Relationship between substrate swelling and hydrogel film growth. (A) Increase in the radius of PAAc–PAAm spheres as a function of immersion time in aqueous solutions with different PVA concentrations: 0 wt% (○), 1 wt% (▸), 2.5 wt% (◆), 5 wt% (▼), 7.5 wt% (■), 10 wt% (▲), and 15 wt% (●). Full lines show best fits by Eq. 1 for the first hour of swelling. (B) Substrate diffusivity measured from fits as a function of PVA concentration. The overlap concentration C* indicates the transition from dilute to semidilute PVA solutions. (C) Thickness of PVA hydrogel films as a function of immersion time for the same experiments as in A. Full lines show model predictions with Eq. 4 for a spherical substrate (Φc = 0.35 wt%). Dashed lines show the results of numerical simulations. (D) Same as C in log-log scale. In all graphs, error bars represent the maximum SD in a time series. They are not shown when smaller than the symbols.