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.
Highlights
Fabrication of micro- and nano-sized structures is an innovative solution for microelectronics, optoelectronics, and micro/ nano-fluidic applications
The numerical approach presented in this study surpasses the long-wave limit inherent in the TF and linear stability (LS) models
Compared to the experimental data,[14] the volume of fluid (VOF) model predicted the characteristic wavelength (λ) with significantly higher accuracy compared to the TF model and LS analysis
Summary
Fabrication of micro- and nano-sized structures is an innovative solution for microelectronics, optoelectronics, and micro/ nano-fluidic applications. The TC-induced instabilities are categorized into two fundamental modes: short-wavelength (SW) and long-wavelength (LW) The former leads to a cellular convection pattern without any nonlinear surface deformations, and it occurs commonly in relatively thicker or less viscous liquid films or a combination of both. Chou and Zhuang[52] were the pioneers who reported the creation of micrometer-sized features on the ultrathin molten polymer films using high transverse thermal gradients They introduced the surface charge (SC) model, based on the image charge-induced electrohydrodynamic instabilities, as the underlying mechanism for TC-induced instability. A majority of these studies utilized an analytical approach to evaluate the length and time scales in the TC-induced patterning process.[14,33] This non-linear model, called the “thin-film” (TF) equation, relies on the Stokes flow and the lubrication approximation. The presented analyses aim to provide an insight into the mechanism of thermal-induced patterning and to save time and cost in designing related experiments
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