A ternary model for hydrogel swelling in a bath of a liquid mixture

Hydrogels play a central role in applications ranging from biomedical materials to the wet spinning of sustainable fibers, where performance is governed by the coupled processes of swelling, solvent exchange, and mechanical deformation. This thesis develops a thermodynamically consistent continuum framework for binary and ternary polymer gels, with a focus on organic non-solvent coagulation baths. Building on a recent binary poroelastic model, we first reformulate the equations in cylindrical coordinates to represent a single gel filament under external shear flow. We compare linearly elastic and neo-Hookean constitutive laws to assess their impact on filament behavior. Simulations demonstrate that tangential shear does not affect radial swelling, while the internal axial flow exhibits non-monotonic evolution due to Darcy drag enhanced by gel shrinkage. The framework is then generalized to a ternary polymer–solvent–antisolvent system using Flory–Huggins mixing free energy and Maxwell–Stefan multicomponent diffusion. The model is validated against swelling data for ethanol–water–polymer membranes and successfully recovers the inelastic limit as network elasticity vanishes. Parametric studies in an open-bath configuration demonstrate how interaction parameters control the equilibrium solvent composition. Furthermore, interfacial permeability and diffusivities are shown to govern swelling timescales, revealing the coupled nature of multicomponent diffusion and internal mechanical stresses. This framework provides a predictive basis for characterizing the non-equilibrium interplay between transport and deformation that governs the swelling and deswelling kinetics of hydrogels in ternary systems.