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Journal of Applied Mechanics and Technical Physics

2016 year, number 1

Marangoni Convection in a Finite-Size Cylinder

E.P. Magdenko
Institute of Computational Modeling, Siberian Branch, Russian Academy of Sciences, Krasnoyarsk, 660036 Russia
Keywords: критические числа Марангони, деформируемая свободная плоская граница, конвекция, метод разделения переменных, critical Marangoni number, deformable free flat boundary, convection, method of separation of variables


This paper considers a liquid in a finite-size cylinder in which Marangoni instability occurs. The upper boundary of the liquid is free and deformable. The problem of the occurrence of convection in a cylindrical container is solved using the method of separation of variables. A homogeneous differential equation of the sixth order with constant coefficients and complex boundary conditions is obtained. In the case of monotonic perturbations, an analytical expression for critical Marangoni numbers is derived. The case of a weightless liquid in the cylinder is considered.