Brownian dynamics simulations of bead-rod and bead-spring chains: numerical algorithms and coarse-graining issues

Abstract

The efficiency and robustness of various numerical schemes have been evaluated by performing Brownian dynamics simulations of bead-rod and three popular nonlinear bead-spring chain models in uniaxial extension and simple shear flow. The bead-spring models include finitely extensible nonlinear elastic (FENE) springs, worm-like chain (WLC) springs, and Pade approximation to the inverse Langevin function (ILC) springs. For the bead-spring chains two new predictor–corrector algorithms are proposed, which are much superior to commonly used explicit and other fully implicit schemes. In the case of bead-rod chain models, the mid-point algorithm of Liu [J. Chem. Phys. 90 (1989) 5826] is found to be computationally more efficient than a fully implicit Newton’s method. Furthermore, the accuracy and computational efficiency of two different stress expressions for the bead-rod chains, namely the Kramers–Kirkwood and the modified Giesekus have been evaluated under both transient and steady conditions. It is demonstrated that the Kramers–Kirkwood with stochastic filtering is the preferred choice for transient flow while the Giesekus expression is better suited for steady state calculations. The issue of coarse graining from a bead-rod chain to a bead-spring chain has also been investigated. Though bead-spring chains are shown to capture only semi-quantitatively the response of the bead-rod chains in transient flows, a systematic coarse-graining procedure that provides the best description of bead-rod chains via bead-spring chains is presented.