Abstract
A conjugated initial-boundary-value problem occurring in the movement of a binary mixture and viscous heat-conductive liquid with a common interface surface under the action of thermal-concentration forces is under consideration. A solution describing a stationary flow in layers, temperature distribution, and concentration distribution is determined. The Laplace transform method is used to obtain a nonstationary solution for the problem in images, which makes it possible to describe the evolution of the movement using the numerical inversion of images.
Similar content being viewed by others
References
V. K. Andreev, V. E. Zakhvataev, and E. A. Ryabitskii, Thermocapillary Instability (Nauka, Novosibirsk, 2000) [in Russian].
V. K. Andreev, “Evolution of the Joint Motion of Two Viscous Heat–Conducting Fluids in a Plane Layer under the Action of an Unsteady Pressure Gradient,” Prikl. Mekh. Tekh. Fiz. 49 (4), 94–107 (2008) [J. Appl. Mech. Tech. Phys. 49 (4), 598–609 (2008)].
N. L. Sobachkina, “Joint Motion of a Binary Mixture and Viscous Fluid in a Heat–Insulated Cylindrical Pipe,” Vychisl. Tekhnol. 16 (4), 120–133 (2011).
E. N. Lemeshkova, “Direct and Inverse Problem on the Joint Motion of Three Viscous Fluids in Plane Layers,” Zh. Sib. Feder. Univ., Ser. Mat. Fiz. 4 (3), 363–370 (2011).
K. Hiemenz, “Die Grenzschicht an einem in den gleichförmigen Flüssigkeitsstrom eingetauchten geraden Kreiszylinder,” Dinglers Poliytech. J. 1911 (3326), 321–324 (1911).
J. F. Brady and A. Acrivos, “Steady Flow in a Channel or Tube with an Accelerating Surface Velocity,” J. Fluid Mech. 112, 127–150 (1981).
D. Riabouchinsky, “Quelques Considerations sur les Mouvements Plans Rotationnels d’un Liquide,” C. R. Acad. Sci. 179, 1133–1136 (1924).
A. G. Petrov, “Exact Solution of the Navier–Stokes Equations in a Fluid Layer between the Moving Parallel Plates,” Prikl. Mekh. Tekh. Fiz. 53 (5), 13–18 (2012) [J. Appl. Mech. Tech. Phys. 53 (5), 642–646 (2012)].
A. G. Petrov, “Constructing Solutions of the Navier–Stokes Equations for a Fluid Layer between Moving Parallel Plates at Low and Moderate Reynolds Numbers,” Prikl. Mekh. Tekh. Fiz. 54 (1), 51–56 (2013) [J. Appl. Mech. Tech. Phys. 54 (1), 44–48 (2013)].
A. G. Petrova, V. V. Pukhnachev, and O. A. Frolovskaya, “Nonstationary Motion near a Critical Point,” in Advances in Continuous Media Mechanics, Proc. of the Int. Conf. Devoted to 75th Anniversary of Academician V. A. Levin, Vladivostok, September 28 to October 4, 2014 (Megaprint, Irkutsk, 2014).
V. V. Pukhnachev, “Group Properties of the Navier–Stokes Equations in a Plane Case,” Prikl. Mekh. Tekh. Fiz., No. 1, 83–90 (1960).
M. A. Lavrentiev and B. V. Shabat, Methods of the Theory of Functions of a Complex Variable (Nauka, Moscow, 1973) [in Russian].
V. K. Andreev and E. N. Cheremnykh, “Joint Creep Motion of Three Viscous Fluids in a Plane Layer: A Priori Estimates and Convergence to a Stationary Regime,” Sib. Zh. Indust. Mat. 19 (1), 3–17 (2016).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © M.V. Efimova, N. Darabi.
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 59, No. 5, pp. 93–103, September–October, 2018.
Rights and permissions
About this article
Cite this article
Efimova, M.V., Darabi, N. Thermal-Concentration Convection in a System Of Viscous Liquid and Binary Mixture in a Plane Channel with Small Marangoni Numbers. J Appl Mech Tech Phy 59, 847–856 (2018). https://doi.org/10.1134/S0021894418050115
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021894418050115