The rheological properties of dilute polymer solutions in exponential shear, uniaxial, and planar extensional flows are compared using Brownian dynamics simulations of both freely draining, flexible bead-rod and bead-spring chains. We introduce a novel stress function for exponential shear which uses the extinction angle χ to take into account the orientation of the chain as it aligns in the flow. Comparing this new stress function during startup and relaxation in exponential shear with in planar extensional flow and in uniaxial extensional flow, we find that for both models there is a quantitative agreement among the three different flows over a large range of Wi, strain, and chain length. Furthermore, the distributions of maximum extension show a microstructural equivalence between ensembles of chains in all three flows up to strains of 3 or 4 at all values of Wi simulated. Finally, we show three comparisons between experiment and simulation of the various flows: (a) simulations and exponential shear experiments of a polyisobutylene/polybutene Boger fluid, (b) simulations and uniaxial extension data from literature, and (c) exponential shear and planar extensional data of a low-density polyethylene melt from literature.
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