| Riassunto: | We analyse the dynamics of different routes to collapse of a constrained
polyelectrolyte gel in contact with an ionic bath. The evolution of the gel is
described by a model that incorporates non-linear elasticity, Stefan-Maxwell
diffusion and interfacial gradient free energy to account for phase separation
of the gel. A bifurcation analysis of the homogeneous equilibrium states
reveals three solution branches at low ion concentrations in the bath, giving
way to only one above a critical ion concentration. We present numerical
solutions that capture both the spatial heterogeneity and the multiple
time-scales involved in the process of collapse. These solutions are
complemented by two analytical studies. Firstly, a phase-plane analysis that
reveals the existence of a depletion front for the transition from the highly
swollen to the new collapsed equilibrium state. This depletion front is
initiated after the fast ionic diffusion has set the initial condition for this
time regime. Secondly, we perform a linear stability analysis about the
homogeneous states that show that for a range of ion concentrations in the
bath, spinodal decomposition of the swollen state gives rise to localized
solvent-rich(poor) and, due to the electro-neutrality condition, ion-poor(rich)
phases that coarsen on the route to collapse. This dynamics of a collapsing
polyelectrolyte gel has not been described before.
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