Abstract.
The paper deals with the investigation of the onset and non-linear regimes of convection of liquid binary mixtures with negative Soret effect heated from above. The linear stability of a convectionless state in a horizontal layer is studied by the numerical solution of the linearized problem on the temporal evolution of small perturbations of the unsteady base state. Non-linear regimes of convection are investigated by the numerical solution of the non-linear unsteady equations for a horizontally elongated rectangular cavity. The calculations are performed for water-ethanol and water-isopropanol liquid mixtures and for colloidal suspensions. The dependences of the instability onset time and wave number of the most dangerous perturbations on the solutal Rayleigh number (gravity level) obtained by a linear stability analysis and non-linear calculations are found to be in a very good agreement. A favorable comparison with the existing experimental and numerical data is presented.
Graphical abstract
Similar content being viewed by others
References
D.T.J. Hurle, E. Jakeman, J. Fluid Mech. 47, 667 (1971)
G. Zimmermann, U. Müller, Int. J. Heat Mass Transfer 35, 2245 (1992)
D. Melnikov, A. Mialdun, V. Shevtsova, J. Non-equilib. Thermodyn. 32, 259 (2007)
J. Colombani, H. Dez, J. Bert, J. Dupuy-Philon, Phys. Rev. E 58, 3202 (1998)
D.A. Nield, J. Fluid Mech. 29, 545 (1967)
D.T.J. Hurle, E. Jakeman, Phys. Fluids 12, 2704 (1969)
J.C. Chen, G.P. Neitzel, D.F. Jankowski, Phys. Fluids 28, 749 (1985)
C.K. Choi, J.H. Park, H.K. Park, H.J. Cho, T.J. Chung, M.C. Kim, Int. J. Therm. Sci. 43, 817 (2004)
M.C. Kim, S. Kim, B.J. Chung, C.K. Choi, Int. Commun. Heat Mass Transfer 30, 225 (2003)
D. Lyubimov, T. Lyubimova, S. Amiroudine, D. Beysens, Eur. Phys. J. ST 192, 129 (2013)
B.S. Maryshev, T.P. Lyubimova, Eur. Phys. J. E 39, 66 (2016)
B.S. Maryshev, T.P. Lyubimova, D.V. Lyubimov, Trans. Porous Media 111, 239 (2016)
A. Selim, D.A.S. Rees, J. Porous Media 10, 1 (2007)
M.I. Shliomis, M. Souhar, Europhys. Lett. 49, 55 (2000)
M.C. Kim, C.K. Choi, J.-K. Yeo, Phys. Fluids 19, 084103 (2007)
K.-K. Tan, T. Sam, H. Jamaludin, Int. J. Heat Mass Transfer 46, 2857 (2003)
J.-P. Caltagirone, Quart J. Mech. Appl. Math. 33, 47 (1980)
J.P. Ennis-King, L. Paterson, SPE J. 10, 349 (2005)
A. Riaz, M. Hesse, H.A. Tchelepi, F.M. Orr, J. Fluid Mech. 548, 87 (2006)
D.A.S. Rees, A. Selim, J.P. Ennis-King, The instability of unsteady boundary layers in porous media. Emerging Topics in Heat and Mass Transfer in Porous Media, edited by P. Vadasz (Springer, Berlin, 2008) pp. 85--110
R. Cerbino, S. Mazzoni, A. Vailati, M. Giglio, Phys. Rev. Lett. 94, 064501 (2005)
V.M. Shevtsova, D.E. Melnikov, J.C. Legros, Phys. Rev. E 73, 047302 (2006)
A. Mialdun, V.M. Shevtsova, Int. J. Heat Mass Transfer 51, 3164 (2008)
A. Thom, C.J. Apelt, Field computations in engineering and physics (Van Nostrand, London, 1961)
S. Mazzoni, V. Shevtsova, A. Mialdun, D. Melnikov, Yu. Gaponenko, T. Lyubimova, M.Z. Saghir, Europhys. News 41, 14 (2010)
V. Shevtsova, Y.A. Gaponenko, V. Sechenyh, D.E. Melnikov, T. Lyubimova, A. Mialdun, J. Fluid Mech. 767, 290 (2015)
I.I. Ryzhkov, Thermal diffusion in mixtures: equations, symmetries and solutions and their stability (Institute of Computational Modelling SB RAS, Krasnoyarsk, 2012) p. 215
F. Giavazzi, A. Vailati, Phys. Rev. E 80, 015303 (2009)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lyubimova, T., Zubova, N. & Shevtsova, V. Onset and non-linear regimes of Soret-induced convection in binary mixtures heated from above. Eur. Phys. J. E 40, 27 (2017). https://doi.org/10.1140/epje/i2017-11517-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epje/i2017-11517-5