Abstract:
An exact solution is obtained for the problem of steady flow in a system of two horizontal layers of immiscible fluids with a common interface. The stability of the flow is studied by a linearization method. It is shown that the occurrence of instabilities is due to the different governing parameters of the fluids (thickness, heating conditions, viscous and thermal conductivity of the fluids). It is found that under constant gravity conditions, the perturbations are monotonic, and in zero gravity, oscillatory thermocapillary instability occurs.
Citation:
V. B. Bekezhanova, “Convective instability of Marangoni–Poiseuille flow under a longitudinal temperature gradient”, Prikl. Mekh. Tekh. Fiz., 52:1 (2011), 92–100; J. Appl. Mech. Tech. Phys., 52:1 (2011), 74–81
\Bibitem{Bek11}
\by V.~B.~Bekezhanova
\paper Convective instability of Marangoni--Poiseuille flow under a longitudinal temperature gradient
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2011
\vol 52
\issue 1
\pages 92--100
\mathnet{http://mi.mathnet.ru/pmtf1446}
\elib{https://elibrary.ru/item.asp?id=15580547}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2011
\vol 52
\issue 1
\pages 74--81
\crossref{https://doi.org/10.1134/S0021894411010111}
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https://www.mathnet.ru/eng/pmtf1446
https://www.mathnet.ru/eng/pmtf/v52/i1/p92
This publication is cited in the following 5 articles:
Natalya V. Burmasheva, Evgeniy Yu. Prosviryakov, “On Marangoni shear convective flows of inhomogeneous viscous incompressible fluids in view of the Soret effect”, Journal of King Saud University - Science, 32:8 (2020), 3364
V. B. Bekezhanova, I. A. Shefer, “Influence of Gravity on the Stability of Evaporative Convection Regimes”, Microgravity Sci. Technol., 30:4 (2018), 543
E. A. Lukashev, E. V. Radkevich, N. N. Yakovlev, O. A. Vasil'eva, “Introduction to the generalized theory of non-equilibrium Cahn-Hilliard phase transitions
(Thermodynamic problems in continuum mechanics)”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 221:3 (2017), 437–472
Éliton Fontana, Erasmo Mancusi, Antônio A.U. de Souza, Selene M.A.G.U. de Souza, “Stability analysis of stratified Rayleigh–Bénard–Poiseuille convection. Part II: Influence of thermocapillary forces”, Chemical Engineering Science, 155 (2016), 99
R. V. Sagitov, A. N. Sharifulin, “Long-wave instability of an advective flow in an inclined fluid layer with perfectly heat-conducting boundaries”, J. Appl. Mech. Tech. Phys., 52:6 (2011), 857–864