We present a fully parametrized bead-spring chain model for stained -phage DNA. The model accounts for the finite extensibility of the molecule, excluded volume effects, and fluctuating hydrodynamic interactions ͑HI͒. Parameters are determined from equilibrium experimental data for 21 m stained -phage DNA, and are shown to quantitatively predict the non-equilibrium behavior of the molecule. The model is then used to predict the equilibrium and nonequilibrium behavior of DNA molecules up to 126 m. In particular, the HI model gives results that are in quantitative agreement with experimental diffusivity data over a wide range of molecular weights. When the bead friction coefficient is fit to the experimental relaxation time at a particular molecular weight, the stretch in shear and extensional flows is adequately predicted by either a free-draining or HI model at that molecular weight, although the fitted bead friction coefficients for the two models differ significantly. In shear flow, we find two regimes at high shear rate (␥ ) that follow different scaling behavior. In the first, the viscosity and first normal stress coefficient scale roughly as ␥ Ϫ6/11 and ␥ Ϫ14/11 , respectively. At higher shear rates, these become ␥ Ϫ2/3 and ␥ Ϫ4/3 . These regimes are found for both free-draining and HI models and can be understood based on scaling arguments for the diffusion of chain ends.

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.

The dynamics of dissolved long-chain macromolecules are different in highly confined environments than in bulk solution. A computational method is presented here for detailed prediction of these dynamics, and applied to the behavior of ϳ1-100 m DNA in micron-scale channels. The method is comprised of a self-consistent coarse-grained Langevin description of the polymer dynamics and a numerical solution of the flow generated by the motion of polymer segments. Diffusivity and longest relaxation time show a broad crossover from free-solution to confined behavior centered about the point HϷ10S b , where H is the channel width and S b is the free-solution chain radius of gyration. In large channels, the diffusivity is similar to that of a sphere diffusing along the centerline of a pore. For highly confined chains (H/S b Ӷ1), Rouse-type molecular weight scaling is observed for both translational diffusivity and longest relaxation time. In the highly confined region, the scaling of equilibrium length and relaxation time with H/S b are in good agreement with scaling theories. In agreement with the results of Harden and Doi ͓J. Phys. Chem. 96, 4046 ͑1992͔͒, we find that the diffusivity of highly confined chains does not follow the scaling relation predicted by Brochard and de Gennes ͓J. Chem. Phys. 67, 52 ͑1977͔͒; that relationship does not account for the interaction between chain and wall.

An extended Brownian dynamics simulation method is used to characterize the dynamics of long DNA molecules flowing in microchannels. The relaxation time increases due to confinement in agreement with scaling predictions. During flow the molecules migrate toward the channel center line, and thereby segregate according to molecular weight. Capturing these effects requires the detailed incorporation of solvent flow in the simulation method, demonstrating the importance of hydrodynamic effects in the dynamics of confined macromolecules.

We have simulated Brownian bead-spring chains of up to 125 units with fluctuating hydrodynamic and excluded volume interactions using the Chebyshev polynomial approximation proposed by Fixman ͓Macromolecules 19, 1204 ͑1986͔͒ for the square root of the diffusion tensor. We have developed a fast method to continuously determine the validity of the eigenvalue range used in the polynomial approximation, and demonstrated how this range may be quickly updated when necessary. We have also developed a weak first order semiimplicit time integration scheme which offers increased stability in the presence of steep excluded volume potentials. The full algorithm scales roughly as O(N 2.25 ) and offers substantial computational savings over the standard Cholesky decomposition. The above algorithm was used to obtain scaling exponents for various static and zero shear rate dynamical properties, which are found to be consistent with theoretical and/or experimental predictions.