Accurate Closure for the Configuration Dynamics and Rheology of Dilute Polymer Chains in Arbitrary Flows

We present a new, “FENE-mode”, constitutive model for conformation and stress dynamics of dilute polymer chains in arbitrary flows, obtained by preaveraging equations for the normal modes using a “representative” spring constant that depends on the magnitudes of both the first and second modes, accounting for both overall chain stretch and chain folds. Simulations with this model are orders of magnitude faster than with multi-spring Brownian dynamics (BD) simulations and yet retain more of their accuracy than other preaveraged models. This is demonstrated by comparing the predictions of the FENE-mode model with those from BD simulations in startup of uniaxial extension, relaxation after cessation of this flow, steady shear, and mixed flows. For all cases, we find that, even when few modes are used, the transient and final steady-state conformations and stresses are in much better agreement with BD predictions than those of the existing preaveraged FENE-P and FENE-PM models. The possibility of extension of the approach to the more important case of entangled polymers is also discussed. Because the model allows cost-accuracy trade-offs to be made through choice of the number of modes used, the model should be ideal for multidimensional simulations of polymer flows.