Dynamic Wetting on a Thin Film of Soluble Polymer: Effects of Nonlinearities in the Sorption Isotherm

The wetting dynamics of a solvent on a soluble substrate interestingly results from the rates of the solvent transfers into the substrate. When a supported film of a hydrosoluble polymer with thickness e is wet by a spreading droplet of water with instantaneous velocity U, the contact angle is measured to be inversely proportionate to the product of thickness and velocity, eU, over two decades. As for many hydrosoluble polymers, the polymer we used (a polysaccharide) has a strongly nonlinear sorption isotherm phi(a(w)), where phi is the volume fraction of water in the polymer and a(w) is the activity of water. For the first time, this nonlinearity is accounted for in the dynamics of water uptake by the substrate. Indeed, by measuring the water content in the polymer around the droplet phi at distances as small as 5 mu m, we find that the hydration profile exhibits (i) a strongly distorted shape that results directly from the nonlinearities of the sorption isotherm and (ii) a cutoff length xi below which the water content in the substrate varies very slowly. The nonlinearities in the sorption isotherm and the hydration at small distances from the line were not accounted for by Tay et al., Soft Matter 2011, 7, 6953. Here, we develop a comprehensive description of the hydration of the substrate ahead of the contact line that encompasses the two water transfers at stake: (i) the evaporation condensation process by which water transfers into the substrate through the atmosphere by the condensation of the vapor phase, which is fed by the evaporation from the droplet itself, and (ii) the diffusion of liquid water along the polymer film. We find that the eU rescaling of the contact angle arises from the evaporation condensation process at small distances. We demonstrate why it is not modified by the second process.