Thermal vibrational convection in near-critical fluids. Part 1. Non-uniform heating

Lyubimov, D. V.; Lyubimova, T. P.; Vorobev, Anatoliy; Mojtabi, Abdelkader; Zappoli, Bernard

doi:10.1017/s0022112006001418

Cited by 14 publications

(6 citation statements)

References 23 publications

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“…First, we write down the different orders of equations (19), (20) and (21). The first orders of the mass (19) and species balances (20) are as follows…”

Section: Separation Of the Processes Occuring On Different Time Scmentioning

confidence: 99%

“…Finally, we note that, firstly, the quick time-scale processes are damping and, secondly, there is no energy injection into fast processes as it could, for example, happen in the case of imposed high-frequency vibrations [20,21]. These two facts allow us to draw a conclusion that the short-term processes, even if existed at the initial moment, are to be rapidly damped out and are not to affect the long-term evolution on the convective and diffusive time-scales.…”

Section: Separation Of the Processes Occuring On Different Time Scmentioning

confidence: 99%

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Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations

Vorobev

2010

Phys. Rev. E

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We use the Cahn-Hilliard approach to model the slow dissolution dynamics of binary mixtures. An important peculiarity of the Cahn-Hilliard-Navier-Stokes equations is the necessity to use the full continuity equation even for a binary mixture of two incompressible liquids due to dependence of mixture density on concentration. The quasicompressibility of the governing equations brings a short time-scale ͑quasiacoustic͒ process that may not affect the slow dynamics but may significantly complicate the numerical treatment. Using the multiple-scale method we separate the physical processes occurring on different time scales and, ultimately, derive the equations with the filtered-out quasiacoustics. The derived equations represent the Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations. This approximation can be further employed as a universal theoretical model for an analysis of slow thermodynamic and hydrodynamic evolution of the multiphase systems with strongly evolving and diffusing interfacial boundaries, i.e., for the processes involving dissolution/nucleation, evaporation/condensation, solidification/melting, polymerization, etc.

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“…First, we write down the different orders of equations (19), (20) and (21). The first orders of the mass (19) and species balances (20) are as follows…”

Section: Separation Of the Processes Occuring On Different Time Scmentioning

confidence: 99%

Section: Separation Of the Processes Occuring On Different Time Scmentioning

confidence: 99%

Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations

Vorobev

2010

Phys. Rev. E

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“…In recent decades, multiple studies have shown that an inertial field tuned from the outside can be a powerful tool for controlling heat and mass transfer processes in liquid media Gershuni and Lyubimov (1998); Allali et al (2002); Lyubimov et al (2006); Shevtsova et al (2010); . In this case, different types of inertial fields have distinct effects on the liquid.…”

Section: Introductionmentioning

confidence: 99%

Pattern Formation in Miscible Rotating Hele-Shaw Flows Induced by a Neutralization Reaction

Utochkin

Siraev

Bratsun

2021

Microgravity Sci. Technol.

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We study the centrifugal buoyancy-driven chemoconvection in a Hele-Shaw cell that uniformly rotates around e perpendicular axis. The slot is considered thin enough to neglect the influence of the Coriolis force. The initial configuration of the system consists of two aqueous reacting solutions separated by a concentric boundary. The acid solution fills the center of the cavity, while the base solution is in the periphery. Bringing liquids into contact initiates a neutralization reaction to form a salt. We show that reaction-diffusion processes produce a potential well near the reaction front, which determines the pattern formation of the system. For some ratios of initial concentrations, there appears a periodic sequence of chemoconvective vortices in the well, while for others, when the well collapses, a shock-like density wave occurs. When the density of the acid solution is higher, the Rayleigh-Taylor instability develops in the system. We found that an increase in the rotation speed leads to a gradual disruption of the structure periodicity. It can even result in the ejection of some vortices from the potential well. We show that the density wave is extremely sensitive to the magnitude of the centrifugal force, occurring only at some critical value. Finally, we obtained a stability map of the system by performing direct numerical simulations for increasing the centrifugal Rayleigh number and the dimensionless distance of the initial contact surface between the solutions from the axis of rotation.

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“…Acoustic field impact on heat and mass transfer processes is the subject of thermoacoustic convection research in different mono‐ and heterophase hydrodynamic systems with high sensitivity to external effects. Thermal acoustic and vibrational convection is relevant in the study of heat and mass transfer in unstable media with complex rheology (eg, liquid metals, nonlinearly viscous media), 1,2 convective processes in near‐critical fluids 3 and in microgravitation, 4,5 and crystallization processes of binary solutions or melts 6,7 . Experimental and numerical studies also demonstrate significant acoustic field effects on the dynamics of heat convection in compressible media 8‐10 .…”

Section: Introductionmentioning

confidence: 99%

Thermal convection of fluid‐saturated granular medium in acoustic field

Sorokin

Perepechko

2020

Numerical Methods in Fluids

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SummaryThis article presents the results of numerical analysis of acoustic impact generated by small finite source on heat and mass transfer of fluid‐saturated granular medium in a cavity heated from below. Thermodynamically consistent model of two‐phase medium is obtained by the method of conservation laws suggesting no equilibrium in pressure between the phases. The transition from diffusive to convective regime of heat and mass transfer in fluid‐saturated granular medium as a consequence of acoustic impact is shown. Effect of source frequency and initial flow pattern on the intensity of convective instability and configuration of dissipative structure is studied. Formation of stable and symmetric convective structure by choosing the source frequency is illustrated.

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Thermal vibrational convection in near-critical fluids. Part 1. Non-uniform heating

Cited by 14 publications

References 23 publications

Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations

Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations

Pattern Formation in Miscible Rotating Hele-Shaw Flows Induced by a Neutralization Reaction

Thermal convection of fluid‐saturated granular medium in acoustic field

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