Rayleigh-Bénard convection in binary mixtures with separation ratios near zero

Dominguez-Lerma, M. A.; Ahlers, Guenter; Cannell, David S.

doi:10.1103/physreve.52.6159

Cited by 29 publications

(33 citation statements)

References 45 publications

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“…This abrupt transition was first derived for the five-variable model by Platten and Chavepeyer [10], first observed experimentally by Le Gal et al [22], and the two regimes identified and named the Soret and Rayleigh regimes by Moses and Steinberg [30,45]. The Soret-to-Rayleigh transition has also been reproduced experimentally in [29,41,54] and numerically in [41,44,52,59]. We will interpret this transition as a manifestation of the avoided crossing phenomenon which occurs at the separation between the solutal and thermal regimes.…”

Section: Soret and Rayleigh Regimesmentioning

confidence: 75%

“…However, the wavenumber actually realized in full nonlinear simulations [52] for the Soret problem with rigid boundaries in a two-dimensional geometry is close to π, as is the wavenumber for the square patterns observed experimentally, e.g. [45,54]. Considerations of pattern selection clearly play no role in the mechanism we have discussed since, in the thermosolutal problem, the boundary conditions on T and C are identical and we have fixed k at k crit = π/ √ 2.…”

Section: Soret and Rayleigh Regimesmentioning

confidence: 99%

“…Moses and Steinberg [45], who have carried out the most extensive experimental investigation, observe the Soret regime for L 0.85 < S < L 0.27 . Other experimental observations are at S = L 1.12 [29], at S = L 1.15 [41], and at S = L 0.99 [54]. Numerical observations should be possible over a larger range: since r and E ranges can effectively be magnified as required, the thresholds forr mid − r PF and E(r mid ) are not as constraining.…”

Section: Soret and Rayleigh Regimesmentioning

confidence: 99%

“…[17,18,31,47,48,59], and, on the other hand, realistic and physical exploration of the spatial complexity of the Soret and other problems in a large container for negative [19,20,23,24,25,27,29,28,32,33,34,35,36,37,42,44,43,49,50,51,52,53,54,55,56,57,58] and positive [22,30,29,38,39,40,41,44,45,46,52,54,59,60,61] values of the separation ratio. The first line of research has led to an understanding of the mechanisms producing global bifurcations, period-doubling, and chaos in two-dimensional convection in a confined geometry.…”

Section: Introductionmentioning

confidence: 99%

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Thermosolutal and binary fluid convection as a 2×2 matrix problem

Tuckerman

2001

Physica D: Nonlinear Phenomena

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We describe an interpretation of convection in binary fluid mixtures as a superposition of thermal and solutal problems, with coupling due to advection and proportional to the separation parameter S. Many of the properties of binary fluid convection are then consequences of generic properties of 2 × 2 matrices. The eigenvalues of 2 × 2 matrices varying continuously with a parameter r undergo either avoided crossing or complex coalescence, depending on the sign of the coupling (product of off-diagonal terms). We first consider the matrix governing the stability of the conductive state. When the thermal and solutal gradients act in concert (S > 0, avoided crossing), the growth rates of perturbations remain real and of either thermal or solutal type. In contrast, when the thermal and solutal gradients are of opposite signs (S < 0, complex coalescence), the growth rates become complex and are of mixed type. Surprisingly, the kinetic energy of nonlinear steady states is also governed by an eigenvalue problem very similar to that governing the growth rates. More precisely, there is a quantitative analogy between the growth rates of the linear stability problem for infinite Prandtl number and the amplitudes of steady states of the minimal five-variable Veronis model for arbitrary Prandtl number. For positive S, avoided crossing leads to a distinction between low-amplitude solutal and high-amplitude thermal regimes. For negative S, the transition between real and complex eigenvalues leads to the creation of branches of finite amplitude, i.e. to saddle-node bifurcations. The codimension-two point at which the saddle-node bifurcations disappear, leading to a transition from subcritical to supercritical pitchfork bifurcations, is exactly analogous to the Bogdanov codimension-two point at which the Hopf bifurcations disappear in the linear problem.

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Section: Soret and Rayleigh Regimesmentioning

confidence: 75%

Section: Soret and Rayleigh Regimesmentioning

confidence: 99%

Section: Soret and Rayleigh Regimesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Thermosolutal and binary fluid convection as a 2×2 matrix problem

Tuckerman

2001

Physica D: Nonlinear Phenomena

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“…For the classical Rayleigh-Bénard system without porous medium, there has been a large body of work dealing with binary mixtures under the influence of the Soret effect (Eaton et al (1991); Barten et al (1995); Huke. & Lücke (2002); Le Gal et al (1985); Dominguez-Lerma et al (1995); Barten et al (1989); Schöpf & Zimmermann (1993); Knobloch & Moore (1988); Cross & Kim (1988); Kolodner et al (1986); Fütterer & Lücke (2002); Touiri et al (1996); Ahlers & Rehberg (1986); Walden et al (1985)). In particular, the roll convection and the corresponding stability mechanisms are well known (see Huke et al (2000)).…”

Section: Introductionmentioning

confidence: 99%

Roll convection of binary fluid mixtures in porous media

et al. 2010

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We investigate theoretically the nonlinear state of ideal straight rolls in the RayleighBénard system of a fluid layer heated from below with a porous medium using a Galerkin method. Applying the Oberbeck-Boussinesq approximation, binary mixtures with positive separation ratio are studied and compared to one-component fluids. Our results for the structural properties of roll convection resemble qualitatively the situation in the Rayleigh-Bénard system without porous medium except for the fact that the streamlines of binary mixtures are deformed in the so-called Soret regime. The deformation of the streamlines is explained by means of the Darcy equation which is used to describe the transport of momentum. In addition to the properties of the rolls, their stability against arbitrary infinitesimal perturbations is investigated. We compute stability balloons for the pure fluid case as well as for a wide parameter range of Lewis numbers and separation ratios which are typical for binary gas and fluid mixtures. The stability regions of rolls are found to be restricted by a crossroll, a zigzag and a new type of oscillatory instability mechanism, which can be related to the crossroll mechanism.

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Convective Patterns in Binary Fluid Mixtures with Positive Separation Ratios

Huke

Lücke

2002

Thermal Nonequilibrium Phenomena in Fluid Mixtures

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Abstract. We summarize our findings about laterally periodic convection structures in binary mixtures in the Rayleigh-Bénard system for positive Soret effect. Stationary roll, square, and crossroll solutions and their stability are determined with a multimode Galerkin expansion. The oscillatory competition of squares and rolls in the form of crossroll oscillations is reviewed. They undergo a subharmonic bifurcation cascade where the oscillation period grows in integer steps as a consequence of an entrainment process.

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Rayleigh-Bénard convection in binary mixtures with separation ratios near zero

Cited by 29 publications

References 45 publications

Thermosolutal and binary fluid convection as a 2×2 matrix problem

Thermosolutal and binary fluid convection as a 2×2 matrix problem

Roll convection of binary fluid mixtures in porous media

Convective Patterns in Binary Fluid Mixtures with Positive Separation Ratios

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