Weakly Nonlinear Analysis of Electroconvection in a Suspended Fluid Film

The mathematical model of a rotating electrohydrodynamic flow in a thin suspended liquid film is proposed and studied. The motion is driven by the given difference of potentials in one direction and constant external electrical field $\vE_\text{out}$ in another direction in the plane of a film. To derive the model we employ the spatial averaging over the normal coordinate to a film that leads to the average Reynolds stress that is proportional to $|\vE_\text{out}|^3$. This st...

The common description of the electrical behavior of a nematic liquid crystal as an anisotropic dielectric medium with (weak) ohmic conductivity is extended to an electrodiffusion model with two active ionic species. Under appropriate, but rather general conditions the additional effects can lead to a distinctive change of the threshold behavior of the electrohydrodynamic instability, namely to travelling patterns instead of static ones. This may explain the experimentally ob...

The unsteady electrorotation of a drop of a viscous weakly conducting polarizable liquid suspended in another viscous weakly conducting polarizable liquid immiscible with the former in an applied constant uniform electric field is theoretically investigated. The surface tension of the drop is regarded as sufficiently large for deformation of the drop under the action of the applied electric field and the electrohydrodynamic flow can be considered small and the drop can be con...

Motivated by experiments in electroconvection in nematic liquid crystals with homeotropic alignment we study the coupled amplitude equations describing the formation of a stationary roll pattern in the presence of a weakly-damped mode that breaks isotropy. The equations can be generalized to describe the planarly aligned case if the orienting effect of the boundaries is small, which can be achieved by a destabilizing magnetic field. The slow mode represents the in-plane direc...

We consider the gravity-driven flow of a perfect dielectric, viscous, thin liquid film, wetting a flat substrate inclined at a non-zero angle to the horizontal. The dynamics of the thin film is influenced by an electric field which is set up parallel to the substrate surface - this nonlocal physical mechanism has a linearly stabilizing effect on the interfacial dynamics. Our particular interest is in fluid films that are hanging from the underside of the substrate; these film...

Electroconvection and its coupling with a morphological instability are important in many applications, including electrodialysis, batteries and fuel cells. In this work, we study the effects of a two-dimensional channel flow on the electroconvective and morphological instabilities using two approaches. In the bulk analysis, we consider the instability of the electroneutral bulk region driven by a second kind electroosmosis slip velocity boundary condition and derive the asym...

I consider a dielectric fluid heated from above and subjected to an electric potential difference between its top and bottom. I show that for a suitably chosen electric potential difference, the layer of fluid can become unstable. For the case of a strongly polar fluid like pure water, an electric potential difference of a few hundreds of volts can trigger convection. Although the analysis in this paper cannot explain the phenomenon described in [Gross & Porter(1966)], it cou...

We investigate the coupled dynamics of the local hydrodynamics and global electric response of an electrodialysis system, which consists of an electrolyte solution adjacent to a charge selective membrane under electric forcing. Under a DC electric current, counterions transport through the charged membrane while the passage of co-ions is restricted, thereby developing ion concentration polarization (ICP) or gradients. At sufficiently large currents, simultaneous measurements ...

We formulate the thin-film hydrodynamics of a suspension of polar self-driven particles and show that it is prone to several instabilities through the interplay of activity, polarity and the existence of a free surface. Our approach extends, to self-propelling systems, the work of Ben Amar and Cummings [Phys Fluids 13 (2001) 1160] on thin-film nematics. Based on our estimates the instabilities should be seen in bacterial suspensions and the lamellipodium, and are potentially ...

Measurements of the mean-square amplitude of thermally-induced fluctuations of a thin layer of the nematic liquid crystal I52 subjected to a voltage V < Vc are reported. They yield the limit of stability Vc of the spatially uniform conduction state to infinitesimal perturbations. Localized long-lived convecting structures known as worms form spontaneously from the fluctuations for V well below Vc. This, as well as measurements of the lifetime of the conduction state for V < V...