Influence of Composition Dependent Diffusion Coefficient, Viscosity and Relaxation Time on Evaporative Rayleigh-Bénard-Marangoni Instabilities Induced by Solvent Evaporation in a Polymer Solution

In this study, a linear stability analysis is performed for both monotonic and oscillatory modes within a horizontal polymer solution layer, which solely the solvent evaporates into air. The approach is based on general thermodynamic principles and also on the physics of the gas phase and its interactions with the liquid phase. Due to evaporation, the solvent mass fraction changes and cooling occurs at the liquid-gas interface. This can trigger solutal and thermal Rayleigh-Benard-Marangoni instabilities in the system. For the monotonic mode, the effects of composition dependent diffusion coefficient and dynamic viscosity on the onset of Rayleigh-Benard-Marangoni convection are studied. Moreover, the effect of different total heights of the liquid-gas system on the behavior of convection onset is considered. The results show that a variable diffusion coefficient and a variable viscosity can notably change the onset of instability for a polyisobutylene (PIB)/toluene solution. Our model for the monotonic mode is also satisfactorily compared with an experimental study. For the oscillatory mode, where the relaxation time is also composition dependent, we observe that very thin layers will be susceptible to an oscillatory instability when drying occurs in the system. Finally, an approximate model is derived exploiting the fact that the solutal Marangoni is by far the most dominant instability mechanism here. A negligible difference with respect to the full model confirms the predominance of the solutal Marangoni mechanism.