Modeling hydrodynamic interaction in Brownian dynamics: simulations of extensional flows of dilute solutions of DNA and polystyrene

We describe a method to include full hydrodynamic interactions (HI) using the Rome-Prager tensor into the bead-spring model without excluded-volume interactions in away suitable for Brownian dynamics (BD) simulations of the transient nonlinear rheological properties of dilute polymer solutions. First, we develop a scheme to determine the HI parameter h* and bead radius "a" that keeps the number of beads N modest at high molecular weight and yet matches the bead-spring model to the "real" polymer both in its longest relaxation time or diffusivity near equilibrium and in the drag on the chain at full extension, the latter being estimated by a formula of Batchelor. Second, we compare three different numerical integration methods, namely an explicit Euler's method, a semi-implicit Newton's method and a semi-implicit predictor-corrector method, and conclude that the predictor-corrector method is the best one available now, because of its ability to use larger time-steps and the relatively low computational expense for each step. Third, we perform simulations for two different macromolecules, namely lambda-phage DNA and high molecular weight polystyrene (PS). We find that we can model lambda-phage DNA with full HI with only 10 beads, and find that HI has negligible effect on extensional-flow behavior because of DNA's expanded configuration even at rest, and therefore, its small value of h* = 0.03. For PS in a theta solvent, however, molecular configurations are much more compact, and to avoid bead overlap we must keep h* < 0.5. This requires the use of more beads, at least N = 20 for a molecular weight of 2 million, even if we drop the requirement that we match the longest relaxation time. Surprisingly, despite our inability to match the experimental longest relaxation time with a limited number of beads, excellent agreement with experimental filament-stretching strain-stress data is obtained except for the plateau Trouton ratio for PS of molecular weight of 2 million at various Weissenberg numbers. The inclusion of HI eliminates the "lag", the delay in growth of the Trouton ratio relative to experimental data, seen in earlier simulations. (C) 2003 Elsevier B.V. All rights reserved.