Does shear induced demixing resemble a thermodynamically driven instability?

Abstract

In the present paper, we continue our recent studies on a two-fluid Rolie-Poly approximation of entangled polymer solutions in simple shear flows. We review the existing literature on shear induced demixing (SID) in two-fluid models and highlight the apparent similarities to a thermodynamic model of demixing. Focusing on steady unidirectional simple shear flows driven by a constant applied shear stress, we show that when the frictional drag between solvent and polymer is asymptotically large, our two-fluid model is mathematically equivalent to a thermodynamic model in terms of its long-time concentration dynamics. In particular, we show that SID minimizes a Lyapunov functional L distinct from the system's free energy F. We apply our asymptotic model to make predictions regarding nucleation (finite amplitude instabilities) and coalescence phenomena in SID. Numerical calculations with the full model corroborate the asymptotic model predictions. Finally, we apply the same asymptotic analysis to two flows in which a thermodynamic mapping fails. First, we consider steady simple shear flows driven by a constant boundary velocity (as opposed to a constant boundary stress), wherein the hydrodynamic instability appears to have the same character but can no longer be mapped to an equivalent thermodynamic instability. Second, we consider unsteady simple shear flows driven by an oscillating boundary stress, wherein the nonlinear dynamics of demixing are totally distinct from what a thermodynamic model predicts.In the present paper, we continue our recent studies on a two-fluid Rolie-Poly approximation of entangled polymer solutions in simple shear flows. We review the existing literature on shear induced demixing (SID) in two-fluid models and highlight the apparent similarities to a thermodynamic model of demixing. Focusing on steady unidirectional simple shear flows driven by a constant applied shear stress, we show that when the frictional drag between solvent and polymer is asymptotically large, our two-fluid model is mathematically equivalent to a thermodynamic model in terms of its long-time concentration dynamics. In particular, we show that SID minimizes a Lyapunov functional L distinct from the system's free energy F. We apply our asymptotic model to make predictions regarding nucleation (finite amplitude instabilities) and coalescence phenomena in SID. Numerical calculations with the full model corroborate the asymptotic model predictions. Finally, we apply the same asymptotic analysis to two flows in...