The onset of convection of a poorly conducting fluid in a modulated thermal field

The stability of a poorly conducting fluid in a constant electric field of a horizontal capacitor is investigated under a variable temperature gradient. It is assumed that free charge in the fluid is generated only due to the nonhomogeneous conductivity of the fluid. The Floquet theory is used to determine the convection thresholds. The instability boundaries and the characteristics of critical perturbations are determined. In addition to the synchronous and subharmonic responses to an external action, the instability can be attributed to quasiperiodic perturbations. The low-frequency limit of modulation is considered by an asymptotic method. The critical electric Rayleigh number is represented as a function of inverse frequency and heating level.     

One type of hydrodynamic instability in joule heating of a fluid near an ion-selective surface

The stability of the equilibrium state of an electrolyte in a horizontal microgap between two ionselective surfaces in an electric field is studied with the Joule heating of the fluid taken into account. It is established that the Joule heating can lead to instability at the potential differences, which are several times smaller than those in the isothermal case. The effects of microscale thermal instability differ from the Rayleigh–Benard thermal convection: the destabilization occurs upon heating in the upper part of the gap.     

Electroconvection between coaxial cylinders of arbitrary ratio subjected to strong unipolar injection

This study deals with the electroconvection phenomenon that takes place in a dielectric liquid layer placed between two annular electrodes and subjected to the action of an electric field.The full set of governing equations describing the combined Electro-Hydro-Dynamic (EHD) flow is directly solved with the finite volume method.The development of electroconvective motion is investigated in details in the case of strong injection when the emitter electrode is the inner cylinder.We first examine the stability of such flow. As in the plane–plane configuration we have highlighted the existence of a linear and non-linear critical electric Rayleigh numbers giving rise to a hysteresis loop. The flow structure under the effect of the electric field is analyzed and the distribution of electric charge density is presented. In particular we investigate the effect of various parameters involved in this configuration, such as the radius ratio, injection strength and electric Rayleigh number.A multicellular convective pattern is particularly observed and it is shown that the number of cells is increased when the annular gap is narrower. Finally a significant increase of the rotational speed of the vortex with the electric Rayleigh number is recorded.     

Onset of parametric electroconvection in a nematic liquid crystal

The behavior of a nematic liquid crystal (NLC) in an external ac electric field is studied in terms of the weak electrolyte model. Since electroconvection of certain types of NLCs can occur in a constant field in an oscillatory mode, a quasi-periodic response of a nematic to the external action is possible in an ac field, as well as a sharp reduction of the electroconvective stability thresholds at resonance frequencies. Stability maps for NLCs are plotted on the plane of amplitude-frequency parameters of the external field. Phase portraits are constructed for subharmonic and synchronous perturbations. The optical response of a NLC in the ac electric field is studied; the time dependences of the relative intensity of light, which passed through the nematic liquid crystal cell, are obtained.     

Rossby waves in the magnetic fluid dynamics of a rotating plasma in the shallow-water approximation

We have studied rotating magnetohydrodynamic flows of a thin layer of astrophysical plasma with a free boundary in the β-plane. Nonlinear interactions of the Rossby waves have been analyzed in the shallow-water approximation based on the averaging of the initial equations of the magnetic fluid dynamics of the plasma over the depth. The shallow-water magnetohydrodynamic equations have been generalized to the case of a plasma layer in an external vertical magnetic field. We have considered two types of the flow, viz., the flow in an external vertical magnetic field and the flow in the presence of a horizontal magnetic field. Qualitative analysis of the dispersion curves shows the presence of three-wave nonlinear interactions of the magnetic Rossby waves in both cases. In the particular case of zero external magnetic field, the wave dynamics in the layer of a plasma is analogous to the wave dynamics in a neutral fluid. The asymptotic method of multiscale expansions has been used for deriving the nonlinear equations of interaction in an external vertical magnetic field for slowly varying amplitudes, which describe three-wave interactions in a vertical external magnetic field as well as three-wave interactions of waves in a horizontal magnetic field. It is shown that decay instabilities and parametric wave amplification mechanisms exist in each case under investigation. The instability increments and the parametric gain coefficients have been determined for the relevant processes.     

On the initiation of a corona discharge near the surface of a nonlinearly oscillating liquid layer on the surface of a charged hailstone

An expression is derived for the electric field strength near a wet hailstone in an approximation quadratic in the oscillation amplitude of a charged liquid layer on its surface. It is found that the electric field strength in a small neighborhood of the capillary wave crests grows with the number of a mode governing the initial deformation of the equilibrium (spherical) shape of the liquid layer. Even if the charge is small (when the Rayleigh parameter of the hailstone equals one-hundredth of the value critical for stability against the self-charge), the electric field near the hailstone is high enough for initiating a corona discharge in its vicinity.     

EHD convection in dielectric micropolar fluid layer

The onset of instability in a layer of dielectric micropolar fluid under the simultaneous action of an AC electric field and temperature gradient has been investigated. The dispersion relation has been derived and various critical values of non-dimensional Rayleigh number in the fluid layer have been determined. The influence of micropolar viscosity and electric Rayleigh number on the onset of convection has been analyzed. Thermal Rayleigh number has been computed for various values of electric Rayleigh number for the onset of instability. The stabilizing and destabilizing effects of electric Rayleigh number, micropolar viscosity and Prandtl number have been discussed.     

Effect of tilted electrostatic field on the Kelvin–Helmholtz instability in a liquid dielectric and gas flow

The effect of surface ponderomotive forces on the Kelvin–Helmholtz instability is studied in the linear formulation based on the equations and boundary conditions of the electrostatics and fluid dynamics of an ideal incompressible fluid. Conditions to be satisfied by the values of determining parameters of the problem for the transition of an unstable flow in zero electric field into a stable regime after the application of a horizontal electric field have been written in the form of inequalities. It has been shown that, at the stability bound, the wavelength of the most instable mode is independent of the ponderomotive forces. In case of a liquid with large permittivity a stable flow regime exists for which the stability condition only differs in small dimensionless values from the stability condition for the charged surface of a quiescent liquid conductor in contact with a gas at rest.     

磁场对二元合金凝固过程中糊状层稳定性的影响

利用线性稳定性方法研究了外加磁场对二元合金凝固过程中糊状层稳定性的影响,且模型同时考虑了温度场、浓度场和流动的耦合作用.利用计算得出的色散关系式分析了磁场对糊状层稳定性的影响,其中包括直接模式和振荡模式.给出了不同情况下外加磁场对糊状层稳定性的影响,发现磁洛伦兹力可以减小由浮力引起的失稳效应.振荡模式下外加磁场对糊状层产生稳定作用,但直接模式下外加磁场对糊状层的稳定作用具有不确定性.本文所给出结果为工业中利用外加磁场改善产品的质量提供了重要的理论参考.     

Linear stability analysis on the onset of Soret-driven motion in a nanoparticles suspension

The onset of Soret-driven instability in binary mixture heated from above is analysed using the linear stability theory. The horizontal fluid layer placed between two plates is in a thermally stable state but the Soret diffusion can induce buoyancy-driven convection in the case of a negative Soret coefficient. It is well known that convective motion sets in from both boundaries if the Rayleigh number exceeds its critical value. For the case of highly unstable density stratification the buoyancy-driven motion sets in during the transient diffusion stage. The new stability equations are derived and are solved analytically and numerically. Here the stability limits which are related to the onset time of instabilities and wave number are presented as a function of the Rayleigh number, Lewis number and the separation ratio. The present stability criteria are compared with the existing experimental data.     

Instability development on the charged free surface of a horizontal liquid layer with thermal convection

The instability of the charged free surface of a horizontal liquid layer heated from the solid bottom against excess electric charge is studied theoretically for the case in which this type of instability is combined with thermal-convective instability. The structure of the total spectrum of unstable wave flows and physical parameters influencing the structure of the spectrum are determined.     

Dynamic stability of a slender beam under horizontal–vertical excitations

The dynamic stability of a vertically standing cantilevered beam simultaneously excited in both horizontal and vertical directions at its base is studied theoretically. The beam is assumed to be an inextensible Euler–Bernoulli beam. The governing equation of motion is derived using Hamilton's principle and has a nonlinear elastic term and a nonlinear inertia term. A forced horizontal external term is added to the parametrically excited system. Applying Galerkin's method for the first bending mode, the forced Mathieu–Duffing equation is derived. The frequency response is obtained by the harmonic balance method, and its stability is investigated using the phase plane method. Excitation frequencies in the horizontal and vertical directions are taken as 1:2, from which we can investigate the influence of the forced response under horizontal excitation on the parametric instability region under vertical excitation. Three criteria for the instability boundary are proposed. The influences of nonlinearities and damping of the beam on the frequency response and parametric instability region are also investigated. The present analytical results for instability boundaries are compared with those of experiments carried out by one of the authors.     

Instability of a flat horizontal interface between a thin layer of a ferrofluid and a thin layer of a nonmagnetic liquid in the presence of a vertical magnetic field

An asymptotic analysis of the equations and boundary conditions of fluid dynamics is performed, and a nonlinear model is constructed for the onset of the development of Rosensweig instability in a thin horizontal ferrofluid layer at rest covered with a thin layer of a lighter nonmagnetic liquid. The surface of a nonmagnetized slab is the lower boundary of the ferrofluid, and the interface with a gas is the upper boundary of the nonmagnetic liquid. The pressure in the gas is constant. The instability being considered arises upon the application of a rather strong uniform vertical magnetic field. The proposed model involves five dimensionless parameters. The critical magnetization of the initial ferrofluid layer with a flat upper boundary and the threshold wave number are found. The effect of the governing parameters on the instability region and on the wavelength of the fastest growing mode is studied in the linear formulation of the problem.     

Transient electrohydrodynamic convective flow and heat transfer of MWCNT - Dielectric nanofluid in a heated enclosure

A computational research was performed to analyze the electrohydrodynamic (EHD) convective heat transfer in a differentially heated dielectric-MWCNT nanofluid layer. The study was conducted on a square enclosure subjected to a temperature gradient between these two vertical walls as well as a potential difference between these horizontal walls. The enclosure was filled with MWCNT oil-based nanofluid; the MWCNT nanoparticles were dispersed in a perfectly insulating thermal oil with a volume fraction of hardly exceeded 0.4%. The governing equations were derived with the assumption of homogeneous nanofluid and were solved with employing finite volume method. Based on the obtained results, it was found that the increase of Rayleigh number, electric Rayleigh number and nanoparticle concentration enhanced the heat transfer. For high thermal and electric Rayleigh number values, the flow and heat transfer became time dependent and accordingly a frequency study was also performed. It was found that the inclusion of an electric field with the addition of nanoparticles led to a significant heat transfer enhancement of about 43%.     

Phase field simulation of single bubble behavior under an electric field

Based on the Cahn-Hilliard phase field model, a three-dimensional multiple-field coupling model for simulating the motion characteristics of a rising bubble in a liquid is established in a gas-liquid two-phase flow. The gas-liquid interface motion is simulated by using a phase-field method, and the effect of the electric field intensity on bubble dynamics is studied without electric field, or with vertical electric field or horizontal electric field. Through the coupling effect of electric field and flow field, the deformation of a single rising bubble and the formation of wake vortices under the action of gravity and electric field force are studied in detail. The correctness of the results is verified by mass conservation, and the influences of different electric field directions and different voltages on the movement of bubbles in liquid are considered. The results show that the ratio of the length to axis is proportional to the strength of the electric field when the air bubble is stretched into an ellipsoid along the electric field line under the action of electrostatic gravity and surface tension. In addition, the bubble rising speed is affected by the electric field, the vertical electric field accelerates the bubble rise, and the horizontal direction slows it down.     

Effect of the marangoni convection on the injection mechanism of instability

Electroconvective instability of a nonisothermal layer of a weakly conductive liquid with a free boundary whose surface tension depends linearly on temperature is considered for the case where charge injection is performed through this surface. When calculating the unperturbed stationary distribution of the charge and field, we supposed that the injector is separated from the liquid by an air gap of finite thickness. It was, however, assumed when analyzing the stability of the system that the motion in the air gap has no effect on the motion in the liquid phase and the disturbances of the electric field and charge in the air gap decay rapidly because of its high conductivity.     

Exact partial solutions for the surface dynamics of a dielectric liquid with a charged surface in the gravitational field

We study the evolution of instability in the boundary of a perfect dielectric liquid with a free surface charge in an external electric field. Conformal variables are used to find exact partial solutions to the equations of motion for the case when the charge completely shields the field above the liquid, the electrostatic and gravitational forces being taken into account. The solutions describe the development of instability of the initially planar boundary until sharp dimples are formed on it.     

Dynamics of electroconvective nematic liquid crystal structures in a nonharmonic electric field

The emergence of electroconvection in a nematic liquid crystal under the action of a nonharmonic electric field is investigated. Analysis is carried out using a 2D model. We propose new forms of the varying electric field acting on the system, for which subharmonic oscillations exist: (a) electric field of a trapezoidal form and (b) external field varying in accordance with the law of “joined cosines.” The behavior of synchronous excitations in the insulating and conducting regimes, as well as subharmonic oscillations, is analyzed. The parametric instability domains are found, and the critical frequencies of transition between different response regimes are determined. The stability maps of the nematic liquid crystal are constructed on the frequency-voltage amplitude plane.     

Synchrotron x-ray study of the smectic layer directional instability

We have investigated the phenomenon of field-induced smectic layer instability, as monitored by synchrotron x-ray scattering. This instability means that, upon application of time-asymmetric electric fields to chiral smectics, the layer direction seems to "rotate" locally around an axis given by the direction of the applied field. For moderate values of field amplitude and asymmetry, domains with a favored layer inclination grow at the expense of unfavored ones, while larger fields and asymmetries generally lead to a chaotic flow behavior. At moderate amplitudes, we have followed the process of the horizontal layer folding (or horizontal chevron domain formation) and the smectic C* layer reorientation of ferroelectric liquid crystals by applying symmetric and asymmetric wave forms, respectively, and performing time resolved x-ray measurements. The studies unambiguously show the formation of a horizontal (in-plane, i.e., in a plane parallel to the cell substrates) chevron domain structure from a nonoriented sample by application of a symmetric electric field of sufficient amplitude. It is then demonstrated that a transition from the horizontal chevron domain structure to an in-plane uniform smectic layer direction takes place on application of asymmetric electric wave forms. Reversal of the field asymmetry reverses the inclination direction and selects the other layer normal direction as the uniform end state. The in-plane smectic layer reorientation process is followed here as it evolves, and analyzed directly by means of x-ray scattering.