Convection in Liquids

Platten, J. K.; Legros, Jean Claude

doi:10.1007/978-3-642-82095-3

Cited by 330 publications

(169 citation statements)

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“…This is already known from the suppression of oscillatory or steady convection instabilities in narrow channels [22,52,89]. The no-slip conditions at the side-walls generate a nontrivial y-variation of the velocity field that introduces additional internal friction and that has to be compensated by a higher heating rate [18,90,91].…”

Section: B Strong Soret Coupling Strengthmentioning

confidence: 95%

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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Section: B Strong Soret Coupling Strengthmentioning

confidence: 95%

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

Jung

Lücke

2005

Phys. Rev. E

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“…The dynamics of the system is governed by the continuity equation, the Navier-Stokes equations and the energy and mass conservation equations [19]. If we nondimensionalize the equations using the height of the layer d as the unit of length, the vertical thermal di usion time d 2 =Ä (Ä being the thermal di usivity), as the unit of time and the imposed vertical temperature di erence T as the unit of temperature, the dimensionless equations in the Boussinesq approximation read as follows…”

Section: The Test Problemmentioning

confidence: 99%

Continuation of travelling-wave solutions of the Navier–Stokes equations

Mercader

Batiste

Alonso

2006

Int. J. Numer. Meth. Fluids

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SUMMARYAn e cient way of obtaining travelling waves in a periodic uid system is described and tested. We search for steady states in a reference frame travelling at the wave phase velocity using a ÿrst-order pseudospectral semi-implicit time scheme adapted to carry out the Newton's iterations. The method is compared to a standard Newton-Raphson solver and is shown to be highly e cient in performing this task, even when high-resolution grids are used. This method is well suited to three-dimensional calculations in cylindrical or spherical geometries.

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“…Here ̺ 0 is the mean density, D th the thermal diffusivity, ν the kinematic viscosity, and α = −(1/ρ)∂ρ/∂T and β = −(1/ρ)∂ρ/∂C are thermal and solutal expansion coefficients, respectively. Using the Oberbeck-Boussinesq approximation the balance equations read [2,9] ∇ · u = 0 (4a)…”

Section: System and Basic Equationsmentioning

confidence: 99%

“…Convection in binary mixtures shows a rich spectrum of pattern formation behavior [1][2][3]. But the knowledge about these structures and in particular about their stability is more limited than for pure fluids.…”

Section: Introductionmentioning

confidence: 99%

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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Convection in Liquids

Cited by 330 publications

References 0 publications

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

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

Continuation of travelling-wave solutions of the Navier–Stokes equations

Convective Patterns in Binary Fluid Mixtures with Positive Separation Ratios

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