Two-layer modeling of thermally induced Bénard convection in thin liquid films: Volume of fluid approach vs thin-film model

Abstract

This study focuses on a detailed analysis of thermally induced Bénard convection, thermocapillary instability, and interfacial deformation of a nanofilm. The dynamics, instability, and morphological evolution of a thin liquid film investigated using a volume of fluid (VOF) numerical scheme that incorporates the Marangoni stress to model the gas–liquid interface deformation. The results obtained from VOF are then compared with those of the “thin-film” model in many cases to find an accurate model for predicting the characteristic wavelength for the growth of instabilities. We also present a correlation to predict the relation between the characteristic wavelength found by VOF numerical results and the analytical linear stability analysis predictions. This is followed by examining the protrusion width and the distance between the protrusions on the structures’ final shape and interface evolution time. Finally, linear theoretical relations for the formation of secondary pillars are presented based on the width of protrusions, their separation distance, and the inverse filling ratio. The results show that the number of pillars increases when the width and distance between two protrusions are greater than a critical value.