Abstract
We present the results of numerical simulations of onset and nonlinear regimes of a ternary mixture convection in a square cavity subjected to the gravity field and vertical gradients of temperature and concentration. The stability problem for the non-convective state of the mixture is solved using a software package for the investigation of the stability of flows. Nonlinear regimes of convection are studied numerically by the finite difference method. The dependences of critical parameters on the net separation ratio are obtained for the cases of heating from above and below. Numerical data on the temporal evolution of the integral characteristics of flow and heat and mass transfer and of the fields of stream function, temperature and concentration are obtained for different values of the Rayleigh number and net separation ratio.
Graphical abstract
Similar content being viewed by others
References
G.Z. Gershuni, E.M. Zhukhovitskii, Convective Stability of Incompressible Fluid (Israel Program for Scientific Translations, Jerusalem, 1976).
M. Lücke, W. Barten, P. Büchel, C. Fütterer, St. Hollenger, Ch. Jung, Lect. Notes Phys. 55, 127 (1998).
V.M. Shevtsova, D.E. Melnikov, J.C. Legros, Phys. Rev. E 73, 047302 (2006).
M.C. Kim, C.K. Choi, J.-K. Yeo, Phys. Fluids. 19, 084103 (2007).
M.I. Shliomis, M. Souhar, Europhys. Lett. 49, 55 (2000).
R. Cerbino, A. Vailati, M. Giglio, Phys. Rev. E 66, 055301(R) (2002).
S. Mazzonia, R. Cerbino, D. Brogioli, A. Vailati, M. Giglio, Eur. Phys. J. E 15, 305 (2004).
R. Cerbino, S. Mazzoni, A. Vailati, M. Giglio, Phys. Rev. Lett. 94, 064501 (2005).
F. Croccolo, F. Scheffold, A. Vailati, Phys. Rev. Lett. 111, 014502 (2013).
M. Italia, F. Croccolo, F. Scheffold, A. Vailati, Eur. Phys. J. E 37, 101 (2014).
I.I. Ryzhkov, Thermal Diffusion in Mixtures: Equations, Symmetries and Solutions and their Stability (Institute of Computational Modelling SB RAS, Krasnoyarsk, 2012) p. 215.
S.M. Cox, I.M. Moroz, Physica D 93, 1 (1996).
J.P. Larre, J.K. Platten, G. Chavepeyer, Int. J. Heat Mass Transfer 40, 545 (1997).
A. Mialdun, V.M. Shevtsova, Int. J. Heat Mass Transfer 51, 3164 (2008).
A. Leahy-Dios, A. Firoozabadi, J. Phys. Chem. B 111, 191 (2007).
M.C. Charrier-Mojtabi, B. Elhajjar, A. Mojtabi, Phys. Fluids 19, 124104 (2007).
A. Vailati, M. Giglio, Phys. Rev. E 58, 4361 (1998).
K. Jamshidi-Ghaleh, M.T. Tavassoly, N. Mansour, J. Phys. D: Appl. Phys. 37, 1993 (2004).
A. Firoozabadi, K. Ghorayeb, SPE J. 5, 158 (2000).
T. Lyubimova, N. Zubova, Micrograv. Sci. Technol. 26, 241 (2014).
I.I. Ryzhkov, V.M. Shevtsova, Phys. Fluids 21, 014102 (2009).
A.Yu. Gelfgat, J. Comput. Phys. 156, 300 (1999).
D.V. Lyubimov, T.P. Lyubimova, V.A. Morozov, Bull. Perm Univ. Info. Syst. Technol. 5, 74 (2001).
E.T. Whittaker, G. Robinson, The Newton-Raphson Method, Ch.44 in The Calculus of Observations: A Treatise on Numerical Mathematics, 4th edition (Dover, New York, 1967) pp. 84–87.
A. Thom, C.J. Apelt, Field Computations in Engineering and Physics (Van Nostrand, London, 1961).
P. Blanco, M.M. Bou Ali, J.K. Platten, D.A. Nezquia, J.A. Madariaga, C. Santamaria, J. Chem. Phys. 132, 114506 (2010).
Author information
Authors and Affiliations
Corresponding author
Additional information
Contribution to the Topical Issue “Thermal nonequilibrium phenomena in multi-component fluids” edited by Fabrizio Croccolo and Henri Bataller.
Rights and permissions
About this article
Cite this article
Lyubimova, T., Zubova, N. Onset and nonlinear regimes of ternary mixture convection in a square cavity. Eur. Phys. J. E 38, 19 (2015). https://doi.org/10.1140/epje/i2015-15019-2
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1140/epje/i2015-15019-2