Electrohydrodynamic Instability Research Articles

A general analysis for the electrohydrodynamic instability of stratified immiscible fluids

A general solution approach for the electrohydrodynamic instability of stratified immiscible fluids is presented. The problems of two and three fluid layers subject to normal electric fields are analysed. Analytical solutions are obtained by employing the transfer relations (Melcher 1981 Continuum Electromechanics. MIT Press) relating the disturbance stresses to the flow variables at the interface(s). This approach provides a convenient alternative to the direct solution of the linearized problem. The results assume a general format. Both new dispersion relations and those from various previous works are shown to be special cases when proper simplifications are considered. As a specific example, the instability behaviour of a three-layer channel flow is investigated in detail using this framework. This work provides a unifying method to treat a generic class of instability problems.

Electro-hydrodynamic instability patterning of polymers

Electro-HydroDynamic Instability Patterning, EHDIP, is a novel micro-manufacturing process that makes use of the instability of viscous polymeric thin films when exposed to electrostatic fields. By using non uniform electrostatic fields, it is possible to shape the polymer into defined meso- and micro-scale structures which are subsequently cured to defined 2D and 3D microstructures. The relatively rapid process time, the one-step manufacturing approach, as well as the ability to produce hitherto unrealised topographies - such as continuous profile structures, makes EHDIP an attractive manufacturing process.

Self‐Organization of Thin Polymer Films Guided by Electrostatic Charges on the Substrate

The self-organization of thin polymer films into functional patterns is important both scientifically and technologically. Electric fields have been exploited as an efficient and powerful means to induce the destabilization and self-organization of soft materials. Previous attention, however, has mainly focused on externally applied electric fields. It is shown herein that the internal electric field is strong enough to guide the self-organization of thin polymer films as well. Patterns of electrostatic charges with micrometer resolution are first introduced on a dielectric substrate. A thin polymer film is then spin-coated onto the topographically flat substrate. Upon thermal annealing, the thin polymer film destabilizes due to a lateral gradient of electrostatic stress and flows away from the electroneutral regime to the charged area, resembling the patterns of charges on the substrate. Theoretical and numerical modeling based on the electrohydrodynamic instability shows excellent agreement with experimental observations both qualitatively and quantitatively. It is also demonstrated that the interplay between charge-driven instability with spinodal dewetting and Rayleigh instabilities can generate finer and hierarchical polymeric patterns that are completely different from the charge patterns preintroduced on the substrate. This study provides direct evidence that the internal electric field caused by charges on the substrate is strong enough to destabilize thin polymeric films and generate patterns. This study also demonstrates new strategies for bottom-up fabrication of structured functional materials.

The effect of Joule-heating-induced buoyancy on the electrohydrodynamic instability in a fluid layer with electrical conductivity gradient

Applying an electric field across a fluid layer with a conductivity gradient can induce an electrical body force destabilizing the flow and simultaneously generate Joule-heating effect. For microfluidic devices with high surface area to volume ratio, the Joule heating can be removed and the onset of instability occurs only when the electrical body force overcomes the viscous force. For mini-scale devices containing conducting solutions, the Joule heating can induce thermal buoyancy sufficiently to affect the stability. This paper performs an analysis to examine the possible impact on the stability due to the presence of Joule-heating-induced buoyancy. Results show that for the cases of low conductivity gradient, the induced buoyancy always appears to enhance the electrohydrodynamic instability regardless of the direction of buoyancy. However, at high conductivity gradients, the buoyancy may become a stabilizing mechanism if the electrical field and the buoyancy are on the opposite direction.

Flexoelectricity and pattern formation in nematic liquid crystals

We present in this paper a detailed analysis of the flexoelectric instability of a planar nematic layer in the presence of an alternating electric field (frequency ω), which leads to stripe patterns (flexodomains) in the plane of the layer. This equilibrium transition is governed by the free energy of the nematic, which describes the elasticity with respect to the orientational degrees of freedom supplemented by an electric part. Surprisingly the limit ω→0 is highly singular. In distinct contrast to the dc case, where the patterns are stationary and time independent, they appear at finite, small ω periodically in time as sudden bursts. Flexodomains are in competition with the intensively studied electrohydrodynamic instability in nematics, which presents a nonequilibrium dissipative transition. It will be demonstrated that ω is a very convenient control parameter to tune between flexodomains and convection patterns, which are clearly distinguished by the orientation of their stripes.

Microlens array fabricated using electrohydrodynamic instability and surface properties

We fabricated polarization-dependent and polarization-independent microlens arrays (MLA) through the electrohydrodynamic instability of the optically anisotropic organic layer. The anisotropic flow induced by the instability of the organic layer leads to making the lens profile on the patterned electrode. We can easily control the polarization dependence of the MLA by controlling the surface alignment properties, even with the optically anisotropic organic layer. This method is a straightforward, fast, and reliable process for MLA fabrication since it does not require cumbersome developing and molding processes.

On the theory of the noncoalescence effect for oppositely charged droplets

A theory is proposed and numerical simulation is conducted for oppositely charged mutually approaching droplets of an aqueous electrolytic solution in silicon oil. It is shown that at small distances between droplets, a conductive bridge leveling out the potentials of the droplets may form between them due to electrohydrodynamic instability of the equilibrium surface of one of the droplets. As a result, the droplets start to repel each other and may drift apart without coagulation. The proposed theory is confirmed by the effect of nonconfluent droplets observed in experiments [W.D. Ristenpart, J.C. Bird, A. Belmonte, et al., Nature 461, 377 (2009)].

Water−Ions Induced Nanostructuration of Hydrophobic Polymer Surfaces

When hydrophobic surfaces are in contact with water in ambient conditions a layer of reduced density is present at the interface, preventing the intimate contact between the two phases. Reducing the extent of this layer by degassing the water can have remarkable implications for the interaction between the two phases. The enhanced proximity between a hydrophobic polymer film and an aqueous solution can induce a self-assembled nanostructure on the solid surface through the development of an electro-hydrodynamic instability, due to the adsorption of the water-ions (hydronium and hydroxyl) at the interface. The self-assembled structure spontaneously relaxes back to the original flat morphology after few weeks at room temperature. This instability and the self-assembled structure are controlled by the hydrophobic surface charge, which is determined by the pH of the aqueous phase, and by the amount of gas dissolved. This effect can be easily adjusted to modify different hydrophobic polymeric substrates at the submicrometer level, opening pathways for producing controlled patterns at the nanoscale in a single simple waterborne step.

Electrohydrodynamic instability at the interface between two leaky dielectric fluid layers

The effects of an external electric field on the stability and dynamics of a planar interface between Transformer/Silicone oils (Tr/Si) layers are studied experimentally. Experiments performed in a configuration help in clarifying the effects of electrical stresses on the interface dynamics. Results demonstrate that application of electric field, higher than the critical value ( E ≥ E cr ), to the considered system enhances the spontaneous fluctuations at the interface and leads to an instability and formation of a filamentary structure at the interface. It is found that the presence of free charges made by dissociation process plays the main role in interface instability under applied electric field. Migration of the generated charge carriers drags fluid into motion and forms two counter-rotating vortices in the enclosure. Moreover, results confirm that application of electric field is an effective method for promoting mixing of two fluids, which can be helpful to step forward in design of new generation of fluid mixers here we call “ EHD Mixers”.

Electrohydrodynamic instabilities in thin liquid trilayer films

Experiments by Dickey et al. [Langmuir 22, 4315 (2006)] and Leach et al. [Chaos 15, 047506 (2005)] show that novel pillar shapes can be generated from electrohydrodynamic instabilities at the interfaces of thin polymer/polymer/air trilayer films. In this paper, we use linear stability analysis to investigate the effect of free charge and ac electric fields on the stability of trilayer systems. Our work is also motivated by our recent theoretical study [S. A. Roberts and S. Kumar, J. Fluid Mech. 631, 255 (2009)] which demonstrates how ac electric fields can be used to increase control over the pillar formation process in thin liquid bilayer films. For perfect dielectric films, the effect of an ac electric field can be understood by considering an equivalent dc field. Leaky dielectric films yield pillar configurations that are drastically different from perfect dielectric films, and ac fields can be used to control the location of free charge within the trilayer system. This can alter the pillar instability modes and generate smaller diameter pillars when conductivities are mismatched. The results presented here may be of interest for the creation of complex topographical patterns on polymer coatings and in microelectronics.

Direct numerical simulation of forced flow dielectric EHD within charge injection atomizers

A charge injection atomizer functions by introducing electric charge discharged from a high voltage electrode into a dielectric liquid, which subsequently atomizes the ejected liquid jet. Atomizer evolution thus far has proceeded through trial and error analysis of the experimentally measured electrical characteristics of the atomizer and of the quality of atomization. Within the atomizer, a coupled space charge and electric field exist, which can alter the internal flow pattern, thus creating electrohydrodynamic (EHD) instabilities that affect atomizer operation. Such a system has not been simulated in the past under forced flow conditions. In this work we simulate the internal flow of such a charge injection device in two dimensions; using experimental based boundary conditions. Initial results indicate that in the linear injection regime defined by the experimental data, the flow is only slightly unstable but in the transitional and highly non-linear regimes, the coupled space charge and electric field produce more instability in the liquid that must be investigated further.

Electrohydrodynamic instabilities at interfaces subjected to alternating electric field

Instabilities at the interface of two immiscible fluids, either perfect or leaky dielectrics, subjected to alternating electric fields, is studied using a linear stability analysis in the limit of the electrode spacing being large compared to the wavelength of the perturbation. The Floquet analysis of the stability of this system indicates a significant effect of the frequency on the value of smax, the growth rate of the fastest growing instabilities and ETaylor, the minimum field required to excite an instability. It is seen that alternating fields act to damp the system instabilities compared to the direct current (dc) case. Moreover, the growth rate of the instabilities can be tuned from that of leaky dielectric fluids subjected to dc fields, in the low frequency limit, to that of perfect dielectrics in the high frequency limit. It is also observed that for a leaky dielectric-leaky dielectric interface, the alternating current (ac) fields can induce instabilities in a system which is stable at zero frequency, by increasing the frequency of the applied voltage.

Electrohydrodynamic instability of a charged liquid jet in the presence of an axial magnetic field

Electrified liquid jets subjected to electrical destabilizing mechanisms often deform asymmetrically, creating an uncontrollable random motion that prevents the formation of uniform drops or organized microstructures. Employing a magnetic field is a potentially effective method of inhibiting the onset of unstable motion. This paper develops a theoretical model to investigate the effect of an axial magnetic field on the instability of a charged liquid jet. To demonstrate the stabilizing ability of this approach, this study uses temporal linear stability analysis to manifest the magnetic effect in various parameter domains including the Rayleigh regime, the atomization zone, and the bending instability for a viscous jet. Results show that the magnetic force induced by the motion of charged surface is insignificant in comparison with the electric force and does not have effect on the instability of a dielectric liquid jet. However, for a liquid with high electrical conductivity, the Lorentz force induced by a conducting current becomes significant, suppressing destabilizing mechanisms and substantially improving jet stability. In the atomization zone, the effect of magnetic inhibition is relatively limited because the imposed axial magnetic field does not affect long-wave nonaxisymmetric disturbances.

Coarsening in the electrohydrodynamic patterning of thin polymer films

Periodic pillarlike microstructures can be created from initially flat polymer films via the electrohydrodynamic instabilities. Those patterns, however, are metastable. Our experimental observations show that the average pillar size increases slowly after linear growth. Major coarsening events then take place over times several orders of magnitude longer than the linear growth time. For all fill ratios, a logarithmic time dependence of the average pillar size can be identified, i.e., <S> proportional to ln t. Thicker films, however, have faster coarsening rates than thinner films. Linear stability analysis of the pseudosteady states reveals two major coarsening mechanisms, collision and Ostwald ripening, which can also be identified from experimental images. We then reduce the original partial differential equation (PDE) into a pair of ODEs, which govern the interaction between pillars due to the above two coarsening mechanisms. From this, a logarithm scaling law is obtained for both low and high fill ratios and the coarsening rate is slower for lower fill ratios, consistent with experimental observations. We also find that arrays with more uniform sizes tend to start coarsening later, but they coarsen faster than more "disperse" arrays, which could be possibly utilized in experiments for controlling the onset and speed of coarsening. The logarithm scaling in the electrohydrodynamic coarsening phenomenon, which differs from coarsening in spinodal decomposition and dewetting of thin liquid films, is due to the significant nonlinear effect of Maxwell stresses and geometric confinement on the disjoining pressure at both top and bottom electrodes.

Effect of rotation on the electrohydrodynamic instability of a fluid layer with an electrical conductivity gradient

The electrohydrodynamic instability of a horizontal rotating fluid layer with a vertical electrical conductivity gradient is considered. An external electric field is applied across the fluid layer to induce an unstably stratified electrical body force. A linear stability analysis has been performed to study the effect of rotation on the onset of electrohydrodynamic instability in the fluid layer. Results show that the instability behaviors depend heavily on the boundary condition of bottom surface. In the case of stress-free condition, rotation enhances the stability and the onset of instability will be dominated by the oscillatory mode once the speed of rotation (or Taylor number) exceeds a critical value. In contrast, in the case of rigid bottom surface, rotation also tends to stabilize the fluid layer and the stationary mode will prevail eventually with increasing Taylor number. However rotation becomes destabilizing as the critical mode shifts from oscillatory to stationary. Moreover, under the same electrical conductivity gradient, the case with stress-free bottom surface is always more unstable than that with rigid bottom surface in the small Taylor number domain. However this situation is reversed at high Taylor number region since the stability of the stress-free case will be enhanced more rapidly than the rigid case.

Electroconvection in nematic liquid crystals via nanoparticle doping

It is known that a small fraction of nanoparticles dispersed in a liquid crystal can alter the electrooptic response, completely. The present study on gold nanoparticles dispersed in 5-n-heptyl-2-(4-n-octyloxy-phenyl)-pyrimidine shows that the contrast inversion observed earlier is initiated by a change from parallel to homeotropic anchoring, thereby causing an instability, which in turn leads to the appearance of convection rolls. After rapid cooling from the isotropic phase, the nanoparticle dispersion shows a regular field-induced Fréedericksz transition, like the pure liquid crystal. The electrohydrodynamic instability is presumably an example for the behavior of (+, -) systems that was predicted by de Gennes, and only recently observed experimentally for the first time.

Observation of Bessel beams from electric-field-induced patterns on polymer surfaces

We report the observation of Bessel-like beams from periodic patterns induced on viscoelastic polymer surfaces by electric field. The patterns resembling a microaxicon array originate from electrohydrodynamic instabilities in polymer films, where the feature dimensions can be easily controlled. The output beam characteristics from these patterns revealed characteristic traits of Bessel beams.

Effect of electrooptical memory in suspensions of carbon nanotubes in liquid crystals

Electrooptical response and microstructure of dispersions of multiwall carbon nanotubes in N-(4-ethoxybenzilidene)-4-n-butyl aniline nematic liquid crystal (LC) are studied. Irreversible response on the applied electric field (electrooptical memory) was revealed in oriented layers of such suspensions. The essence of this effect consists in the fact that, after the switch-on and subsequent switch-off of the field, the optical transmittance of suspension layer placed between two crossed polarizers substantially increases compared to the initial value which is typical for homeotropic orientation of LC. The efficiency of electrooptical memory nonmonotonically depends on the concentration of nanotubes in suspension, cCNT, reaching its maximum at cCNT = 0.02–0.05 wt %. It is shown that the memory of suspensions is caused by the incomplete relaxation of LC molecules from planar to initial homeotropic state after the electric field switch-off. The model is proposed and substantiated, according to which the planar state of LC is stabilized by the network of nanotubes formed upon the disintegration of aggregates under the action of electrohydrodynamic flows. The disclosed memory effect is rather common; it is brought about in the suspensions of carbon nanotubes based on other LCs in which electrohydrodynamic instabilities are developed.

Electrohydrodynamic instability in a horizontal fluid layer with electrical conductivity gradient subject to a weak shear flow

The stability of electrohydrodynamic flow between two horizontal plates with a vertical electrical conductivity gradient has been investigated in the presence of an imposed weak shear flow. The weak shear flow is driven by the horizontal pressure gradient, and the electrical conductivity gradient is generated by the concentration variation of the charge-carrying solute. An external electric field is applied across the fluid layer, and then the interaction between the unstable stratification of electrohydrodynamic flow and the shear arising from the plane Poiseuille flow is studied. A linear stability analysis has been implemented by considering both the longitudinal and transverse modes. Unlike the thermally stratified plane Poiseuille flow in which the longitudinal mode always dominates the onset of instability and is virtually unaffected by the superimposed shear flow, the instability of this mixed electrohydrodynamic– Poiseuille flow system is found to depend heavily on the shear flow, and the transverse mode may prevail over the longitudinal mode when the momentum of shear flow is sufficiently small. Particularly, an oscillatory longitudinal mode is found to exist, and it may become the critical mode when the conductivity gradient is small enough. The present results verify that an imposed weak shear flow may enhance the electrohydrodynamic instability in a fluid layer with electrical conductivity gradient.

Coherent backscattering and dynamical light localization in liquid crystals driven throughout chaotic regimes

An important effect of dynamical localization of light waves in liquid crystal electro-hydrodynamic instabilities is reported by investigating coherent backscattering effects. Recurrent multiple scattering in dynamic and chaotic complex fluids lead to a cone of enhanced backscattered light. The cone width and the related mean free path dependence on the dynamic scattering regimes emphasize the diverse light localization scales related to the internal structures present in the sample. The systems investigated up to now were mainly nano-powdered solutions or biological tissues, without any external control on the disorder. Here, an anisotropic complex fluid is "driven" throughout chaotic regimes by an external electric field, giving rise to dynamics that evolve through several spatio-temporal patterns.