The effect of temperature-dependent solubility on the onset of thermosolutal convection in a horizontal porous layer

Pritchard, David; Richardson, Chris N.

doi:10.1017/s0022112006003211

Cited by 57 publications

(57 citation statements)

References 29 publications

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“…Indeed, RT and DD modes are encountered in numerous systems, and it is therefore important to know whether the properties of RT and DD patterns are the same or not in reactive systems. Some theoretical works have already demonstrated that reactions can affect the stability properties of DD modes, [35][36][37] however, their active influence on nonlinear dynamics remains largely unexplored.…”

Section: Introductionmentioning

confidence: 99%

Asymmetric Rayleigh-Taylor and double-diffusive fingers in reactive systems

et al. 2013

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Buoyancy-driven flows induced by the hydrodynamic Rayleigh-Taylor or doublediffusive instabilities develop symmetrically around the initial contact line when two solutions of given solutes with different densities are put in contact in the gravitational field. If the solutes affecting the densities of these solutions are involved in chemical reactions, changes in composition due to the underlying reaction-diffusion processes can modify the density profile in space and time, and affect the hydrodynamic patterns. In particular, if the density difference between the two reactant solutions is not too large, the resulting chemo-hydrodynamic patterns are asymmetric with regard to the initial contact line. We quantify both experimentally and numerically this asymmetry showing that fingers here preferentially develop above the reaction zone and not across the mixing zone as in the non reactive situation. In some cases, the reaction can even lead to the onset of a secondary double-diffusive instability between the product of the reaction, dynamically generated in situ, and one of the reactants.

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Section: Introductionmentioning

confidence: 99%

Asymmetric Rayleigh-Taylor and double-diffusive fingers in reactive systems

et al. 2013

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“…They considered the Darcy model to study the onset of thermosolutal convection using linear instability technique. Wang and Tan [1] extended the previous work of Pritchard and Richardson [28] in which Wang and Tan [1] considered Darcy-Brinkman model and used normal mode analysis to carry out a linear instability analysis.…”

Section: Introductionmentioning

confidence: 92%

“…More studies were carried out by Gatica et al [24,25], Viljoen et al [26] and Malashetty and Gaikwad [27]. Pritchard and Richardson [28] figured out a model similar to that of Steinberg and Brand [22,23]. They considered the Darcy model to study the onset of thermosolutal convection using linear instability technique.…”

Section: Introductionmentioning

confidence: 99%

The non-linear energy stability of Brinkman thermosolutal convection with reaction

Al-Sulaimi

2016

Ricerche mat

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We use the energy method to obtain the non-linear stability threshold for thermosolutal convection porous media of Brinkman type with reaction. The obtained non-linear boundaries for different values of the reaction terms are compared with the relevant linear instability boundaries obtained by Wang and Tan (Phys Lett A 373:776-780, 2009). Using the energy theory we obtain the non-linear stability threshold below which the solution is globally stable. The compound matrix numerical technique is implemented to solve the associated system of equations with the corresponding boundary conditions. Two systems are investigated, the heated below salted above case and the heated below salted below case. The effect of the reaction terms and Brinkman term on the Rayleigh number is discussed and presented graphically.

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“…They found analytical expressions for the onset of stationary and oscillatory instabilities. Pritchard and Richardson (2007) have been considered the effect of temperature dependent solubility on the onset of thermosolutal convection in an isotropic porous medium. Malashetty and Biradar (2011) have studied the onset of double diffusive reactionconvection in an anisotropic porous layer.…”

Section: Introductionmentioning

confidence: 99%

Onset of Darcy-Brinkman Reaction-Convection in an Anisotropic Porous Layer

Gaikwad

Dhanraj²

2016

JAFM

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The linear and nonlinear stability analysis of double diffusive reaction-convection in a sparsely packed anisotropic porous layer subjected to chemical equilibrium on the boundaries is investigated analytically. The linear analysis is based on the usual normal mode method and the nonlinear theory on the truncated representation of Fourier series method. The Darcy-Brinkman model is employed for the momentum equation. The onset criterion for stationary, oscillatory and finite amplitude convection is derived analytically. The effect of Darcy number, Damkohler number, anisotropy parameters, Lewis number, and normalized porosity on the stationary, oscillatory, and finite amplitude convection is shown graphically. It is found that the effect of Darcy number and mechanical anisotropy parameter have destabilizing effect, while the thermal anisotropy parameter has stabilizing effect on the stationary, oscillatory and finite amplitude convection. The Damkohler number has destabilizing effect in the case of stationary mode, with stabilizing effect in the case of oscillatory and finite amplitude modes. Further, the transient behavior of the Nusselt and Sherwood numbers are investigated by solving the nonlinear system of ordinary differential equations numerically using the Runge-Kutta method.

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The effect of temperature-dependent solubility on the onset of thermosolutal convection in a horizontal porous layer

Cited by 57 publications

References 29 publications

Asymmetric Rayleigh-Taylor and double-diffusive fingers in reactive systems

Asymmetric Rayleigh-Taylor and double-diffusive fingers in reactive systems

The non-linear energy stability of Brinkman thermosolutal convection with reaction

Onset of Darcy-Brinkman Reaction-Convection in an Anisotropic Porous Layer

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