Analysis and simulation of a model of polyelectrolyte gel in one spatial dimension

作者：Chen Haoran^*; Calderer Maria Carme; Mori Yoichiro

来源：Nonlinearity, 2014, 27(6): 1241-1285.

DOI：10.1088/0951-7715/27/6/1241

• polyelectrolyte gel
• ionic electrodiffusion
• two phase model
• Onsager's variational principle
• stability analysis

We analyse a model of polyelectrolyte gels that was proposed by the authors in previous work. We first demonstrate that the model can be derived using Onsager's variational principle, a general procedure for obtaining equations in soft condensed matter physics. The model is shown to have a unique steady state under the assumption that a suitably defined mechanical energy density satisfies a convexity condition. We then perform a detailed study of the stability of the steady state in the spatially one-dimensional case, obtaining bounds on the relaxation rate. Numerical simulations for the spatially one-dimensional problem are presented, confirming the analytical calculations on stability.

• 出版日期2014-6