Thermal convection in a rotating binary viscoelastic liquid mixture

In this work we report theoretical and numerical results on convection in a viscoelastic binary mixture under rotation. In particular, we focus in the Maxwelian case of viscoelastic fluid. We obtain explicit expressions for the convective thresholds in terms of the mixture parameters of the system in the case of idealized boundary conditions. We also calculate numerically the convective thresholds for the case of realistic rigid–rigid boundary conditions.     

Vibrational convection of a binary mixture in connected channels

The influence of high-frequency vibrations on the thermal convection of a binary mixture in connected channels is investigated theoretically. The oscillatory and stationary convective flows are calculated using the finite difference method in combination with the Galerkin procedure. Numerical simulation has revealed that the vertical vibrations substantially affect the threshold of convection and different characteristics of the supercritical regimes.     

双组分混合流体中Eckhaus不稳定调谐的行波对流

在双组分混合流体的Rayleigh-Bénard对流系统中，数值模拟获得了周期性时空位错缺陷调谐的扩展行进波对流状态.研究了该状态的时空演化特性.结果表明，Eckhaus不稳定触发的对流涡卷对的产生是调谐的起源，对流涡卷在边界处生成与湮没频率的不同，又使系统返回不稳定区域，系统在稳定与不稳定的波数之间振荡.还探讨了一个周期内传热与混合特性的改变及其控制参数的变化规律. 关键词： 双组分混合流体 行波对流 时空位错缺陷 Eckhaus不稳定调谐     

Nonlinear dynamics of convection patterns in a binary mixture subjected to finite-frequency vibration

Nonlinear evolution of two-dimensional convection patterns is considered for an incompressible binary mixture with negative Soret coupling in a horizontal layer subjected to finite-frequency vertical vibration of arbitrary amplitude. A numerical analysis is performed under impermeability conditions on rigid boundaries, which can be implemented in a laboratory experiment. The dependence of flow intensity on vibration amplitude is examined for the first and second resonance regions in the parameter space of thermal vibrational convection. The numerical results agree with the stability boundaries of equilibrium states predicted by linear theory. A qualitative difference in the dynamics of nonlinear oscillation is exposed between the regions corresponding to critical perturbations at the subharmonic and fundamental frequencies. Regular and chaotic dynamics, as well as hysteretic transitions between the fundamental and subharmonic modes, are revealed.     

Application of the hypothesis of isomorphism of critical phenomena for calculating the correlation function of a binary mixture in a gravitational field

Questions concerning the application of the theory of scaling transformations with the use of the hypothesis of isomorphism are considered for an analysis of the behavior of the correlation functions of binary mixtures which are at the liquid -vapor critical point in a gravitational field. Explicit expressions are obtained for the height and temperature dependence of the correlation functions of a binary mixture for the limiting directions which are isomorphous to the critical isotherm and isochore of a system with an isolated critical point.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 89–93, January, 1976.The authors are grateful to Prof. Yu. I. Shimanskii for useful discussions.     

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.     

Unstable periodic solution controlling collision of localized convection cells in binary fluid mixture

We study the collision processes of spatially localized convection cells (pulses) in a binary fluid mixture by the extended complex Ginzburg-Landau equations. Both counter- and co-propagating pulse collisions are examined numerically. For counter-propagating pulse collision, we found a special class of unstable time-periodic solutions that play a critical role in determining the output after collision. The solution profile right after collision becomes close to such an unstable pattern and then evolves along one of the unstable manifolds before reaching a final destination. The origin of such a class of unstable solutions, called scattors, can be traced back to two-peak bound states which are stable in an appropriate parameter regime. They are destabilized, as the parameter is varied, and become scattors which play the role of separators of different dynamic regimes. Delayed feedback control is useful to detect them. Also, there is another regime where the origin of the scattors is different from that of the above case. For co-propagating pulse collision, it is revealed that the result of pulse collision depends on the phase difference between pulses. Moreover, we found that a coalescent pulse keeps a profile of two-peak bound state, which is not observed in the case of counter-propagating pulse collision. Complicated collision dynamics become transparent to some extent from the viewpoint of those unstable objects.     

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.     

Convection in a gravitational field

We set up a classical stochastic model for the irreversible dynamics of a lattice gas under gravity. We show that for a class of initial states the system converges to equilibrium, which obeys the laws of thermostatics.Dedicated to Oliver Penrose.     

Soret-driven convection of binary mixture in a horizontal porous layer in the presence of a heat or concentration source

Soret-driven convection of a binary mixture in a shallow porous layer is analyzed. The analysis focuses on the behavior of the system in the presence of a concentration or heat source. In the long-wavelength limit, regimes are found in which the flow regions near the source and at the periphery are separated by narrow annular transition regions. It is also shown that the outward concentration flux from the source is dominated by convection, whereas heat can be transferred from the source both by convection and by diffusion. Multistability between these two regimes is possible.     

Effect of electric field on reentrance transition in a binary mixture of liquid crystals

Employing a phenomenological mean field theory, we analyze the effect of an electric field on the N ? SmA phase transition for pure liquid crystal and on the reentrant nematic phase in a binary mixture of liquid crystals exhibiting the phase sequence I ? N ? SmA ? N_R on cooling. The basic idea of the work is to explain the phase transition behavior of the system by assuming that certain Landau coefficients associated with the order parameters coupling terms of the free-energy density expansion are field dependent. These parameters play a crucial role and show a rapid variation at the SmA ? N_R transition as compared to the SmA ? N transition.     

Electrostatic potential in a gravitational field

The electrostatic potential in a gravitational field is estimated up to the order ofe ² G ² in the framework of the conventional quantum field theory. It is shown that the electrostatic potential is different from the classical one. We find that this discrepancy is attributable to the process in which a particle emits three massless ones which are absorbed by three other particles.     

Black hole in a gravitational field

An exact solution of the vacuum Einstein field equations representing a Schwarzschild black hole in an external gravitational field is derived using a formalism developed by Ernst.     

Transitional regimes of penetrative convection in a plain layer

Penetrative convection in a plain layer of water is considered for the interval of temperatures containing the point of density maximum. When the unstable and stable layers are equal in the static conductive state, the development of convective instability is investigated from the formation of steady structures to chaotic motion. Scales of the periodicity cell for regimes with a strong nonlinear effect were chosen with particular attention. Specifics are shown for steady structures with small-scale vortices near upper boundaries and for periodic motions with synchronized oscillations of the lower parts of vertically elongated profiles of temperature that move symmetrically. With the increase of supercriticality, the motion loses reflection symmetry, becomes doubly periodic, and finally becomes quasi-periodic before transition to chaotic motion. Domains of hysteresis are investigated for which motions with different structure and heat fluxes coexist, and it is illustrated by the dependence of the Nusselt number on supercriticallity.     

Pressure dependence of the mixing rate for the free convection of a binary gas mixture in a two-flask apparatus

A theoretical model of steady-state mixing is considered for a binary gas mixture under conditions of free gravitational convection in a vertical channel with impenetrable walls that connects two flasks. It is shown that the mixing rate in the supercritical regime has a peak and then deceases monotonically with increasing pressure. The experimental results are shown to be in good agreement with theoretical data.