A minimal model for solvent evaporation and absorption in thin films

Abstract

We present a minimal model of solvent evaporation and absorption in thin films consisting of a volatile solvent and nonvolatile solutes. An asymptotic analysis yields expressions that facilitate the extraction of physically significant model parameters from experimental data, namely the mass transfer coefficient and composition-dependent diffusivity. The model can be used to predict the dynamics of drying and film formation, as well as sorption/desorption, over a wide range of experimental conditions. A state diagram is used to understand the experimental conditions that lead to the formation of a solute-rich layer, or "skin", at the evaporating surface during drying. In the case of solvent absorption, the model captures the existence of a saturation front that propagates from the film surface towards the substrate. The theoretical results are found to be in excellent agreement with data produced from dynamic vapour sorption experiments of ternary mixtures comprising an aluminum salt, glycerol, and water. Moreover, the model should be generally applicable to a variety of practical contexts, from paints and coatings, to personal care, packaging, and electronics.

Effect of including a gas layer on the gel formation process during the drying of a polymer solution

“…1, is comprised of a mixture of a volatile solvent and a non-volatile polymer placed on a flat solid and non-permeable substrate, under a layer of inert air. Our model of the evaporation process introduces a thermodynamics-based expression for the evaporation flux and this approach will be compared with two models from the literature that express the evaporation flux, respectively, as a linear [20] and a nonlinear [22] function of the mass fraction at the interface. In Fig.…”

“…Diffusion is assumed to be the only mechanism of mass transport within the bulk and a Fick law is used, with a composition dependent diffusion coefficient. Any temperature variations, such as those resulting from evaporative cooling, are presumed to be sufficiently small so that the system can be treated as isothermal [22,24]. We will also consider that the solvent and polymer densities are not too different, which allows to consider that during the drying process, the mixture keeps a constant density, equal to the initial density of the liquid mixture.…”

“…Let us now briefly describe two other phenomenological models of evaporation to which ours will be compared [20,22]. For these models, the behavior of the gas layer is no longer described and a simple phenomenological law is proposed to describe the evaporation flux.…”

“…In both cases, the flux depends on the concentration of the evaporating component in the liquid along the interface. For solvent-polymer mixtures, linear and non-linear expressions were proposed by Ozawa et al [20] and Hennessy et al [22] respectively. The corresponding non-dimensional evaporation fluxes are denoted L ζ and nL ζ and take the form:…”

“…They found that the shortest drying time occurs in the limit of strong gravitational effects due to the rapid formation of a bilayer with a polymer-rich lower layer and a solvent-rich upper layer, while drag leads to the formation of a polymer-rich skin below the free surface and causes the drying time to increase significantly. In another study, Hennessy et al [22] considered a model of solvent evaporation in a thin film comprised of volatile solvent and a nonvolatile solute which can be used to predict the dynamics of drying and film formation.…”