Shear-induced migration in flowing polymer solutions: Simulation of long-chain DNA in microchannels

Abstract

We simulate dilute solution dynamics of long flexible polymer molecules in pressure driven flow in channels with widths of roughly 0.1-10 times the polymer bulk radius of gyration. This is done using a self-consistent coarse-grained Langevin description of the polymer dynamics and a numerical simulation of the flow in the confined geometry that is generated by the motions of polymer segments. Results are presented for a model of DNA molecules of ϳ10-100 m contour length in micron-scale channels. During flow, the chains migrate toward the channel centerline, in agreement with well-known experimental observations. The thickness of the resulting hydrodynamic depletion layer increases with molecular weight at constant flow strength; higher molecular weight chains therefore move with a higher average axial velocity than lower molecular weight chains. In contrast, if the hydrodynamic effects of the confining geometry are neglected, depletion of concentration is observed in the center of the channel rather than at the walls, contradicting experimental observations. The mechanisms for migration are illustrated using a simple kinetic theory dumbbell model of a confined flexible polymer. The simple theory correctly predicts the trends observed in the detailed simulations. We also examine the steady-state stretch of DNA chains as a function of channel width and flow strength. The flow strength needed to stretch a highly confined chain away from its equilibrium length is shown to increase with decreasing channel width, independent of molecular weight; this is fairly well explained using a simple blob picture.

Theory of shear-induced migration in dilute polymer solutions near solid boundaries

“…58 More interestingly, the simulations predict that during pressure-driven flow in a channel, the molecules will tend to migrate toward the centerline, forming depletion layers that are much larger than the radius of gyration of the molecules. 11,12,59 The goal of the present work is to complement those detailed simulations with theoretical results that provide a more fundamental understanding of the migration phenomenon.…”

“…The model provides an accurate representation of experimental data ͑structural and dynamic͒ for DNA in bulk solution, 55,56 and has been extended to capture the dynamics of DNA solutions in microchannels, including hydrodynamic effects. [10][11][12] Relaxation and diffusion of chains in a channel of square cross section 10,11 follow the predictions of a simple scaling theory, due to Brochard and de Gennes, 57 that is based on the screening of segmentsegment hydrodynamic interactions by the confining walls. Furthermore, the simulation results for diffusion in a slit channel ͑i.e., between parallel infinite walls͒ agree very well with experiments.…”

“…If HI are included, but not their modifications due to the presence of a wall, then migration toward regions of higher shear rate is found; this is opposite to the trend observed experimentally. 12 For example, Sekhon, Armstrong, and Jhon 43 considered bulk hydrodynamic interactions in rectilinear slit flow using kinetic theory for a bead-spring dumbbell model, and concluded that cross-stream migration is possible with HI, and Brunn 44,45 and Brunn and Chi 46 predicted migration toward the walls using Oseen-Burgers free-space hydrodynamic interactions for a bead-spring chain model. To our knowledge, only two studies in the polymer literature aside from our own ͑dis-cussed below͒ have addressed the effect of hydrodynamic interactions in wall-bounded flows of dilute polymer solutions.…”

“…1-7͒ have fueled substantial interest in the structure and dynamics of confined solutions of DNA. [8][9][10][11][12][13][14][15] Predictive methods capable of describing the conformation and motion of polymer chains in microfluidic geometries would be of considerable significance for the conception and design of such devices. Finally, new experimental tools such as the surface forces apparatus 16 allow investigation of confinement effects down into the nanoscale region, and refinements in fabrication technology allow construction of "nanofluidic" devices with dimensions in the sub-100-nm regime.…”

Confined dynamics of a single DNA molecule

“…However, this approach is difficult to apply in confined geometries because the hydrodynamics interaction tensor cannot be calculated analytically and a numerical procedure is required (see also [9,10]). To overcome this difficulty, many groups have used an appropriate beads-springs model with a coarse-grained solvent whose momentum transport is explicitly computed (e.g.…”