Continuum theory of swelling material surfaces with applications to thermo-responsive gel membranes and surface mass transport

•We model a swelling gel membrane as a material surface with a thickness microstructure.•We study problems involving a three-dimensional body coated with a swelling membrane.•We discuss the constitutive theory for polymer gel membranes.•We present the finite element implementation of the swelling material surface model.•We analyze applications in biomedicine, micro-motility and coating technology.

Soft membranes are commonly employed in shape-morphing applications, where the material is programmed to achieve a target shape upon activation by an external trigger, and as coating layers that alter the surface characteristics of bulk materials, such as the properties of spreading and absorption of liquids. In particular, polymer gel membranes experience swelling or shrinking when their solvent content change, and the non-homogeneous swelling field may be exploited to control their shape. Here, we develop a theory of swelling material surfaces to model polymer gel membranes and demonstrate its features by numerically studying applications in the contexts of biomedicine, micro-motility, and coating technology. We also specialize the theory to thermo-responsive gels, which are made of polymers that change their affinity with a solvent when temperature varies.