Weakly Nonlinear Analysis of Electroconvection in a Suspended Fluid Film

The deformation of a viscous liquid droplet suspended in another liquid and subject to an applied electric field is a classic multiphase flow problem best described by the Melcher-Taylor leaky dielectric model. The main assumption of the model is that any net charge in the system is concentrated on the interface between the two liquids as a result of the jump in Ohmic currents from the bulk. Upon application of the field, the drop can either attain a steady prolate or oblate ...

Electro-hydrodynamic phenomena in liquid crystals constitute an old but still very active research area. The reason is that these phenomena play the key role in various applications of liquid crystals and due to the general interest of physical community to out-of-equilibrium systems. Nematic liquid crystals (NLCs) are ideally representative for such investigations. Our article aims to study theoretically the linear NLCs dynamics. We include into consideration orientation ela...

Weakly conducting dielectric liquid drops suspended in another dielectric liquid and subject to an applied uniform electric field exhibit a wide range of dynamical behaviors contingent on field strength and material properties. These phenomena are best described by the Melcher-Taylor leaky dielectric model, which hypothesizes charge accumulation on the drop-fluid interface and prescribes a balance between charge relaxation, the jump in Ohmic currents from the bulk and charge ...

A theoretical analysis of surface fluctuations of a freely standing thermotropic smectic-A liquid crystal film is provided, including the effects of viscous hydrodynamics. We find two surface dynamic modes (undulation and peristaltic). For long wavelengths and small frequencies in a thin film, the undulation mode is the dominant mode. Permeation enters the theory only through the boundary conditions. The resulting power spectrum is compared with existing experiments. It is al...

We consider a mathematical model that describes the flow of a Nematic Liquid Crystal (NLC) film placed on a flat substrate, across which a spatially-varying electric potential is applied. Due to their polar nature, NLC molecules interact with the (nonuniform) electric field generated, leading to instability of a flat film. Implementation of the long wave scaling leads to a partial differential equation that predicts the subsequent time evolution of the thin film. This equatio...

The stability of liquid film flows are important in many industrial applications. In the dip-coating process, a liquid film is formed over a substrate extracted at a constant speed from a liquid bath. We studied the linear stability of this film considering different thicknesses $\hat{h}$ for four liquids, spanning a large range of Kapitza numbers ($\rm Ka$). By solving the Orr-Sommerfeld eigenvalue problem with the Chebyshev-Tau spectral method, we calculated the neutral cur...

We report measurements of thermally-induced mean-square director-angle fluctuations <theta^2> below primary supercritical bifurcations to electroconvection of the nematic liquid crystals I52 and "Merck Phase V". For epsilon_mf = V^2/V_c,mf^2 - 1 < -0.1 (V is the amplitude of the applied alternating voltage) we find <theta^2> proportional to epsilon_mf^(-gamma) with gamma given by linear theory (LT). Closer to the bifurcation there are deviations from LT with a smaller gamma a...

Applying an electric field to an aqueous colloidal dispersion establishes a complex interplay of forces among the highly mobile simple ions, the more highly charged but less mobile colloidal spheres, and the surrounding water. This interplay can induce a wide variety of visually striking dynamical instabilities, even when the applied field is constant. This Article reports on the highly organized patterns that emerge when electrohydrodynamic forces compete with gravity in thi...

In contrast to the predictions of the standard theory of electroconvection (EC), our experiments showed that the action of superposed ac and dc voltages rather inhibits pattern formation than favours the emergence of instabilities; the patternless region may extend to much higher voltages than the individual ac or dc thresholds. The pattern formation induced by such asymmetrical voltage was explored in a nematic liquid crystal in a wide frequency range. The findings could be ...

Electroconvection in rechargeable batteries enhances the growth of dendrites at the electrode surface. The addition of low molecular weight polymers to the electrolyte in batteries results in the formation of a thin layer of higher polymer concentration near the electrode. This is due to van der Waals forces of attraction between the metal electrode and the polymers dissolved in the electrolyte. The van der Waals forces act as a restoring body force on the electrolyte and opp...