Droplet absorption and spreading into thin layers of polymer hydrogels

From biological tissues to micro actuators and absorption of solvents into layers of paint, macroscopically non-porous materials with the capacity to swell when in contact with a solvent are ubiquitous. In these systems, owing to strong solid–fluid interactions, chemically- driven flows can yield large geometric changes. We study experimentally and theoretically the canonical problem of the swelling of a thin hydrogel layer by a single water drop. Recent quantitative studies of hydrogel swelling have mostly considered one-dimensional spherically symmetric geometries such as spheres. In contrast, our system considers a two dimensional axisymmetric inherently non-linear problem. Using a bespoke experimental setup, we observe fast absorption leading to a radially spreading axisymmetric blister. We use a fully three-dimensional linear poroelastic framework with nonlinear kinematic equations to obtain governing equations, which we then reduce with thin-layer scaling's to a one dimensional nonlinear diffusion equation for the evolution of the blister geometry. In the limit of large and small deformation, the evolution of the blister characteristic height and radius are self-similar, following power laws in time with exponents that depend on the empirical relation between the effective hydrogel permeability and the polymer volume fraction. Our experimental measurements show that the evolution of the blister is broadly within the theoretical predictions in the large and small deformation regimes. In the general intermediate deformation regime, the measurements are well captured by our reduced one-dimensional diffusion model, which does not require the sophisticated and computationally expensive numerical approaches necessary for the original two-dimensional nonlinear coupled transport problem. By adapting modelling techniques from the fluid dynamics of thin porous elastic layers to a polymer swelling problem, our modelling framework extends the range of polymer swelling problems that can be treated with semi-analytical methods and may inspire future studies. Moreover, our detailed experimental data can serve as a test case for future nonlinear poroelastic frameworks of swelling polymer materials.