Peculiar properties of density wave formation in a two-layer system of reacting miscible liquids
DOI:
https://doi.org/10.7242/1999-6691/2018.11.3.23Keywords:
density wave, chemoconvective instability, neutralization reaction, concentration-dependent diffusion, miscible liquidsAbstract
The emergence of an internal density wave in a two-layer miscible system consisting of acid and base placed in a vertically Hele-Shaw cell is studied theoretically and experimentally. When the solutions come in contact, an exothermic neutralization reaction A+B→C starts, which is accompanied by the release of the reaction product - salt. This process is associated with a strong dependence of the diffusion coefficients of the reagents concentration that leads to the appearance of a local density pocket in which cellular convection develops. Under certain concentrations, the low density pocket collapses, and no previously observed chemoconvective regime that is characterized by the formation of a shock-like density wave. It has been experimentally shown that the wave movement is accompanied by an effective mixing of the reactants and continuous reaction product withdrawal, which ensures a high reaction rate. The emergence of a shock-like density wave is confirmed and studied in detail for various combinations of pairs of the acid (HNO3) and alkali (LiOH, NaOH, KOH) that confirms the universality of the instability mechanism. It is shown that the previously proposed dimensionless parameter, which is the ratio of the density of the reaction zone to the density of the upper reagent, is a similarity criterion for all the combinations of reagent pairs studied and determines the boundary for the chemoconvective regime appearance. We propose a mathematical model for the phenomenon, which under certain assumptions can be reduced to the Saint-Venant equations for the surface gravitational waves in the shallow water approximation, which allow for shock-wave type solutions. Numerical simulations of the density wave dynamics for different values of the control parameter are presented. The transition from diffusion-controlled solution to the shock-wave-like solution when the governing parameter is varied is investigated. Comparison of numerical calculations with experimental data is given.
Downloads
References
Loskutov A. Yu., Mikhailov A.S. Vvedeniye v sinergetiku [Introduction to synergetics]. Moscow, Nauka, Fizmatlit, 1990. 272 p.
Nikolis G., Prigozhin Samoorganizatsiya v neravnovesnykh sistemakh [Self-organizing in nonequilibrum systems]. Moscow, Mir, 1979. 512 p.
Pismen L.M. Patterns and interfaces in dissipative dynamics. Berlin/Heidelberg: Springer Science & Business Media, 2006. 373 p.
Quincke G. Ueber periodische Ausbreitung an Flussigkeitsoberflachen und dadurch hervorgerufene Bewegungserscheinungen. Ann. Phys., 1888, vol. 271, no. 12, pp. 580-642. DOI
Levich V.G. Physicochemical hydrodynamics. Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1962. 700 p.
Kutepov A.M., Polyanin A.D., Zapryanov A.D., Vyaz’min A.D., Kazenin D.A. Khimicheskaya gidrodinamika. Spravochnoye posobiye [Chemical hydrodynamics. Reference Manual]. Moscow, Kvantum, 1996. 336 p.
Dupeyrat M., Nakache E. 205 – Direct conversion of chemical energy into mechanical energy at an oil water interface. Bioenerg., 1978, vol. 5, no. 1, pp. 134-141. DOI
Belk M., Kostarev K.G., Volpert V., Yudina T.M. Frontal photopolymerization with convection. J. Phys. Chem. B., 2003, vol. 107, no. 37, pp. 10292-10298. DOI
Bratsun D.A., De Wit A. Control of chemoconvective Structures in a slab reactor. Phys., 2008, vol. 53, no. 2, pp. 146‑153. DOI
Karlov S.P., Kazenin D.A., Baranov D.A., Volkov A.V., Polyanin D.A., Vyaz’min A.V. Interphase effects and macrokinetics of chemisorption in the absorption of CO2 by aqueous solutions of alkalis and amines. J. Phys. Chem. A, 2007, vol. 81, no 5, pp. 665-679. DOI
Thomson P.J., Batey W. Watson R.J. of the Extraction ’84: Symposium on Liquid-Liquid Extraction Science. Dounreay, Scotland, November 27-29, 1984. Vol. 88, pp. 231-244.
Wylock C., Rednikov A., Haut B., Colinet P. Nonmonotonic Rayleigh-Taylor instabilities driven by gas-liquid CO2 J. Phys. Chem. B, 2014, vol. 118, no. 38, pp. 11323-11329. DOI
Asad A., Yang Y.H., Chai C., Wu J.T. Hydrodynamic instabilities driven by acid-base neutralization reaction in immiscible system. J. Chem. Phys., 2010, vol. 23, no. 5, pp. 513-520. DOI
Almarcha C., R’Honi Y., De Decker Y., Trevelyan P.M.J., Eckert K., De Wit A. Convective mixing induced by acid-base reactions. Phys. Chem. B, 2011, vol. 115, no. 32, pp. 9739-9744. DOI
Eckert K., Acker M., Shi Y. Chemical pattern formation driven by a neutralization reaction. I. Mechanism and basic features. Fluid., 2004, vol. 16, no. 2, pp. 385-399. DOI
Almarcha C., Trevelyan P.M.J., Riolfo L.A., Zalts A., El Hasi C., D’Onofrio A., De Wit A. Active role of a color indicator in buoyancy-driven instabilities of chemical fronts. J. Phys. Chem. Lett., 2010, vol. 1, no. 4, pp. 752-757. DOI
Eckert K., Grahn A. Plume and finger regimes driven by an exothermic interfacial reaction. Rev. Lett., 1999, vol. 82, no. 22, pp. 4436-4439. DOI
Trevelyan P.M.J., Almarcha C. and De Wit A. Buoyancy-driven instabilities around miscible A+B→C reaction fronts: A general classification. Phys. Rev. E, 2015, vol. 91, no. 2, 023001. DOI
Bratsun D., Kostarev K., Mizev A., Mosheva E. Concentration-dependent diffusion instability in reactive miscible fluids. Physical Review E, 2015, vol. 92, no. 1, 011003(R). DOI
Aitova E.V., Bratsun D.A., Kostarev K.G., Mizev A.I., Mosheva E.A. Convective instability in a two-layer system of reacting fluids with concentration-dependent diffusion. Appl. Mech. Tech. Phys., 2016, vol. 57, no 7, pp. 1226-1238. DOI
Bratsun D.A., Stepkina O.S., Kostarev K.G., Mizev A.I., Mosheva E.A. Development of concentration-dependent diffusion instability in reactive miscible fluids under influence of constant or variable inertia. Microgravity Sci. Technol., 2016, vol. 28, no. 6, pp. 575-585. DOI
Bratsun D., Mizev A., Mosheva E., Kostarev K. Shock-wave-like structures induced by an exothermic neutralization reaction in miscible fluids. Rev. E, 2017, vol. 96, no. 5, 053106. DOI
Bratsun D.A. Internal density waves of shock type induced by chemoconvection in miscible reacting liquid. Phys. Lett., 2017, vol. 43, no. 10, pp. 944-947. DOI
Baroud C.N., Okkels F., Ménétrier L., Tabeling P. Reaction-diffusion dynamics: Confrontation between theory and experiment in a microfluidic reactor. Rev. E, 2003, vol. 67, no. 6, 060104(R). DOI
Koo Y.E.L., Kopelman R. Space-and time-resolved diffusion-limited binary reaction kinetics in capillaries: experimental observation of segregation, anomalous exponents, and depletion zone. Stat. Phys., 1991, vol. 65, no. 5-6. pp. 893-918. DOI
Koza Z., Taitelbaum H. Motion of the reaction front in the A+ B → C reaction-diffusion system. Rev. E, 1996, vol. 54, no. 2, R1040(R). DOI
Rongy L., Trevelyan P.M.J., De Wit A. Dynamics of A+ B→ C reaction fronts in the presence of buoyancy-driven convection. Rev. Lett., 2008, vol. 101, no. 8, 084503. DOI
Rongy L., Trevelyan P.M.J., De Wit A. Influence of buoyancy-driven convection on the dynamics of A+ B→ C reaction fronts in horizontal solution layers. Eng. Sci., 2010, vol. 65, no. 7, pp. 2382-2391. DOI
Demin V.А., Popov Е.А. The estimation of Damkohler number in chemiconvective problems. Vestnik Permskogo universiteta. Fizika – Bulletin of Perm University. Physics, 2015, vol. 2, no. 30, pp. 44-50.
Isaachsen I. Innere Vorgänge in strömenden Flüssigkeiten und Gasen [Internal processes in flowing liquids and gases]. Zeitschrift des Vereines deutscher Ingenieure – Journal of the Association of German Engineers, 1911, vol. 55, pp. 428‑431.
Landau L.D., Lifshits E.M. Teoreticheskaya fizika [Course of Theoretical Physics]. Moscow, Nauka, 1986, vol. VI. Gidrodinamika [Fluid Mechanics]. 736 p.
Te Chow V. Open-channel hydraulics. New York, McGraw-Hill, 1959. 698 p.
Petrosyan A.S. Dopolnitel’nye glavy teorii melkoj vody. Moscow, IKI RAN, 2014. 64 p.
Bratsun D.A. On Rayleigh-Bénard mechanism of alignment of salt fingers in reactive immiscible two-layer systems. Microgravity Sci. Technol., 2014, vol. 26, no. 5, pp. 293-303. DOI
Zel’dovich Ya.B., Semenov N.N. Teoriya goreniya i detonacii gazov [Theory of combustion and detonation of gases]. Moscow, AN SSSR, 1944. 71 p.
Downloads
Published
Issue
Section
License
Copyright (c) 2018 Computational Continuum Mechanics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.