Flexible polymer chain dynamics and rheological properties in steady flows

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Abstract
A stochastic approach equivalent to the kinetic theory of a dilute solution of polymer molecules idealized as Kramers freely jointed bead–rod chains is presented. This stochastic approach forms the basis for a Brownian dynamics simulation algorithm that generates sample trajectories of Kramers chains from which steady-state rheological properties of the model polymer solution can be extracted. In steady shear flow, the solution exhibits both shear-thinning viscosity and first normal stress coefficient. In steady elongational flow, the elongational viscosity of the solution increases sharply with increasing elongation rate and approaches an asymptotic value many times its low elongation rate value. Computer animations of sample trajectories of Kramers chains generated by the simulations also reveal a wealth of information about the rotation, stretching, and alignment of polymer molecules in shear and elongational flows.