Nonlinear dynamics in colloidal model systems under confined flow

Abstract

In the recent years, not only the physical size of computer chips decreased, also the size of microfluidic devices changed drastically. These so called Lab on a chip devices have seen great progress and find applications in many physical, biological or chemical systems. An essential part of all these devices is the precise manipu- lation of suspended particles on the micron scale. Therefore, it is of fundamental importance to understand the nonlinear dynamics of colloidal systems in confined geometries, not only for the development of such devices, but also to gain a better understanding of biological processes. In this work we present two different colloidal model systems, where the sus- pended particles are confined between two planar walls and are driven out of equilibrium using the pressure driven Poiseuille flow. In the first model, we investigate the cross-streamline migration of semiflexible polymers. We introduce the semiflexible polymer as a bead-spring chain, which is a discrete representation of the well known worm-like chain. We take the hydrodynamic interactions between the pointlike beads into account by the two- wall Green tensor of the Stokes equations. With the help of Brownian dynamics simulations we investigate the probability distribution of the center-of-mass of the polymer across the channel. Our simulations reproduce the typical bimodal distribution, as observed in previous experiments and simulations. To gain a better understanding of the origin of this distribution, we derive a Smoluchowski equation for the center-of-mass distribution and carefully analyze the different contributions to the probability current that causes the bimodal distribution. In contrast to previous studies, where the migration away from the centerline was explained by a position-dependent diffusivity, we clearly identify a deterministic drift current as the major cause for migration away from the centerline. We even show that diffusional currents due to a position-dependent diffusivity become less