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.
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.
An analytical solution is developed for the unsteady flow of fluid through a parallel rotating plate microchannel, under the influence of electrokinetic force using the Debye-Hückel (DH) approximation.Transient Navier-Stokes equations are solved exactly in terms of the cosine Fourier series using the separation of variables method. The effects of frame rotation frequency and electroosmotic force on the fluid velocity and the flow rate distributions are investigated. The rotating system is found to have a damped oscillatory behavior. It is found that the period and the decay rate of the oscillations are independent of the DH parameter (k). A time dependent structure of the boundary layer is observed at higher rotational frequencies. Furthermore, the rotation is shown to generate a secondary flow and a parameter is defined (b(t)) to examine the ratio of the flow in the y and x directions. It showed that both the angular velocity and the Debye-Hückel parameters are influential on the induced transient secondary flow in the y direction. At high values of the Debye-Hückel parameter and the rotation parameter the flow rates in the x and y directions are found to be identical. The analytical solution results are found to be in good agreement with the numerical method results and previously published work in this field.
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).
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