Systematic derivation of hydrodynamic equations for viscoelastic phase separation
Dominic Spiller1, Aaron Brunk2, Oliver Habrich3
1Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany.
Summary
We developed a new two-fluid model for polymer solutions, incorporating viscoelasticity and phase separation. This model offers a molecular basis for describing polymer dynamics and rheology, differing from standard models.
Area of Science:
- Polymer Physics
- Soft Matter Physics
- Non-equilibrium Thermodynamics
Background:
- Phase separation in polymer solutions is influenced by viscoelastic effects.
- Existing models often lack a direct molecular interpretation or consistent thermodynamic grounding.
Purpose of the Study:
- To derive a simple hydrodynamic two-fluid model for non-entangled polymer solutions undergoing phase separation.
- To ensure the model is consistent with equilibrium and non-equilibrium thermodynamics.
- To provide a clear molecular interpretation of all model components.
Main Methods:
- Coarse-graining of a molecular model to derive hydrodynamic equations.
- Incorporation of free-energy functional and splitting dynamics into conservative and dissipative parts.
- Satisfying Onsager relations and the second law of thermodynamics.
Main Results:
- A simplified two-fluid model comprising momentum conservation, convection-diffusion, and relaxation equations.
- Inclusion of interfacial and elastic stresses and contributions.
- Derivation of a rheological constitutive equation distinct from the standard Oldroyd-B model.
Conclusions:
- The derived model provides a thermodynamically consistent framework for viscoelastic phase separation in polymer solutions.
- The model treats hydrodynamic and macromolecular degrees of freedom on an equal footing.
- Future work will investigate the model's ability to reproduce experimental phenomena.
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