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.     

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.     

Analysis of onset of bio-thermal convection in a fluid containing gravitactic microorganisms by the energy method

The bio-thermal convection in a suspension containing gravitactic microorganisms saturated by a fluid is investigated within the framework of linear and nonlinear stability theory. Energy method is used for nonlinear stability analysis. Effect of Péclet number (swimming speed of microorganisms) and bioconvection Rayleigh number (concentration of microorganisms) on the stability of the system is analyzed numerically by using the Galerkin weighted residual method. The subcritical region of instability for faster swimmers is large as compared to slowly swimmers. Bioconvection Rayleigh number destabilizes the onset of bio- thermal convection and this effect is more predominant for high speed of microorganisms. The Péclet number, bioconvection Rayleigh number increase the size of cell.     

On the parametric excitation of electrothermal instability in a dielectric liquid layer using an alternating electric field

The onset of electrothermal convective instability of a liquid dielectric subjected to an unsteady electric field is studied in the EHD approximation, when charge formation is produced only due to dielectrophoresis. Convective thresholds are found in two different cases: (i) instability of the liquid equilibrium in a horizontal layer, and (ii) instability of the liquid flow in a vertical layer. The stability boundaries are obtained when there is interaction of dielectrophoretic and gravitational forces. Stability plots of electrical Rayleigh number versus thermal Rayleigh number are given. We show that only synchronous response to variations of the external electric field of finite frequency exists when heating a horizontal layer from above. Quasiperiodic response to the external alternating action is possible in the case of a vertical layer. The influence of the Prandtl number on the stability thresholds is also examined. The asymptotic behavior of the critical parameters in the limiting case of low-frequency modulation is studied using the Wentzel–Kramers–Brillouin method.     

Instability of water jet: Aerodynamically induced acoustic and capillary waves

High-speed water jet cutting has important industrial applications. To further improve the cutting performance it is critical to understand the theory behind the onset of instability of the jet. In this paper, instability of a water jet flowing out from a nozzle into ambient air is studied. Capillary forces and compressibility of the liquid caused by gas bubbles are taken into account, since these factors have shown to be important in previous experimental studies. A new dispersion equation, generalizing the analogous Rayleigh equation, is derived. It is shown how instability develops because of aerodynamic forces that appear at the streamlining of an initial irregularity of the equilibrium shape of the cross-section of the jet and how instability increases with increased concentration of gas bubbles. It is also shown how resonance phenomena are responsible for strong instability. On the basis of the theoretical explanations given, conditions for stable operation are indicated.     

Relaxation on the energy method for the transient Rayleigh-Bénard convection

The onset of buoyancy-driven instability in initially quiescent fluid layers having the various boundary conditions is analyzed by using the energy method. New energy stability equation is derived under the Boussinesq approximation and the relative stability concept. The predicted critical conditions are compared with the previous results based on the conventional energy method. The stability limits which are related to the onset time of instabilities are presented as a function of the Rayleigh number Ra and the Prandtl number Pr. The present stability results predict that the onset time of convective instability decreases with increasing Ra and Pr. For the case of high Ra, the onset time of the instability is relatively insensitive to the boundary conditions of the upper boundaries.     

Stability analysis of a Maxwell fluid in a porous medium heated from below

Based on a modified-Darcy–Brinkman–Maxwell model, stability analysis of a horizontal layer of Maxwell fluid in a porous medium heated from below is performed. By solving the eigenvalue problems, the critical Rayleigh number, wave number and frequency for overstability are determined. It is found that the critical Rayleigh number for overstability decreases as the relaxation time increases and the elasticity of a Maxwell fluid has a destabilizing effect on the fluid layer in porous media. On the other hand, the critical Rayleigh number for overstability increases by increasing the porous parameter which acts to stabilize the system. In limiting cases, some previous results for viscoelastic fluids in nonporous media are recovered from our results.     

Plume dynamics in quasi-2D turbulent convection

We have studied turbulent convection in a vertical thin (Hele-Shaw) cell at very high Rayleigh numbers (up to 7x10(4) times the value for convective onset) through experiment, simulation, and analysis. Experimentally, convection is driven by an imposed concentration gradient in an isothermal cell. Model equations treat the fields in two dimensions, with the reduced dimension exerting its influence through a linear wall friction. Linear stability analysis of these equations demonstrates that as the thickness of the cell tends to zero, the critical Rayleigh number and wave number for convective onset do not depend on the velocity conditions at the top and bottom boundaries (i.e., no-slip or stress-free). At finite cell thickness delta, however, solutions with different boundary conditions behave differently. We simulate the model equations numerically for both types of boundary conditions. Time sequences of the full concentration fields from experiment and simulation display a large number of solutal plumes that are born in thin concentration boundary layers, merge to form vertical channels, and sometimes split at their tips via a Rayleigh-Taylor instability. Power spectra of the concentration field reveal scaling regions with slopes that depend on the Rayleigh number. We examine the scaling of nondimensional heat flux (the Nusselt number, Nu) and rms vertical velocity (the Peclet number, Pe) with the Rayleigh number (Ra(*)) for the simulations. Both no-slip and stress-free solutions exhibit the scaling NuRa(*) approximately Pe(2) that we develop from simple arguments involving dynamics in the interior, away from cell boundaries. In addition, for stress-free solutions a second relation, Nu approximately nPe, is dictated by stagnation-point flows occurring at the horizontal boundaries; n is the number of plumes per unit length. No-slip solutions exhibit no such organization of the boundary flow and the results appear to agree with Priestley's prediction of Nu approximately Ra(1/3). (c) 1997 American Institute of Physics.     

Scaling behavior for the onset of convection in a colloidal suspension

We investigate the early stages of mass convection in a colloidal suspension at high solutal Rayleigh number Ras. From the time evolution of shadowgraph images and by assuming a diffusive growth of the boundary layers we obtain an indirect measurement of the concentration boundary layer thickness delta* at the onset of convection. We show that the dimensionless boundary layer thickness delta=delta*/d scales as Ra-ps, where Ras=Rasdelta is a modified solutal Rayleigh number for convection which accounts for the actual density unbalance and d is the thickness of the sample layer. This scaling behavior is analogous to that reported at steady state for turbulent convection in simple fluids. We find p=0.35, a value compatible with the exponent 1/3, reported for turbulent heat convection in simple fluids at steady state.     

Nonlinear evolution of the lower-hybrid drift instability in a current sheet

The lower-hybrid drift instability is simulated in an ion-scale current sheet using a fully kinetic approach with values of the ion to electron mass ratio up to m(i)/m(e)=1836. Although the instability is localized on the edge of the layer, the nonlinear development increases the electron flow velocity in the central region resulting in a strong bifurcation of the current density and significant anisotropic heating of the electrons. This dramatically enhances the collisionless tearing mode and may lead to the rapid onset of magnetic reconnection for current sheets near the critical scale.     

Coupling between aging and convective motion in a colloidal glass of Laponite

We study thermal convection in a colloidal glass of Laponite in formation. Low concentration preparation are submitted to destabilizing vertical temperature gradient, and present a gradual transition from a turbulent convective state to a steady conductive state as their viscosity increases. The time spent under convection is found to depend strongly on sample concentration, decreasing exponentially with mass fraction of colloidal particles. Moreover, at fixed concentration, it also depends slightly on the pattern selected by the Rayleigh Bénard instability: more rolls maintain the convection state longer. This behavior can be interpreted with recent theoretical approaches of soft glassy material rheology.     

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.     

Instability of mechanical equilibrium during diffusion in a three-component gas mixture in a vertical cylinder with a circular cross section

The problem of the emergence of instability of mechanical equilibrium of a three-component gas mixture during diffusion in a vertical channel with the wall impenetrable for the mass flux is considered in the case when the channel has a circular cross section. The critical Rayleigh numbers are determined, and the neutral stability lines are found in analytic form. The results are compared with experimental data.     

Convective instability of a water-vapor-saturated atmospheric layer. The formation of localized and periodic cloud structures

The classical Rayleigh problem of convective instability is generalized to the case of water vapor condensation in the atmosphere. We present an analytical solution demonstrating a fundamental difference between moist convection and Rayleigh convection: the curve of the critical Rayleigh number versus the number characterizing the intensity of condensation heat release consists of two parts, with spatially localized neutral solutions corresponding to one of them. Spatially periodic neutral solutions correspond to the second part of the curve; these are characterized by a significant localization of the regions of ascending motions. The theory describes the nucleation and development of individual convective clouds and ordered cloud structures.     

圆内开缝圆自然对流的Ruelle-Takens混沌道路

使用热格子Boltzmann方法针对圆内开缝圆自然对流的流动与换热进行数值模拟,通过相空间、功率谱等进行非线性动力学特性分析,研究其流动与换热的稳定性.结果表明：随着瑞利数Ra的增加,流场的相图从开始稳定的平衡点经历Hopf分岔后转变为极限环,表明流场进入一个倍周期性振荡状态;随着瑞利数进一步增加,稳定的极限环分岔为二维环面,系统相空间结构复杂化;当瑞利数Ra大于某一临界值时,二维环面分岔突变进入混沌状态,系统在相空间中出现非常复杂的轨线结构.总体上,通过系统不同瑞利数所对应的非线性动力学特性的表现形式,表明系统经过Ruelle-Takens道路到达混沌,展现出自然对流从稳定的流动和换热发展到非线性运动特征的混沌历程.     

Effect of helical force on the stationary convection in a rotating ferrofluid

In this paper we studied the onset of instability in a horizontal layer of a rotating ferrofluid in the presence of the helical force. The analytical expression of the Rayleigh number of the system is determined as a function of the dimensionless numbers obtained. Then, the effect of each dimensionless parameter is studied. The helical force, the binary parameter ψ then the magnetic parameters M₁, M₃ and ψ_m accelerate the onset of stationary convection whereas the rotation and the magnetic parameter M₂ delay it. Also all the magnetic parameters, the binary parameter and the rotation cause the convection rolls to shrink while only the helical force increases the size of these structures.     

Lattice Boltzmann simulation of double diffusive natural convection in heterogeneously porous media of a fluid with temperature-dependent viscosity

Double diffusive natural convection inside a porous cavity with non-uniform porosity has been numerically studied. The cavity was filled with two parallel porous layers with different porosity. Considering the effects of temperature-dependent viscosity, simulations have been done via the Lattice Boltzmann method (LBM) at representative elementary volume (REV) scale. In this study, the effect of porosity, buoyancy ratio, the viscosity-variation number and thermal Rayleigh number on heat and mass transfer rates was investigated. The streamlines, isotherms, isoconcentrations, average Nusselt number and average Sherwood number curves of different parameters were discussed in detail. It was observed that the governing parameters has significant impact on the fluid flow, temperature and concentration distributions. In addition, the average Nusselt and Sherwood numbers are increase with an reduce in the viscosity-variation number. Further, as the absolute value of buoyancy ratio and thermal Rayleigh number increases, the effect of porosity and viscosity changes on the heat and mass transfer enhancement was augmented.     

Cross-diffusive effects on the onset of double-diffusive convection in a horizontal saturated porous fluid layer heated and salted from above

Double-diffusive stationary and oscillatory instabilities at the marginal state in a saturated porous horizontal fluid layer heated and salted from above are investigated theoretically under the Darcy's framework for a porous medium. The contributions of Soret and Dufour coefficients are taken into account in the analysis. Linear stability analysis shows that the critical value of the Darcy-Rayleigh number depends on cross-diffusive parameters at marginally stationary convection, while the marginal state characterized by oscillatory convection does not depend on the cross-diffusion terms even if the condition and frequency of oscillatory convection depends on the cross-diffusive parameters. The critical value of the Darcy-Rayleigh number increases with increasing value of the solutal Darcy-Rayleigh number in the absence of cross-diffusive parameters. The critical Darcy-Rayleigh number decreases with increasing Soret number, resulting in destabilization of the system, while its value increases with increasing Dufour number, resulting in stabilization of the system at the marginal state characterized by stationary convection. The analysis reveals that the Dufour and Soret parameters as well as the porosity parameter play an important role in deciding the type of instability at the onset. This analysis also indicates that the stationary convection is followed by the oscillatory convection for certain fluid mixtures. It is interesting to note that the roles of cross-diffusive parameters on the double-diffusive system heated and salted from above are reciprocal to the double-diffusive system heated and salted from below.     

Morphological instability induced by the interaction of a particle with a solid-liquid interface

We show that the interaction of a particle with a directionally solidified interface induces the onset of morphological instability provided that the particle-interface distance falls below a critical value. This instability occurs at pulling velocities that are below the threshold for the onset of the Mullins-Sekerka instability. The expression for the critical distance reveals that this instability is manifested only for certain combinations of the physical and processing parameters. Its occurence is attributed to the reversal of the thermal gradient in the melt ahead of the interface and behind the particle.Received: 3 December 2003, Published online: 19 February 2004PACS: 81.30.Fb Solidification - 81.05.Ni Dispersion-, fiber-, and platelet-reinforced metal-based composites - 81.10.Fq Growth from melts; zone melting and refining     

Instability of a charged spherical drop moving relative to a medium

It is shown that the critical self-charge for the onset of instability of a charged drop in a flow of an ideal fluid decreases as the flow velocity of the fluid past the drop increases, i.e., a complex instability arises which is a superposition of the instabilities of the free surface of the drop with respect to the tangential discontinuity of the velocity field at the free surface of the drop and with respect to the self-charge. Zh. Tekh. Fiz. 69, 7–14 (May 1999)