WIAS Preprint No. 2802, (2020)

A kinetic model of a polyelectrolyte gel undergoing phase separation


  • Celora, Giulia L.
  • Hennessy, Matthew G.
  • Münch, Andreas
  • Wagner, Barbara
  • Waters, Sarah L.

2010 Mathematics Subject Classification

  • 74A30 80A22 34B15

2008 Physics and Astronomy Classification Scheme

  • 83.80.Rs 83.10.Tv


  • Polyelectrolyte gel, phase separation, non-equilibrium thermodynamics




In this study we use non-equilibrium thermodynamics to systematically derive a phase-field model of a polyelectrolyte gel coupled to a thermodynamically consistent model for the salt solution surrounding the gel. The governing equations for the gel account for the free energy of the internal interfaces which form upon phase separation, as well as finite elasticity and multi-component transport. The fully time-dependent model describes the evolution of small changes in the mobile ion concentrations and follows their impact on the large-scale solvent flux and the emergence of long-time pattern formation in the gel. We observe a strong acceleration of the evolution of the free surface when the volume phase transition sets in, as well as the triggering of spinodal decomposition that leads to strong inhomogeneities in the lateral stresses, potentially leading to experimentally visible patterns.

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