Phase separation in swelling and deswelling hydrogels with a free boundary

Abstract

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 freeswelling 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.

Elastic stresses reverse Ostwald ripening

“…While this captures some of the basic phenomenology, recent theories aimed to account for activity, 21,22 large-scale concentration gradients, 23,24 complex compositions, 25 and rheology. 4,11,[26][27][28] Our work further establishes a general framework for evaluating the role of a passive network in crowded systems (see also ref. 29).…”

A kinetic model of a polyelectrolyte gel undergoing phase separation

“…The latter has be experimentally estimated (see e.g. [45] and discussion in [10,60]) and it is found to have the form:…”

“…The dependencies of the (electro)chemical potentials on the mobile species concentrations, the gradient of the solvent concentration, the thermodynamic pressure and the electrostatic potential, as well as the deformation of the gel, means that the solvent and ionic species fluxes are complex expressions. However, as we have shown for a neutral hydrogel [60], it is straightforward to reduce these fluxes to familiar forms in simplifying limits. Neglecting for now terms due to interfacial energies and the electric field, we can consider two sublimits.…”

Fluid-fluid phase separation in a soft porous medium

“…Recently, the problem of liquid-liquid phase separation within an elastic network has attracted substantial attention from the perspective of droplet formation within living cells [15][16][17][18][19][20]. Elastically modulated phase separation has also been studied within the context of hydrogels [21][22][23][24]. It is now well understood that the presence of an elastic network fundamentally alters the phase-separation process by introducing an energetic cost to the rearrangements that are needed for phase separation to occur.…”

“…By conceptualising the transition between pore invasion and cavity formation as a phase-separation process, our phase-field model captures the competing physical processes in a thermodynamically consistent manner. In §II, we derive our model by extending the work of Hennessy et al [23] to include an additional fluid phase and to allow for elastic degradation of the solid skeleton via a damage model [40,41]. Our derivation follows the approach of Gurtin [39], using balance laws to set out an energy inequality that imposes certain restrictions on the allowable constitutive behaviours.…”