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.     

Modeling the onset of thermosolutal convective instability in a non-Newtonian nanofluid-saturated porous medium layer

The onset of double-diffusive (thermosolutal) convection in horizontal porous layer saturated with an incompressible couple stress nanofluid saturated is studied with thermal conductivity and viscosity dependent on the nanoparticle volume fraction. To represent the momentum equation for porous media, a modified Darcy-Maxwell nanofluid model incorporating the effects of Brownian motion and thermophoresis has been used. The thermal energy equation includes regular diffusion and cross diffusion (Soret thermo-diffusion and Dufour diffuso-thermal) terms. A linear stability analysis depends on the normal mode technique and the onset criterion for stationary and oscillatory convection is derived analytically. The nonlinear theory based on the representation of the Fourier series method is applied to capture the behavior of heat and mass transfer. It is found that the couple stress parameter enhances the stability of the system in both the stationary and oscillatory convection modes. The viscosity ratio and conductivity ratio both enhance heat and mass transfer. Transient Nusselt number is found to be oscillatory when time is small. However, when time becomes very large, all the three transient Nusselt number values approach to their steady state values.     

Unusual thermal diffusion in polymer solutions

Thermal diffusion forced Rayleigh scattering results on thermal diffusion of poly(ethylene oxide) (PEO) in ethanol/water mixtures are presented. In water-rich solvent mixtures, PEO is found to migrate towards regions of lower temperature. This is typical for polymer solutions and corresponds to a positive Soret coefficient of PEO. In solvent mixtures with low water content, however, the polymer is found to migrate towards higher temperatures, corresponding to a negative Soret coefficient of PEO in ethanol-rich solutions. To our knowledge, this is the first observed sign change of the Soret coefficient of a polymer in solution. We also present a simple lattice model for the polymer solvent system and calculate Soret coefficients with statistical mechanics methods. The calculated values agree qualitatively with the experimental results.     

Mode-to-mode energy transfers in convective patterns

We investigate the energy transfer between various Fourier modes in a low-dimensional model for thermal convection. We have used the formalism of mode-to-mode energy transfer rate in our calculation. The evolution equations derived using this scheme is the same as those derived using the hydrodynamical equations for thermal convection in Boussinesq fluids. Numerical and analytical studies of this model show that convective rolls appear as the Rayleigh number R is raised above its critical value R _c. Further increase of Rayleigh number generates rolls in the perpendicular directions as well, and we obtain a dynamic asymmetric square pattern. This pattern is due to Hopf bifurcation. There are two sets of limit cycles corresponding to the two competing asymmetric square patterns. When the Rayleigh number is increased further, the limit cycles become unstable simultaneously, and chaotic motion sets in. The onset of chaos is via intermittent route. The trajectories wander for quite a long time almost periodically before jumping irregularly to one of the two ghost limit cycles.     

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.     

On the two-component Benard problem a numerical solution

A numerical solution for the two-component Bénard problem is presented, taking into account the contribution of thermal diffusion to the total density gradient. The results are compared with the approximate solution obtained by the variational technique of the local potential introduced some years ago by Glansdorff and Prigogine. The results calculated by the two methods are in agreement when the Soret coefficient is not too large. But when the gradients become important, the exact numerical solution presented here shows a small divergence from the variational method.The critical Rayleigh number is also compared with the one extrapolated from the analytical solution obtained for free boundary conditions.     

Effect of Soret diffusion on lean hydrogen/air flames at normal and elevated pressure and temperature

The influence of Soret diffusion on lean premixed flames propagating in hydrogen/air mixtures is numerically investigated with a detailed chemical and transport models at normal and elevated pressure and temperature. The Soret diffusion influence on the one-dimensional (1D) flame mass burning rate and two-dimensional (2D) flame propagating characteristics is analysed, revealing a strong dependency on flame stretch rate, pressure and temperature. For 1D flames, at normal pressure and temperature, with an increase of Karlovitz number from 0 to 0.4, the mass burning rate is first reduced and then enhanced by Soret diffusion of H₂ while it is reduced by Soret diffusion of H. The influence of Soret diffusion of H₂ is enhanced by pressure and reduced by temperature. On the contrary, the influence of Soret diffusion of H is reduced by pressure and enhanced by temperature. For 2D flames, at normal pressure and temperature, during the early phase of flame evolution, flames with Soret diffusion display more curved flame cells. Pressure enhances this effect, while temperature reduces it. The influence of Soret diffusion of H₂ on the global consumption speed is enhanced at elevated pressure. The influence of Soret diffusion of H on the global consumption speed is enhanced at elevated temperature. The flame evolution is more affected by Soret diffusion in the early phase of propagation than in the long run due to the local enrichment of H₂ caused by flame curvature effects. The present study provides new insights into the Soret diffusion effect on the characteristics of lean hydrogen/air flames at conditions that are relevant to practical applications, e.g. gas engines and turbines.     

On the classification of buoyancy-driven chemo-hydrodynamic instabilities of chemical fronts

Exothermic autocatalytic fronts traveling in the gravity field can be deformed by buoyancy-driven convection due to solutal and thermal contributions to changes in the density of the product versus the reactant solutions. We classify the possible instability mechanisms, such as Rayleigh-Benard, Rayleigh-Taylor, and double-diffusive mechanisms known to operate in such conditions in a parameter space spanned by the corresponding solutal and thermal Rayleigh numbers. We also discuss a counterintuitive instability leading to buoyancy-driven deformation of statically stable fronts across which a solute-light and hot solution lies on top of a solute-heavy and colder one. The mechanism of this chemically driven instability lies in the coupling of a localized reaction zone and of differential diffusion of heat and mass. Dispersion curves of the various cases are analyzed. A discussion of the possible candidates of autocatalytic reactions and experimental conditions necessary to observe the various instability scenarios is presented.     

External regulation of convection in a weak electrically conducting non-Newtonian liquid with g-jitter

The effect of time-periodic temperature/gravity modulation at the onset of magneto-convection in weak electrically conducting second order liquids is investigated by making a linear stability analysis. The Venezian [J. Fluid Mech. 35 (1969) 243] approach is adopted in arriving at the critical Rayleigh and wave numbers for small amplitude temperature/gravity modulation. The temperature modulation is shown to give rise to subcritical motion and gravity modulation leads to delayed convection. Subcriticality or super-criticality depends on the sign of a correction Rayleigh number being negative or positive. An asymptotic analysis is also presented for small/large frequencies. A similar role is shown to be played by the Prandtl number. Comparison is made between the effects of temperature, gravity and combined (temperature+gravity) modulations.     

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.     

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.     

Effect of the combined thermal and mass concentration gradients on the stability of a chemically reacting fluid in a porous medium

Summary The onset of instability, due to the combined effects of thermal and mass concentration gradients, is investigated in the hydrodynamic stability regime. It is found that the critical Rayleigh number, which determines the onset of instability, increases as the chemical reaction rate constant increases hyperbolically over a wide range of values at both moderate and high permeabilities. In addition, the instability grows with increase in porosity. Previous results show that the critical Rayleigh number rises linearly when only the mass concentration gradient is considered.     

Viscosity and Diffusion Effects at the Boundary Surface of Viscous Fluid and Thermoelastic Diffusive Solid Medium

This paper concentrates on the wave motion at the interface of viscous compressible fluid half-space and homogeneous isotropic, generalized thermoelastic diffusive half-space. The wave solutions in both the fluid and thermoelastic diffusive half-spaces have been investigated; and the complex dispersion equation of leaky Rayleigh wave motion have been derived. The phase velocity and attenuation coefficient of leaky Rayleigh waves have been computed from the complex dispersion equation by using the Muller's method. The amplitudes of displacements, temperature change and concentration have been obtained. The effects of viscosity and diffusion on phase velocity and attenuation coefficient of leaky Rayleigh waves motion for different theories of thermoelastic diffusion have been depicted graphically. The magnitude of heat and mass diffusion flux vectors for different theories of thermoelastic diffusion have also been computed and represented graphically.     

分离比对混合流体Rayleigh-Bénard对流解的影响

混合流体Rayleigh-Bénard对流是研究非平衡对流的非线性动力学特性的典型模型之一.基于流体力学方程组的数值模拟,首先探讨了矩形腔体中具有强Soret效应(分离比Ψ=-0.60)的混合流体行波对流的分叉特性及斑图演化,沿着分叉曲线的上部分支,随着相对瑞利数的增加,此系统依次出现了局部行波对流、具有缺陷的行波对流、行波对流、摆动行波对流及定常对流5种行波对流解.然后,研究了分离比Ψ对对流解的影响,与弱Soret效应(Ψ=-0.11)时的对流解相比较,强Soret效应(Ψ=-0.60)时出现的对流解更丰富.由于有强Soret效应的对流的复杂性,Ψ=-0.60时的对流解与Ψ=-0.20,-0.4时的对流解不同.     

Reaction driven convection around a stably stratified chemical front

A vertical stratification of a light and hot fluid over a heavy and cold one is expected to be stable with regard to buoyancy-driven convection. Here we show that chemical reactions can trigger convection around chemical fronts even in cases where concentration and heat both contribute to a stable density stratification. The balance between intrinsic thermal and solutal density gradients initiated by a spatially localized reaction zone and double diffusive mechanisms are at the origin of a new convective instability, the mechanism of which is explained by a displaced particle argument. Linear stability analysis of a reaction-diffusion-convection model confirmed by nonlinear simulations delimits the instability region in the parameter space spanned by the thermal and solutal Rayleigh numbers. Experimental systems in which to test our theoretical predictions are proposed.     

Importance of direction of vibration on the onset of Soret-driven convection under gravity or weightlessness

This paper considers the influence of the direction of vibration on the stability threshold of two-dimensional Soret-driven convection. The configuration is an infinite layer filled with a binary mixture, which can be heated from below or from above. The limiting case of high-frequency and small-amplitude vibration is considered for which the time-averaged formulation has been adopted. The linear stability analysis of the quasi-mechanical equilibrium shows that the problem depends on five non-dimensional parameters. These include the thermal Rayleigh number ( Ra_T), the vibrational parameter (R), the Prandtl number ( Pr), the Lewis number (Le), the separation ratio (S) and the orientation of vibration with respect to the horizontal heated plate (). For different sets of parameters, the bifurcation diagrams are plotted Ra_c = f (S) and k_c = g(S), which are the critical thermal Rayleigh and the critical wave numbers, respectively. Our results indicate that, relative to the classical case of static gravity, vibration may affect all regions in Ra_c-S stability diagram. In the case of mono-cellular convection, by using a regular perturbation method, a closed-form relation for the critical Rayleigh number is found. Several physical situations in the presence or in the absence of gravity (micro-gravity) are discussed.     

梯度场中荧光关联谱测量的Monte Carlo模拟

荧光关联谱（FCS）利用少量分子的荧光涨落获得分子运动和反应信息,是一种探测活细胞内生物过程的有力工具。本文利用Monte Carlo方法模拟激光梯度场下瑞利粒子的布郎运动,分析梯度场对FCS测量得到的扩散时间、粒子数等参数的影响,模拟与初步实验结果定性吻合。文中还讨论了Monte Carlo模拟预测的一些实验现象。     

Effects of Soret diffusion on the laminar flame speed and Markstein length of syngas/air mixtures

The effects of Soret diffusion on premixed syngas/air flames at normal and elevated temperatures and pressures are investigated numerically including detailed chemistry and transport. The emphasis is placed on assessing and interpreting the influence of Soret diffusion on the unstretched and stretched laminar flame speed and Markstein length of syngas/air mixtures. The laminar flame speed and Markstein length are obtained by simulating the unstretched planar flame and positively-stretched spherical flame, respectively. The results indicate that at atmospheric pressure the laminar flame speed of syngas/air is mainly reduced by Soret diffusion of H radical while the influence of H₂ Soret diffusion is negligible. This is due to the facts that the main reaction zone and the Soret diffusion for H radical (H₂) are strongly (weakly) coupled, and that Soret diffusion reduces the H concentration in the reaction zone. Because of the enhancement in the Soret diffusion flux of H radical, the influence of Soret diffusion on the laminar burning flux increases with the initial temperature and pressure. Unlike the results at atmospheric pressure, at elevated pressures the laminar flame speed is shown to be affected by the Soret diffusion of H₂ as well as H radical. For stretched spherical flame, it is shown that the Soret diffusion of both H and H₂ should be included so that the stretched flame speed can be accurately predicted. Similar to the laminar flame speed, the Markstein length is also reduced by Soret diffusion. However, the reduction is found to be mainly caused by Soret diffusion of H₂ rather than that of H radical. Moreover, the influence of Soret diffusion on the Markstein length is demonstrated to decrease with the initial temperature and pressure.     

Spatiotemporal chaos in the dynamics of buoyantly and diffusively unstable chemical fronts

Nonlinear dynamics resulting from the interplay between diffusive and buoyancy-driven Rayleigh-Taylor (RT) instabilities of autocatalytic traveling fronts are analyzed numerically for various values of the relevant parameters. These are the Rayleigh numbers of the reactant A and autocatalytic product B solutions as well as the ratio D=D(B)/D(A) between the diffusion coefficients of the two key chemical species. The interplay between the coarsening dynamics characteristic of the RT instability and the constant short wavelength modulation of the diffusive instability can lead in some regimes to complex dynamics dominated by irregular succession of birth and death of fingers. By using spectral entropy measurements, we characterize the transition between order and spatial disorder in this system. The analysis of the power spectrum and autocorrelation function, moreover, identifies similarities between the various spatial patterns. The contribution of the diffusive instability to the complex dynamics is discussed.     

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.