Formation of glassy skins in drying polymer solutions: approximate analytical solutions

We study the formation of a glassy skin at the air interface of drying polymer solutions. We introduce a simple approximation, which is valid for most diffusion problems, and which allows us to derive analytical relationships for the polymer concentration as a function of time. We show that the approximate results differ by less than 15% from those obtained by numerically solving the diffusion equation. We use the approximation to study skin formation in evaporating solutions. We focus on the influence of variations of the mutual diffusion coefficient with concentration, when the latter decreases sharply at high concentrations, as observed in the vicinity of the glass transition. We show that the skin thickness depends very strongly on the exponent characterising the decrease of the diffusion coefficient, in contrast to the polymer volume fraction at the interface, which varies only slightly with the exponent.

Automated summary

We investigate the formation of a glassy skin in drying polymer solutions at the air interface and propose a simple approximation method that provides analytical relationships for the polymer concentration over time. The results obtained from the approximation differ by less than 15% from those obtained by numerically solving the diffusion equation. Using this method, we examine the influence of variations in the mutual diffusion coefficient on the thickness of the skin formed during evaporation. We find that the skin thickness strongly depends on the exponent describing the decrease in the diffusion coefficient, in contrast to the slight variation in the polymer volume fraction at the interface.