The swelling behavior of hydrogels, involving coupled diffusion and large deformations, makes them ideal for biomedical applications such as micro- and nano-scale drug delivery systems. Understanding the transient swelling or drying behavior of hydrogels at relevant length-scales will provide insight for the development of specialized and controlled drug release. At sub-millimeter length-scales, surface stresses have been shown to significantly influence material behavior for soft polymers and hydrogels, but very little is known about the influence of surface stresses on the swelling kinetics of hydrogels. In this paper, we present a non-linear theory and mixed finite element formulation that takes into account mass transport, large deformations, and elastocapillary effects for hydrogels. Focusing on hydrogel micro-spheres, we provide a comparison of swelling kinetics between the presented non-linear theory and an analytical solution using linear poroelasticity that incorporates surface stresses. Our results demonstrate that when the surface free energy is constant per unit current area (fluid-like) and the elastocapillary length-scale is on the order of the size of the hydrogel micro-sphere, the transient response equilibrates approximately an order of magnitude faster in time compared to the case without surface effects irrespective of swelling or drying. This difference in equilibration time suggests the interplay between competing processes of solvent diffusion, large deformations, and surface effects. Furthermore, we demonstrate that a Neo-Hookean type surface free energy can result in an even faster equilibration as compared to a fluid-like surface free energy. Lastly, our finite element implementation predicts the transient response of complex shapes and constrained structures.

水凝胶的膨胀行为（包括耦合的扩散和大的变形）使其成为生物医学应用（如微米和纳米级药物输送系统）的理想选择。理解水凝胶在相关长度尺度上的瞬时溶胀或干燥行为将为开发专门的和受控的药物释放提供见识。在亚毫米的长度尺度上，表面应力已显示出显着影响软聚合物和水凝胶的材料性能，但对表面应力对水凝胶溶胀动力学的影响知之甚少。在本文中，我们提出了一种非线性理论和混合有限元公式，该公式考虑了水凝胶的质量传递，大变形和弹性毛细管效应。专注于水凝胶微球，我们提供了所提出的非线性理论与使用线性多孔弹性并结合了表面应力的解析解之间的溶胀动力学的比较。我们的结果表明，当表面自由能在单位电流面积（流体状）中恒定且弹性毛细管长度尺度在水凝胶微球尺寸的数量级时，瞬态响应的平衡速度大约快一个数量级。与没有表面效果的情况相比，无论是溶胀或干燥的时间都及时。平衡时间的这种差异表明溶剂扩散，大变形和表面效应的竞争过程之间存在相互作用。此外，我们证明，新霍克式的表面自由能与类似流体的表面自由能相比，可以更快地达到平衡。