Numerical Analysis of Density-Driven Reactive Flows in Hele-Shaw Cell Geometry

  • S. Bekkouche Department of Mechanical Engineering, University Freres Mentouri Constantine 1, Algeria
  • M. Kadja Department of Mechanical Engineering, University Freres Mentouri Constantine 1, Algeria

Abstract

In this paper, a two-dimensional numerical simulation of the unsteady state of a two non-isothermal immiscible liquids layer system filling a reactor formed by two closely spaced parallel glass sheets, which is called an Hele-Shaw cell, vertically oriented, with an expected neutralization reaction between an acid and a base in the lower layer, under the action of gravity, is studied. Attention is given on the general behavior of the complete temporal pattern evolution (velocity, temperature, and concentration profiles) and the identification of the exothermic reaction’s role in giving birth to chemo-hydrodynamic patterns that occur because of concentration gradients. The effects of gravity and changes in initial acid and base concentrations on the formed patterns were studied. The mathematical model governing the phenomenon was solved numerically by the CFD software package COMSOL Multiphysics, with the finite element method and a comparison with the experimental data was made. The results show that this numerical tool is promising for the understanding of the reactive instabilities happening when two immiscible fluids come into contact.

Keywords: liquid-liquid reactive system, Hele-Shaw cell, diffusion, chemo hydrodynamic patterns

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References

Y. Shi, E. Kerstin, “Orientation-dependent hydrodynamic instabilities from chemo-marangoni cells to large scale interfacial deformations”, Chinese Journal of Chemical Engineering, Vol. 15, No. 5, pp. 748-753, 2007 DOI: https://doi.org/10.1016/S1004-9541(07)60157-8

E. Bodenschatz, W. Pesch, G. Ahlers, “Recent developments in Rayleigh-Benard convection”, Annual Review of Fluid Mechanics, Vol. 32, pp. 709-778, 2000 DOI: https://doi.org/10.1146/annurev.fluid.32.1.709

A. Thess, M. Bestehorn, “Planform selection in Benard-Marangoni convection: l hexagons versus g hexagons”, Physical Review E, Covering Statistical, Nonlinear, Biological, and Soft Matter Physics, Vol. 50, No. 6, pp. 6358-6367, 1995 DOI: https://doi.org/10.1103/PhysRevE.52.6358

G. I. Taylor, “The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. ”, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 201, No. 1065, pp. 192-196, 1950 DOI: https://doi.org/10.1098/rspa.1950.0052

C. Almarcha, P. M. J. Trevelyan, L. A. Riolfo, A. Zalts, C. El Hasi, A. D'Onofrio, A. De Wit, “Active role of a color indicator in buoyancy-driven instabilities of chemical fronts”, The Journal of Physical Chemistry Letters, Vol. 1, pp. 752–757, 2010 DOI: https://doi.org/10.1021/jz900418d

D. A. Bratsun, A. De Wit, “On Marangoni convective patterns driven by an exothermic chemical reaction in two-layer systems”, Physics of Fluids, Vol. 16, No. 4, pp. 1082–1096, 2004 DOI: https://doi.org/10.1063/1.1648641

D. A. Bratsun, A. De Wit, “Buoyancy-driven pattern formation in reactive immiscible two layer systems”, Chemical Engineering Science, Vol. 66, pp. 5723–5734, 2011 DOI: https://doi.org/10.1016/j.ces.2011.08.010

D. A. Bratsun, Y. Shi, K. Eckert, A. De Wit, “Control of chemo-hydrodynamic pattern formation by external localized cooling”. Europhysics Letters, Vol. 69, No. 5, pp. 746–752, 2005 DOI: https://doi.org/10.1209/epl/i2004-10417-9

K. Eckert, M. Acker, Y. Shi, “Chemical pattern formation driven by a neutralization reaction. I. Mechanism and basic features”, Physics of Fluids, Vol. 16, No. 2, pp. 385-399, 2004 DOI: https://doi.org/10.1063/1.1636160

A. Grahn, K. Eckert, “Plume and finger regimes driven by an exothermic interfacial reaction”, Physical Review Letters, Vol. 82, pp. No. 22, 4436–4439, 1999 DOI: https://doi.org/10.1103/PhysRevLett.82.4436

E. V. Aitova, D. A. Bratsun, K. G. Kostarev, E. A. Mosheva, “Convective instability in a two-layer System of Reacting Fluids with concentration dependent diffusion”, Journal of Applied Mechanics and Technical Physics, Vol. 57, No. 7, pp. 1226–1238, 2016 DOI: https://doi.org/10.1134/S0021894416070026

D. A. Bratsun,“On Rayleigh-Benard mechanism of alignment of salt fingers in reactive immiscible two-layer systems”, Microgravity Science and Technology, Vol. 26 No. 5, pp. 293-303, 2014 DOI: https://doi.org/10.1007/s12217-014-9374-0

S. Kalliadasis, J. Yang, A. De Wit, “Fingering instabilities of exothermic reaction-diffusion fronts in porous media”, Physics of Fluids, Vol. 16, No. 5, pp. 1395-1409, 2004 DOI: https://doi.org/10.1063/1.1689912

D. Villers, J. K. Platten, “Coupled buoyancy and Marangoni convection in acetone: Experiments and comparison with numerical simulations”, Journal of Fluid Mechanics, Vol. 234, pp. 487-510. 1992 DOI: https://doi.org/10.1017/S0022112092000880

A. De Wit, “Chemo-hydrodynamic patterns and instabilities”, Annual Review of Fluid Mechanics, Vol. 52, pp. 531-555, 2020 DOI: https://doi.org/10.1146/annurev-fluid-010719-060349

Y. Shi, K. Eckert, “Acceleration of reaction fronts by hydrodynamic instabilities in immiscible systems”, Chemical Engineering Science, Vol. 61, No. 17, pp. 5523-5533, 2006 DOI: https://doi.org/10.1016/j.ces.2006.02.023

A. Zalts, C. El Hasi, D. Rubio, A. Urena, A. D’Onofrio, “Pattern formation driven by an acid-base neutralization reaction in aqueous media in a gravitational field”, Physical Review E, Covering Statistical, Nonlinear, Biological, and Soft Matter Physics, Vol. 77, Article ID 015304, 2008 DOI: https://doi.org/10.1103/PhysRevE.77.015304

C. Almarcha, P. M. J. Trevelyan, P. Grosfils, A. De Wit, “Thermal effects on the diffusive layer convection instability of an exothermic acid-base reaction front”, Physical Review E, Covering Statistical, Nonlinear, Biological, and Soft Matter Physics, Vol. 88, Article ID 033009, 2013 DOI: https://doi.org/10.1103/PhysRevE.88.033009

C. Almarcha, P. M. J. Trevelyan, P. Grosfils, A. De Wit, “Chemically driven hydrodynamic instabilities”, Physical Review Letters, Vol. 104, Article ID 044501, 2010 DOI: https://doi.org/10.1103/PhysRevLett.104.044501

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