Onset of oscillatory binary fluid convection in finite containers

The onset of oscillatory convection in binary fluid mixtures in a two-dimensional domain with realistic boundary conditions on all boundaries is determined as a function of the fluid parameters and the aspect ratio Gamma of the container. The first unstable mode has either odd or even parity under left-right reflection. Depending on Gamma and the separation ratio S, this mode has the form of a standing wave, or a "chevron," consisting of a pair of waves propagating outwards from the cell center (or, in some cases, inwards towards it). Codimension--two points at which odd and even parity modes are simultaneously marginally stable are determined, as are various Takens-Bogdanov points. For fixed Sinfinity, and to the gap (in Rayleigh number and oscillation frequency) between successively unstable modes. The results quantify the parameter regime in which the weakly nonlinear dynamics of the system can be described in terms of the interaction of the first odd and even parity oscillatory modes.     

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     

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.     

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.     

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.     

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.     

Wave convection regimes in a binary mixture in a modulated gravitational field

Nonlinear wave convection regimes are studied in a horizontal layer of an incompressible binary mixture with anomalous thermal diffusion in the gravitational field modulated with an arbitrary amplitude and finite frequency. Oscillation regimes are numerically simulated by the finite difference method for the case of a layer with impenetrable rigid boundaries, which better corresponds to experimental laboratory conditions. A qualitative difference is found in the dynamics of nonlinear quasi-periodic and subharmonic oscillations appearing in the initially stratified mixture and behaving as modulated and regular standing waves. The dependences of the intensity of convective flows on the modulation amplitude are obtained. The results of nonlinear calculations are compared with data on the boundaries of the equilibrium stability found from the linear theory. It is shown that a region of parameters exists where alternating action suppresses the convective motion.     

Oscillatory binary fluid convection in large aspect-ratio containers

Direct numerical simulations of chevrons, blinking states, and repeated transients in binary fluid mixtures with a negative separation ratio heated from below are described. The calculations are performed in two-dimensional containers for experimental parameter values and boundary conditions. Quantitative agreement with the experiments of Kolodner [Phys. Rev. E 47, 1038 (1993)] is obtained, and the origin of the blinking and repeated transient states is elucidated.     

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.     

Critical fluctuations of a binary fluid mixture confined in a porous medium

We have performed small angle neutron scattering experiments on the binary fluid mixture n-C₆H₁₄+n-C₈F₁₈ imbibed inside porous Vycor glass in the thermodynamic region corresponding to the bulk critical one. The resulting structure can be represented as the sum of a temperature dependent Lorentzian term and a term describing the interference between the porous matrix, a shell part richer in one component coating the glass surface, and a core part richer in the other component. We observe critical fluctuations extending over distances markedly larger than the mean pore size. Received 20 May 1999     

Surface instability on thin fluid layers of a binary mixture

A long-wave model for thin layers consisting of two miscible fluids is presented. The model is a development of a simplified 2D model variant which considers the temperature and the concentration fields as linear functions on the vertical coordinate and neglect the convective terms from the corresponding equations. Now, the 2D thin film equation is coupled to complete 3D energy and mass conservations equation. We discuss the extended system in the linear approximation and in the initial nonlinear stage.