  From biological tissues to layers of paint, macroscopic non-porous materials
with the capacity to swell when brought in contact with an appropriate solvent
are ubiquitous. Here, we study experimentally and theoretically one of the
conceptually simplest of such systems, the swelling of a thin hydrogel layer by
a single water drop. Using a bespoke experimental setup, we observe fast
absorption leading to a radially spreading axisymmetric blister. Employing a
linear poroelastic framework and thin-layer scalings, we develop a non-linear
one-dimensional diffusion equation for the evolution of the blister height
profile, which agrees well with experimental observations.
