Abstract
A new model for viscoelastic phase separation is proposed, based on a systematically derived conservative two-fluid model. Dissipative effects are included by phenomenological viscoelastic terms. By construction, the model is consistent with the second law of thermodynamics. We study well-posedness of the model in two space dimensions, i.e., existence of weak solutions, a weak-strong uniqueness principle, and stability with respect to perturbations, which are proven by means of relative energy estimates. Our numerical simulations based on the new viscoelastic phase separation model are in good agreement with physical experiments. Furthermore, a good qualitative agreement with mesoscopic simulations is observed.
Highlights
In this work we propose and analyze a new viscoelastic phase separation model.The mixing properties of polymer solutions are highly temperature-dependent, leading to the terms “good” and “poor” solvent
We study well-posedness of the model in two space dimensions, i.e., existence of weak solutions, a weakstrong uniqueness principle, and stability with respect to perturbations, which are proven by means of relative energy estimates
In this work we have first considered a suitable reduction of a modified binary fluid model
Summary
In this work we propose and analyze a new viscoelastic phase separation model. The mixing properties of polymer solutions are highly temperature-dependent, leading to the terms “good” and “poor” solvent. In polymer solutions several new effects appear which are related to the different length and time scales of the solvent and the polymer molecules, leading to so-called dynamical asymmetry, see [4]. A closure of the system was obtained by relating the relative velocity between solvent and polymer through an ad-hoc constitutive relation and additional equations for the viscoelastic stresses. Motivated by the considerations in [25], we include additional dissipative terms in the momentum equations and utilize a change of viscoelastic variables to obtain our final model. These deviations from [8] turn out to be essential for the verification of mathematical well-posedness. We refer to [26, 27] where results of numerical simulations in two and three space dimensions are compared with physical experiments from [5] and indicate very good agreement
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