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Deformation of thin viscous liquid films exposed to a transverse thermal gradient results in Bénard–Marangoni instability, which would lead to the formation of micro- and nano-sized features. Linear and nonlinear analyses are performed to investigate the thermally induced pattern formation in shear thinning and shear thickening liquid films. The so-called thin film (TF) equation is re-derived to include viscosity variations using the power-law (PL) model. The characteristic wavelength for the growth of instabilities is found using a linear stability analysis of the PL-TF equation. A finite-difference-based discretization scheme and adaptive time step solver are used to solve the PL-TF equation for the nonlinear numerical model. The results show that the rheological property affects the timescale of the process and the size and final shape of the formed features. The fastest growth pillar reaching the top substrate in a shear thickening fluid is shorter than both the shear thinning and the Newtonian fluid cases. Moreover, morphological changes between patterns of shear thinning and shear thickening fluids are correlated with local viscosity variations. The number of formed pillars considerably increases with the increasing flow behavior index. The existing model also predicts the formation of pillars and bicontinuous structures at very low and high filling ratios.

Electrohydrodynamic (EHD) and thermocapillary (TC) forces are used to destabilize the interface of ultra-thin liquid films and create submicron sized features. EHD instabilities result from normal component of Maxwell stress while the TC induces shear stress to the interface. In this study the accuracy of linear stability (LS) analysis for the prediction of final structures which undergo non-linear stages during pattern evolution are investigated by using new normalizing factors. Then the reason for the deviation between LS analysis and non-linear simulation results are discussed. It is found that despite the positive effect of TC in reducing the structure sizes compared to the EHD case, it causes lateral movement of pillars which results in faster coarsening in later stages of pattern formation. To control the movement of patterns and create well-ordered features, non-uniform electrostatic and TC induced instabilities of the film are examined by using ridge and square block shaped electrodes.

To improve the electrically assisted patterning process and create smaller sized features with the higher active surface area, the combined thermocapillary-electrohydrodynamic (TC-EHD) instability of liquid nanofilms is considered. First, the 3-D thin film equation is rederived for nonisothermal films and then the influential factors on the dynamics and stability of thin liquid film are found using linear stability (LS) analysis. Nonlinear studies are also conducted to investigate the long-time evolution of the interface using an in-house developed Fortran code employing high order finite difference and adaptive time step solver for the spatial and time derivatives. The number density of pillars (columnar raised structure) formed in 1 μm(2) area is significantly increased compared to the EHD base-case and nanosized pillars are created due to the thermocapillary effects. Relative interface area increases of up to 18% due to this pattern miniaturization are realized. It is also found that increase in the thermal conductivity ratio of layers changes the mechanism of pattern formation resulting in nonuniform and randomly distributed micro pillars being generated.

The underlying mechanism of thermal induced patterning is investigated using a numerical phase-field model. Research on the subject has been mostly restricted to lubrication approximation, which is only valid for the cases that the initial film thickness is smaller than the characteristic wavelength of induced instabilities. Since the long-wave approximation is no longer valid in the later stages of pattern evolution, we employed the full governing equations of fluid flow and the thermally induced Marangoni effect to track the interface between the polymer film and the air bounding layer. Conducting a systematic study on the impact of influential parameters, we found that an increase in the temperature gradient, thermal conductivity ratio, and initial thickness of the thin film resulted in shorter processing time and faster pattern formation. Additionally, the contact angle between the polymer film and the bounding plates showed a significant effect on the shape of created features. Compared to the reported experimental observation by Dietzel and Troian [“Mechanism for spontaneous growth of nanopillar arrays in ultrathin films subject to a thermal gradient,” J. Appl. Phys. 108, 074308 (2010)], our numerical modeling provided a more accurate prediction of the characteristic wavelength against the linearized model currently used in the literature. The numerical findings in this study provide valuable insight into thermal-induced patterning, which can be a useful guide for future experimental works.

The dynamics, instability, and pattern formation of thermally triggered thin liquid films are investigated numerically under a long-wave limit approximation. To determine the mechanisms responsible for instability growth and pattern formation in confined heated nanofilms, acoustic phonon (AP) and thermocapillary (TC) models are examined using both linear and nonlinear analyses. Under uniform heating conditions, both AP and TC models predict the formation of raised columnar structures (pillars) and bicontinuous structures for very low and high filling ratios defined as the ratio of the initial film thickness to the plate separation distance, ${D}^{\ensuremath{-}1}$. A transition threshold is observed when $D\ensuremath{\approx}2.5$. However, the TC model predicts smaller features for larger $D$, whereas the opposite prediction applies for the AP model. Under spatially variable cooling conditions involving a patterned top plate, both TC and AP models exhibit similar predictions: pillars form under the top plate protrusions. When the heating is spatially variable, the lower plate is patterned; the AP model predicts pillar formation above ridges, whereas the TC model predicts pillar formation above the valleys.

The influence of electrostatic heterogeneity on the electric-field-induced destabilization of thin ionic liquid (IL) films is investigated to control spatial ordering and to reduce the lateral dimension of structures forming on the films. Commonly used perfect dielectric (PD) films are replaced with ionic conductive films to reduce the lateral length scales to a sub-micron level in the EHD pattering process. The 3-D spatiotemporal evolution of a thin IL film interface under homogenous and heterogeneous electric fields is numerically simulated. Finite differences in the spatial directions using an adaptive time step ODE solver are used to solve the 2-D nonlinear thin film equation. The validity of our simulation technique is determined from close agreement between the simulation results of a PD film and the experimental results in the literature. Replacing the flat electrode with the patterned one is found to result in more compact and well-ordered structures particularly when an electrode with square block protrusions is used. This is attributed to better control of the characteristic spatial lengths by applying a heterogeneous electric field by patterned electrodes. The structure size in PD films is reduced by a factor of 4 when they are replaced with IL films, which results in nano-sized features with well-ordered patterns over the domain.

In the electrohydrodynamic (EHD) patterning process, electrostatic destabilization of the air-polymer interface results in micro- and nano-size patterns in the form of raised formations called pillars. The polymer film in this process is typically assumed to behave like a perfect dielectric (PD) or leaky dielectric (LD). In this study, an electrostatic model is developed for the patterning of an ionic liquid (IL) polymer film. The IL model has a finite diffuse electric layer which overcomes the shortcoming of assuming infinitesimally large and small electric diffuse layers inherent in the PD and LD models respectively. The process of pattern formation is then numerically simulated by solving the weakly nonlinear thin film equation using finite difference with pseudo-staggered discretization and an adaptive time step. Initially, the pillar formation process in IL films is observed to be the same as that in PD films. Pillars initially form at random locations and their cross-section increases with time as the contact line expands on the top electrode. After the initial growth, for the same applied voltage and initial film thickness, the number of pillars on IL films is found to be significantly higher than that in PD films. The total number of pillars formed in 1 μm(2) area of the domain in an IL film is almost 5 times more than that in a similar PD film for the conditions simulated. In addition, the pillar structure size in IL films is observed to be more sensitive to initial film thickness compared to PD films.

The effect of electrostatic force on the dynamics, morphological evolution, and drainage time of ultrathin liquid bilayers (100 nm) are investigated for perfect dielectric-perfect dielectric (PD-PD) and ionic liquid-perfect dielectric (IL-PD) bilayers. The weakly nonlinear "thin film" equation is solved numerically to obtain spatiotemporal evolution of the liquid-liquid interface responses to transverse electric field. In order to predict the electrostatic component of conjoining/disjoining pressure acting on the interface for IL-PD bilayers, an analytical model is developed using the nonlinear Poisson-Boltzmann equation. It is found that IL-PD bilayers with electric permittivity ratio of layers (lower to top), εr, greater than one remain stable under an applied electric field. An extensive numerical study is carried out to generate a map based on εr and the initial mean thickness of the lower layer. This map is used to predict the formation of various structures on PD-PD bilayer interface and provides a baseline for unstable IL-PD bilayers. The use of an ionic liquid (IL) layer is found to reduce the size of the structures, but results in polydispersed and disordered pillars spread over the domain. The numerical predictions follow similar trend of experimental observation of Lau and Russel. (Lau, C. Y.; Russel, W. B. Fundamental Limitations on Ordered Electrohydrodynamic Patterning; Macromolecules 2011, 44, 7746-7751).

Spatiotemporal evolution of liquid-liquid interface leading to dewetting and pattern formation is investigated for thin liquid bilayeres subjected to the long range electrostatic force and the short range van der Waals forces. Based on the 2D weakly non-linear thin film equation three dimensional structure evolution is numerically simulated. A combined finite difference for the spatial dimensions and an adaptive time step ODE solver is used to solve the governing equation. For initially non-wetting surfaces, the stabilizing effects of viscosity and interfacial tension and the destabilizing effect of the Hamaker constant are investigated. Electrostatic interaction is calculated analytically for both perfect dielectric-perfect dielectric and ionic conductive-perfect dielectric bilayers. Ionic conductive-perfect dielectric bilayers based on the electric permittivity ratio of layers are found to be stabilized or deformed in response to the applied external electric field.Copyright © 2014 by ASME