Onset of Rayleigh-Bénard convection in binary liquid mixtures of 3 He in 4 He

Lee, G. W. T.; Lucas, P.; Tyler, Andrew N.

doi:10.1017/s0022112083003067

Cited by 57 publications

(25 citation statements)

References 32 publications

(19 reference statements)

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“…In writing these equations we have ignored the Dufour effect. This is appropriate for water-ethanol mixtures and for normal He 3 -He 4 mixtures provided the mean temperature is sufficiently far from the λ point of the mixture (Lee, Lucas & Tyler 1983).…”

Section: Basic Equationsmentioning

confidence: 99%

Travelling convectons in binary fluid convection

et al. 2013

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Binary fluid mixtures with a negative separation ratio heated from below exhibit steady spatially localized states called convectons for supercritical Rayleigh numbers. With no-slip, fixed-temperature, no-mass-flux boundary conditions at the top and bottom stationary odd-and even-parity convectons fall on a pair of intertwined branches connected by branches of travelling asymmetric states. In appropriate parameter regimes the stationary convectons may be stable. When the boundary condition on the top is changed to Newton's law of cooling the odd-parity convectons start to drift and the branch of odd-parity convectons breaks up and reconnects with the branches of asymmetric states. We explore the dependence of these changes and of the resulting drift speed on the associated Biot number using numerical continuation, and compare and contrast the results with a related study of the Swift-Hohenberg equation by Houghton & Knobloch (Phys. Rev. E, vol. 84, 2011, art. 016204). We use the results to identify stable drifting convectons and employ direct numerical simulations to study collisions between them. The collisions are highly inelastic, and result in convectons whose length exceeds the sum of the lengths of the colliding convectons.

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Section: Basic Equationsmentioning

confidence: 99%

Travelling convectons in binary fluid convection

et al. 2013

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“…The Dufour effect [53,54] that provides a coupling of concentration gradients into the heat current and a change of the thermal diffusivity is discarded in (1.1c) since it is relevant only in few binary gas mixtures [55] and possibly in liquids near the liquid-vapor critical point [56].…”

Section: Wall-attached Structuresmentioning

confidence: 99%

Traveling wave fronts and localized traveling wave convection in binary fluid mixtures

Jung

Lücke

2005

Phys. Rev. E

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Nonlinear fronts between spatially extended traveling wave convection (TW) and quiescent fluid and spatially localized traveling waves (LTWs) are investigated in quantitative detail in the bistable regime of binary fluid mixtures heated from below. A finite-difference method is used to solve the full hydrodynamic field equations in a vertical cross section of the layer perpendicular to the convection roll axes. Results are presented for ethanol-water parameters with several strongly negative separation ratios where TW solutions bifurcate subcritically. Fronts and LTWs are compared with each other and similarities and differences are elucidated. Phase propagation out of the quiescent fluid into the convective structure entails a unique selection of the latter while fronts and interfaces where the phase moves into the quiescent state behave differently. Interpretations of various experimental observations are suggested.

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“…B is the buoyancy. The Dufour effect [20,21] that provides a coupling of concentration gradients into the heat current Q and a change of the thermal diffusivity is discarded in (2.3) since it is relevant only in few binary gas mixtures [22] and possibly in liquids near the liquid-vapor critical point [23].…”

Section: Systemmentioning

confidence: 99%