Phase separation in swelling and deswelling hydrogels with a free boundary

We present a full kinetic model of a hydrogel that undergoes phase separation during swelling and deswelling. The model accounts for the interfacial energy of coexisting phases, finite strain of the polymer network, and solvent transport across free boundaries. For the geometry of an initially dry layer bonded to a rigid substrate, the model predicts that forcing solvent into the gel at a fixed rate can induce a volume phase transition, which gives rise to coexisting phases with different degrees of swelling, in systems where this cannot occur in the free-swelling case. While a nonzero shear modulus assists in the propagation of the transition front separating these phases in the driven-swelling case, increasing it beyond a critical threshold suppresses its formation. Quenching a swollen hydrogel induces spinodal decomposition, which produces several highly localized, highly swollen phases which coarsen and are then ejected from free boundary. The wealth of dynamic scenarios of this system is discussed using phase-plane analysis and numerical solutions in a one-dimensional setting.