A model of semiflexible bead-rod chain with anisotropic friction can mimic closely the hydrodynamics of a slender filament. We present an efficient algorithm for Brownian dynamics simulations of this model with configuration dependent anisotropic bead friction coefficients. The algorithm is an extension of that given previously for the case of configuration independent isotropic friction coefficients by Grassia and Hinch [J. Fluid Mech. 308, 255 (1996)]. We confirm that the algorithm yields predicted values for various equilibrium properties. We also present a stochastic algorithm for evaluation of the stress tensor, and we show that in the limit of stiff chains the algorithm recovers the results of Kirkwood and Plock [J. Chem. Phys. 24, 665 (1956)] for rigid rods with hydrodynamic interactions.
Bibliographical noteFunding Information:
This work was supported through Award No. CTS-CAREER-0134389, through the Nanoscale Science and Engineering Initiative under Award No. EEC-0118007, the Rice Terascale Cluster funded by NSF under Grant No. EIA-0216467, Intel and HP, and the Minnesota Supercomputing Institute. FIG. 1. Distribution of cosine of angles between rods 1 and 2 (엯) and rods 4 and 5 (◇) in a chain of nine beads with anisotropic friction ζ ‖ = 2 ζ ⊥ for κ ∕ ( a k T ) = 1 or L p ∕ L = 0.125 (top) and relative error with respect to the theoretical distribution (bottom). The solid line denotes the normalized theoretical prediction P ( cos θ ) = exp [ κ cos θ ∕ ( a k T ) ] . Solid symbols represent the correct algorithm and empty symbols represent the incorrect algorithm with unprojected noise. The symbols were computed by averaging the configuration of 400 molecules for ten times the rotational diffusion time of a rod of equal length. Initial configurations of the molecules were generated by sampling the theoretical distribution, then letting the system equilibrate for three rotational diffusion times before collecting data. FIG. 2. Distribution of cosine of angles between rods 1 and 2 (엯) and rods 4 and 5 (◇) in a chain of nine beads with anisotropic friction ζ ‖ = 2 ζ ⊥ for κ ∕ ( a k T ) = 4 or L p ∕ L = 0.5 (top) and relative error with respect to the theoretical distribution (bottom). FIG. 3. Relative steady-shear viscosity ( η ∕ η 0 ) vs Weissenberg number Wi = γ ̇ τ r reported by Kirkwood and Plock (Ref. 19 ) for rigid rods with hydrodynamics interactions (continuous line) and by Stewart and Sorensen (Ref. 24 ) for multibead rods without hydrodynamic interactions (dashed line), compared with the results of BD simulations for semiflexible rods with L p ∕ L = 250 and ζ ⊥ ∕ ζ ‖ = 2 (rescaled with η 0 = η 0 rod , τ r = τ rod , ∎) and ζ ⊥ ∕ ζ ‖ = 1 (rescaled with η 0 = η 0 mb , τ r = τ mb , ◇). FIG. 4. Relative error vs Δ t (symbols) and linear fit (lines) for the end to end distance (top) and for the cosine distribution (bottom) for chains with nine beads with anisotropic friction ζ ‖ = 2 ζ ⊥ , κ ∕ ( a k T ) = 1 (엯), and κ ∕ ( a k T ) = 4 (◆). The errors were computed averaging the configurations of 5000 chains for ten times τ rod . Note that the error bars for ϵ cos are smaller than the symbols.