  We investigated theoretically water evaporation from concentrated
supramolecular mixtures, such as solutions of polymers or amphiphilic
molecules, using numerical resolutions of a one dimensional model based on mass
transport equations. Solvent evaporation leads to the formation of a
concentrated solute layer at the drying interface, which slows down evaporation
in a long-time scale regime. In this regime, often referred to as the falling
rate period, evaporation is dominated by diffusive mass transport within the
solution, as already known. However, we demonstrate that, in this regime, the
rate of evaporation does not also depend on the ambient humidity for many
molecular complex fluids. Using analytical solutions in some limiting cases, we
first demonstrate that a sharp decrease of the water chemical activity at high
solute concentration, leads to evaporation rates which depend weakly on the
humidity, as the solute concentration at the drying interface slightly depends
on the humidity. However, we also show that a strong decrease of the mutual
diffusion coefficient of the solution enhances considerably this effect,
leading to nearly independent evaporation rates over a wide range of humidity.
The decrease of the mutual diffusion coefficient indeed induces strong
concentration gradients at the drying interface, which shield the concentration
profiles from humidity variations, except in a very thin region close to the
drying interface.
