Convection in binary fluid mixtures. I. Extended traveling-wave and stationary states

Barten, W.; Lücke, M.; Kamps, Marc de; Schmitz, R.

doi:10.1103/physreve.51.5636

Cited by 86 publications

(115 citation statements)

References 82 publications

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“…Eventually, at ψ ≃ −0.07 a regime is reached where stable LTWs coexist near onset with extended TWs [4,7,24,25,26,27,28]. Increasing the Soret coupling strength further to more negative ψ the band (r LT W min , r LT W max ) of Rayleigh numbers in which stable LTWs exist increases monotonically while shifting upwards as a whole -r LT W max (ψ) grows stronger than r LT W min (ψ).…”

Section: Localized Traveling Wavesmentioning

confidence: 99%

“…In laterally extended TWs ω and with it v p increase when the concentration variations become larger [24,25]. In fact, there is a universal scaling relation between M and ω [67] which shows that M and v p are linearly related to each other.…”

Section: Mixing Numbermentioning

confidence: 99%

“…To find the time-dependent solutions of the above partial differential equations subject to realistic horizontal boundary conditions [25] we performed numerical simulations with a modification of the SOLA code that is based on the MAC method [57,58]. This is a finitedifference method of second order in space formulated on staggered grids for the different fields.…”

Section: Wall-attached Structuresmentioning

confidence: 99%

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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: Localized Traveling Wavesmentioning

confidence: 99%

Section: Mixing Numbermentioning

confidence: 99%

Section: Wall-attached Structuresmentioning

confidence: 99%

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

Jung

Lücke

2005

Phys. Rev. E

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“…It should be noted that the solution belonging to the upper part of the TW branch is highly nonlinear and that, even though the temperature and velocity ÿelds are nearly harmonic in the x-direction, the horizontal concentration proÿle has a trapezoidal shape [21,22]. As a consequence, a high spatial resolution is required to resolve the narrow concentration boundary layers of these solutions.…”

Section: Description and Comparison Of The Different Methodsmentioning

confidence: 99%

“…At R c the phase velocity is c = 2:337 and at R * goes to zero, as corresponds to the parity-breaking bifurcation of the SOC states that takes place there. The structure of the TW, which is shown in Figure 2, and of the SOC states has been discussed extensively in References [21,22].…”

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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Secondary instabilities on double‐diffusive convection in an anisotropic porous layer with Soret effect

Ragoju

Singh

2022

Heat Trans

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In an anisotropic porous matrix with a Soret coefficient, the onset of double-diffusive convection is investigated analytically using weakly nonlinear analysis. The momentum equation is expressed using a generalized Darcy model with a time derivative term. The Newell-Whitehead-Segel equation is acquired, thereby examining the Eckhaus and zigzag secondary instabilities. Nusselt and Sherwood numbers are used to examine convection onset by quantifying heat and mass movement. Heat and mass transmission dynamics are graphically depicted as a consequence of several parameters. An increase of the positive value of the Soret parameter enhances heat transport, whereas, an increase of the negative value of the Soret parameter reduces it.

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Convection in binary fluid mixtures. I. Extended traveling-wave and stationary states

Cited by 86 publications

References 82 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

Secondary instabilities on double‐diffusive convection in an anisotropic porous layer with Soret effect

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