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.

中文翻译：

---

具有自由边界的溶胀和溶胀水凝胶的相分离

我们提出了在溶胀和溶胀过程中经历相分离的水凝胶的完整动力学模型。该模型考虑了共存相的界面能，聚合物网络的有限应变以及自由边界上的溶剂传输。对于结合到刚性基材上的最初干燥层的几何形状，该模型预测，以固定速率将溶剂强制进入凝胶会诱导体积相转变，从而在系统中产生具有不同溶胀度的共存相。自由膨胀情况下不会发生。虽然非零剪切模量有助于在驱动膨胀情况下将这些相分离的过渡前沿传播，但将其增加到超过临界阈值则会抑制其形成。消灭溶胀的水凝胶会诱发旋节线分解，产生几个高度局部化，高度溶胀的相，这些相变粗，然后从自由边界中弹出。使用一维设置中的相平面分析和数值解讨论了该系统的大量动态方案。