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

Abstract

In this paper, we study the influence of the upper gas layer on the drying and gelation of a polymer solution. The gel is formed due to the evaporation of the binary solution into (inert) air. A one-dimensional model is proposed, where the evaporation flux is more realistically described than in previous studies. The approach is based on general thermodynamic principles. A composition-dependent diffusion coefficient is used in the liquid phase and the local equilibrium hypothesis is introduced at the interface to describe the evaporation process. The results show that high thickness of the gas layer reduces evaporation, thus leading to longer drying times. Our model is also compared with more phenomenological descriptions of evaporation, for which the mass flux through the interface is described by the introduction of a Peclet number. A global agreement is found for appropriate values of the Peclet numbers and our model can thus be considered as a tool allowing to link the value of the empirical Peclet number to the physics of the gas phase. Finally, in contrast with other models, our approach emphasizes the possibility of very fast gelation at the interface, which could prevent all Marangoni convection during the drying process.

Influence of evaporation on the morphology of a thin film of a partially miscible binary mixture

“…Considering that the inert gas absorption in the liquid is negligible and that only the solvent is volatile, the evaporation flux calculated at the liquid-gas interface takes the following form [69][70][71]:…”

Evaporation induced demixing in binary sessile drops

“…We will also assume that the cooling effect of evaporation does not modify the thermophysical properties of the mixture. Under these hypotheses, the dimensional form of the temperature and concentration equations in the substrate, liquid and gas phases are given by [39,29]:…”

“…where J and L are the evaporation rate and the latent heat of the solvent, respectively. Considering that the inert gas adsorption in the liquid is negligible, the mass flux J calculated for each phase at the interface will be [29]:…”

“…where ρ is density. Subsequently, the decrease of the fluid layer thickness due to evaporation is described by [29]:…”

“…In order to rationalize the interesting observations during evaporation of binary mixtures, much effort was devoted over the last decade. Very recently, Rabani et al [29] have presented a thermo-hydrodynamic 1-D model of the evaporation process for a polymer solution in a thin film taking into account the physics of the upper gas layer and its interactions with the liquid phase. In another work, Mikishev et al [30] have studied the effect of an insoluble surfactant on the thresholds of an evaporative Bénard-Marangoni instability in a liquid layer evaporating into air using one-sided model formulation, which means that only the lower liquid layer was modelled, while the upper gas layer is not described in detail and its influence on the liquid is introduced in a phenomenological way, by appropriate boundary conditions at the common interface.…”