Keywords: Microfluidics, polymer solutions, Brownian dynamics, blood flow Abstract: Many interesting and important phenomena in flowing complex fluids arise when the length scale of the microstructure becomes comparable with the length scale of the flow geometry. This is the case, for example, for solutions of genomic DNA in a microfluidic device or blood in the microcirculation. We describe here an efficient computational framework, based on a new real-space particle-particle/particle-mesh approach to solution of Stokes equations, for performing Brownian dynamics simulations of polymer solutions in micron-scale geometries and use them to illustrate and understand hydrodynamic migration phenomena of DNA in these geometries. The methodology will also be combined with a novel immersed boundary method for elastic capsules in Stokes flow. With this approach, we take some initial steps toward understanding the observed beneficial effects that addition of drag-reducing polymers have on blood flow.