly in a pressure-driven flow in a grooved channel that is significantly wider than the polymer. SCI migration dominates in the contraction geometry, and produces a migration velocity proportional to Wi2. Using the central limit theorem, we accurately predict the position and width of a band of polymer passing through N periodic contractions, thereby demonstrating the potential for SCI migration as a mechanism of size separation in a multi-step planar contraction channel. We find that the best separation is achieved at Wi around 2, where SCI migration has the greatest resolving power between polymers of different size. We also find that sieving (Mechanism 1) is dominant at low Wi less than unity, where the chains with large radius of gyration are delayed in their entry to the thin channel, relative to shorter polymers. This sieving separation mechanism differs from that of size-exclusion chromatography which yields faster migration by the shorter chains. Our strategy of combining simulation methods with the central limit theorem could also be used to predict separation efficiencies of a wide variety of polymers and colloids in microfluidic geometries.