Accuracy of bead-spring chains in strong flows

Abstract

We have analyzed the response of bead-spring chain models in strong elongational flow as the amount of polymer represented by a spring is changed. We examined the longest relaxation time of the chains which is used to quantify the strength of the flow in terms of a Weissenberg number. A chain with linear springs can be used to predict the longest relaxation time of the nonlinear chains if the linear spring constant is modified correctly. We used the expansion of the elongational viscosity in the limit of infinite Weissenberg number to investigate the change of the viscosity as the scale of discretization was changed. We showed that the viscosity is less sensitive to the details of the spring force law because the chain is fully extended at very large Weissenberg number. However, the approach to that infinite Weissenberg number response is dependent both on the behavior of the spring force at large force and the behavior at small force. New spring force laws to represent the worm-like chain or the freely jointed chain are correct at both of these limits, while other currently used force laws produce and error. We also investigated the applicability of these expansions to chains including hydrodynamic interactions. Our results suggest that the longest relaxation time may not be the appropriate time scale needed to non-dimensionalize the strain rate in such highly extended states.