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The fluid dynamics of propagating fronts with solutal and thermal coupling

Published online by Cambridge University Press:  23 May 2022

S. Mukherjee Open the ORCID record for S. Mukherjee [Opens in a new window]  and
M.R. Paul Open the ORCID record for M.R. Paul [Opens in a new window]
S. Mukherjee
Affiliation:
Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455, USA
M.R. Paul*
Affiliation:
Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA 24061, USA
*
†Email address for correspondence: mrp@vt.edu
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Abstract

We numerically explore the propagation of reacting fronts in a shallow and horizontal layer of fluid. We focus on fronts that couple with the fluid due to density differences between the products and reactants and also due to heat release from the reaction. We explore fronts where this solutal and thermal coupling is cooperative or antagonistic. We quantify the fluid motion induced by the front and investigate the interactions of the front with the fluid as it propagates through quiescent, cellular and chaotic flow fields. The solutal coupling induces an extended convection roll that travels with the front, the thermal coupling due to heat release from the reaction generates a pair of convection rolls that travels with the front, and when both couplings are present there is a complex signature of these contributions. The details of the front dynamics depend significantly upon the interactions of the front-induced flow field with the fluid ahead of the front.

JFM classification

Convection: Buoyancy-driven instability Nonlinear Dynamical Systems: Pattern formation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 942 , 10 July 2022 , A36
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

Abel, M., Celani, A., Vergni, D. & Vulpiani, A. 2001 Front propagation in laminar flows. Phys. Rev. E 64 (4), 046307.CrossRefGoogle ScholarPubMed
Abel, M., Cencini, M., Vergni, D. & Vulpiani, A. 2002 Front speed enhancement in cellular flows. Chaos 12 (2), 481–488.CrossRefGoogle ScholarPubMed
Bargteil, D. & Solomon, T.H. 2012 Barriers to front propagation in ordered and disordered vortex flows. Chaos 22, 037103.CrossRefGoogle ScholarPubMed
Bodenschatz, E., Pesch, W. & Ahlers, G. 2000 Recent developments in Rayleigh–Bénard convection. Annu. Rev. Fluid Mech. 32 (1), 709–778.CrossRefGoogle Scholar
Budroni, M.A., Rongy, L. & De Wit, A. 2012 Dynamics due to combined buoyancy – and Marangoni-driven convective flows around autocatalytic fronts. Phys. Chem. Chem. Phys. 14, 14619–14629.CrossRefGoogle ScholarPubMed
Budroni, M.A., Upadhyay, V. & Rongy, L. 2019 Making a simple $a+b \rightarrow c$ reaction oscillate by coupling to hydrodynamic effect. Phys. Rev. Lett. 122, 244502.CrossRefGoogle Scholar
Buell, J.C. & Catton, I. 1986 Wavenumber selection in large-amplitude axisymmetric convection. Phys. Fluids 29, 23–30.CrossRefGoogle Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Dover.Google Scholar
Chiam, K.-H., Paul, M.R., Cross, M.C. & Greenside, H.S. 2003 Mean flow and spiral defect chaos in Rayleigh–Bénard convection. Phys. Rev. E 67, 056206.CrossRefGoogle ScholarPubMed
Constantin, P., Kiselev, A., Oberman, A. & Ryzhik, L. 2000 Bulk burning rate in passive-reactive diffusion. Arch. Rat. Mech. Anal. 154, 53–91.CrossRefGoogle Scholar
Deville, M.O., Fischer, P.F. & Mund, E.H. 2002 High-Order Methods for Incompressible Fluid Flow. Cambridge University Press.CrossRefGoogle Scholar
De Wit, A. 2020 Chemo-hydrodynamic patterns and instabilities. Annu. Rev. Fluid Mech. 52, 531–555.CrossRefGoogle Scholar
D'Hernoncourt, J., Zebib, A. & De Wit, A. 2007 On the classification of buoyancy-driven chemo-hydrodynamic instabilities of chemical fronts. Chaos 17 (1), 013109.CrossRefGoogle ScholarPubMed
Dominguez-Lerma, M.A., Ahlers, G. & Cannell, D.S. 1984 Marginal stability curve and linear growth rate for rotating Couette–Taylor flow and Rayleigh–Bénard convection. Phys. Fluids 27 (4), 856–860.CrossRefGoogle Scholar
Egolf, D.A., Melnikov, I.V. & Bodenschatz, E. 1998 Importance of local pattern properties in spiral defect chaos. Phys. Rev. Lett. 80, 3228–3231.CrossRefGoogle Scholar
Field, R.J. & Burger, M. 1985 Oscillations and Traveling Waves in Chemical Systems. Wiley.Google Scholar
Fischer, P.F. 1997 An overlapping Schwarz method for spectral element solution of the incompressible Navier–Stokes equations. J. Comput. Phys. 133, 84–101.CrossRefGoogle Scholar
Fisher, R.A. 1937 The wave of advance of advantageous genes. Proc. Annu. Symp. Eugen. Soc. 7, 355–369.CrossRefGoogle Scholar
Hargrove, W.W., Gardner, R.H., Turner, M.G., Romme, W.H. & Despain, D.G. 2000 Simulating fire patterns in heterogeneous landscapes. Ecol. Model. 135 (2–3), 243–263.CrossRefGoogle Scholar
Jacobson, M.Z. 1999 Fundamentals of Atmospheric Modeling. Cambridge University Press.Google Scholar
Jarrige, N., Bou Malham, I., Martin, J., Rakotomalala, N., Salin, D. & Talon, L. 2010 Numerical simulations of a buoyant autocatalytic reaction front in tilted Hele-Shaw cells. Phys. Rev. E 81, 066311.CrossRefGoogle ScholarPubMed
Karimi, A. & Paul, M.R. 2012 Quantifying spatiotemporal chaos in Rayleigh–Bénard convection. Phys. Rev. E 85, 046201.CrossRefGoogle ScholarPubMed
Kolmogorov, A.N., Petrovskii, I.G. & Piskunov, N.S. 1937 A study of the equation of diffusion with increase in the quantity of matter, and its application to a biological problem. Bull. Moscow Univ. Math. 1, 1–25.Google Scholar
Masere, J., Vasquez, D.A., Edwards, B.F., Wilder, J.W. & Showalter, K. 1994 Nonaxisymmetric and axisymmetric convection in propagating reaction-diffusion fronts. J. Phys. Chem. 98, 6505–6508.CrossRefGoogle Scholar
Mehrvarzi, C.O. & Paul, M.R. 2014 Front propagation in a chaotic flow field. Phys. Rev. E 90, 012905.CrossRefGoogle Scholar
Morris, S.W., Bodenschatz, E., Cannell, D.S. & Ahlers, G. 1993 Spiral defect chaos in large aspect ratio Rayleigh–Bénard convection. Phys. Rev. Lett. 71 (13), 2026–2029.CrossRefGoogle ScholarPubMed
Mukherjee, S. 2020 Front propagation and feedback in convective flow fields. PhD thesis, Virginia Tech.Google Scholar
Mukherjee, S. & Paul, M.R. 2019 Velocity and geometry of propagating fronts in complex convective flow fields. Phys. Rev. E 99, 012213.CrossRefGoogle ScholarPubMed
Mukherjee, S. & Paul, M.R. 2020 Propagating fronts in fluids with solutal feedback. Phys. Rev. E 101, 032214.CrossRefGoogle ScholarPubMed
Nagypal, I., Bazsa, G. & Epstein, I.R. 1986 Gravity-induced anisotropies in chemical waves. J. Am. Chem. Soc. 108 (13), 3635–3640.CrossRefGoogle Scholar
Nek5000 2021 See https://nek5000.mcs.anl.gov for more information about the NEK5000 solver.Google Scholar
Nevins, T.D. & Kelley, D.H. 2016 Optimal stretching in advection-reaction-diffusion systems. Phys. Rev. Lett. 117 (16), 164502.CrossRefGoogle ScholarPubMed
Nugent, C.R., Quarles, W.M. & Solomon, T.H. 2004 Experimental studies of pattern formation in a reaction-advection-diffusion system. Phys. Rev. Lett. 93 (21), 218301.CrossRefGoogle Scholar
Paul, M.R., Einarsson, M.I., Fischer, P.F. & Cross, M.C. 2007 Extensive chaos in Rayleigh–Bénard convection. Phys. Rev. E 75, 045203.CrossRefGoogle ScholarPubMed
Pocheau, A. & Harambat, F. 2008 Front propagation in a laminar cellular flow: shapes, velocities, and least time criterion. Phys. Rev. E 77, 036304.CrossRefGoogle Scholar
Pojman, J.A. & Epstein, I.R. 1990 Convective effects on chemical waves. 1. Mechanisms and stability criteria. J. Phys. Chem. 94, 4966–4972.CrossRefGoogle Scholar
Pojman, J.A., Epstein, I.R., McManus, T.J. & Showalter, K. 1991 a Convective effects on chemical waves. 2. Simple convection in the iodate-arsenous acid system. J. Phys. Chem. 95, 1299–1306.CrossRefGoogle Scholar
Pojman, J.A., Nagy, I.P. & Epstein, I.R. 1991 b Convective effects on chemical waves. 3. Multicomponent convection in the iron(II)-nitric acid system. J. Phys. Chem. 95, 1306–1311.CrossRefGoogle Scholar
Pomeau, Y. 2004 Diffusion and reaction-diffusion in fast cellular flows. Chaos 14 (3), 903–909.CrossRefGoogle ScholarPubMed
Rongy, L. & De Wit, A. 2009 Buoyancy-driven convection around exothermic autocatalytic chemical fronts traveling horizontally in covered thin solution layers. J. Chem. Phys. 131, 184701.CrossRefGoogle ScholarPubMed
Rongy, L., Goyal, N., Meiburg, E. & De Wit, A. 2007 Buoyancy-driven convection around chemical fronts traveling in covered horizontal solution layers. J. Chem. Phys. 127 (11), 114710.CrossRefGoogle ScholarPubMed
Rongy, L., Schuszter, G., Sinkó, Z., Tóth, T., Horváth, D., Tóth, A. & De Wit, A. 2009 Influence of thermal effects on buoyancy-driven convection around autocatalytic chemical fronts propagating horizontally. Chaos 19 (2), 023110.CrossRefGoogle ScholarPubMed
Russell, C.A., Smith, D.A., Waller, L.A., Childs, J.E. & Real, L.A. 2004 A priori prediction of disease invasion dynamics in a novel environment. Proc. R. Soc. Lond. B 271, 21–25.CrossRefGoogle Scholar
van Saarloos, W. 2003 Front propagation into unstable states. Phys. Rep. 386, 29–222.CrossRefGoogle Scholar
Schwartz, M.E. & Solomon, T.H. 2008 Chemical reaction fronts in ordered and disordered cellular flows with opposing winds. Phys. Rev. Lett. 100, 028302.CrossRefGoogle ScholarPubMed
Sreenivasan, K.R., Ramshankar, R. & Meneveau, C. 1989 Mixing, entrainment, and fractal dimensions of surfaces in turbulent flows. Proc. R. Soc. Lond. A 421, 79–108.Google Scholar
Tiani, R., De Wit, A. & Rongy, L. 2018 Surface tension- and buoyancy-driven flows across horizontally propagating chemical fronts. Adv. Colloid Interface Sci. 225, 76–83.CrossRefGoogle Scholar
Vasquez, D.A., Littley, J.M., Wilder, J.W. & Edwards, B.F. 1994 Convection in chemical waves. Phys. Rev. E 50 (1), 280–284.CrossRefGoogle ScholarPubMed
Williams, F.A. 1985 Combustion Theory. Benjamin-Cummings.Google Scholar
Wu, Y., Vasquez, D.A., Edwards, B.F. & Wilder, J.W. 1995 Convective chemical-wave propagation in the Belousov-Zhabotinsky reaction. Phys. Rev. E 51, 1119–1127.CrossRefGoogle ScholarPubMed
Xin, J. 2000 Front propagation in heterogeneous media. SIAM Rev. 42 (2), 161–230.CrossRefGoogle Scholar

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