Hydrodynamic interactions in polymer dynamics

Abstract

A modification to the traditional bead-spring model of polymers is proposed, which properly accounts for the full hydrodynamic interactions between the beads. The new model uses the Stokesian dynamics simulation technique to calculate far-field, many-body effects as well as near-field lubrication and excluded-volume effects. No preaveraging of the interactions is required. In addition to the xF, spring contribution to the stress, the Stokesian dynamics model calculates hydrodynamic and direct Brownian contributions to the stress. Orientations and stresses obtained from the Stokesian dynamics dumbbell were compared to predictions of the Rouse dumbbell (no hydrodynamic interaction) and the Zimm dumbbell (Rotne-Prager hydrodynamic interaction). Infinite-dilution behaviors were examined in steady, simple shear and oscillatory shear flows. In steady shear the Stokesian dynamics model provides no improvement over the Zimm model. Both give qualitatively similar results for shear and normal stresses. The hydrodynamic stress is constant and equal to the Einstein viscosity contribution from each bead. The Brownian stress is negligible. The analysis reveals how hydrodynamic interaction causes shear thinning. The interaction between the beads tilts the dumbbell towards the shear axis, reducing the xF contribution to the shear stress. The oscillatory-shear results are similar to the steady-shear results, except that the hydrodynamic stress results in a non-zero high-frequency viscosity. Hydrodynamic and Brownian stresses will provide greater contributions to the rheology of multibead chains, in which many-body effects are more important. This is true of both steady shear and oscillatory shear. Simulations of non-dilute suspensions of Stokesian dynamics dumbbells were compared with results for suspensions of spheres at the same volume fractions. The xF stress reaches a maximum at a bead volume fraction of 0.15, above which hydrodynamic forces dominate the solution rheology. The interparticle forces have little effect on the magnitudes of the hydrodynamic and Brownian stresses. The interparticle forces become very dependent upon initial configuration at high volume fractions. It is hypothesized that there exists a critical volume fraction, above which the polymer distribution function will always be dependent upon the initial configuration and the shear history.