By solving the full equations of an extended two-fluid model in two dimensions, we give the first numerical study revealing non-equilibrium steady states in sheared entangled polymer mixtures. This research provides answers for some fundamental questions in sheared binary mixtures of entangled polymers. Our results reveal that non-equilibrium steady states with finite domain size do exist, and apparent scaling exponents L ∥ ~ γ · − 1 . 05 and L ⊥ ~ γ · − 1 are found over six decades of shear rate. Since the wall effects get involved in our simulations, the dependence of average domain size on system size cannot be strictly eliminated. In addition, as an obvious influence of viscoelasticity, the polymer viscosity η p appears to induce linear translation of the fitted lines. Through two-dimensional numerical simulations, we show the detailed dynamic evolution of microstructure in binary polymer mixtures with asymmetric composition under shear flow. It is found that the phase patterns are significantly different from symmetric fluids studied previously. Finally, we also identify the importance of wall effects and confirm the irreplaceable role of inertia for a non-equilibrium steady state.

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Non-equilibrium steady states of entangled polymer mixtures under shear flow