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Instability of axisymmetric flow in thermocapillary liquid bridges: Kinetic and thermal energy budgets for two-phase flow with temperature-dependent material properties

Article dans une revue avec comité de lecture
Author
STOJANOVIĆ, Mario
19098 Vienna University of Technology = Technische Universität Wien [TU Wien]
ccROMANO, Francesco
531216 Laboratoire de Mécanique des Fluides de Lille - Kampé de Fériet [LMFL]
KUHLMANN, Hendrik C.
19098 Vienna University of Technology = Technische Universität Wien [TU Wien]

URI
http://hdl.handle.net/10985/24482
DOI
10.1017/s0956792523000189
Date
2023-07
Journal
European Journal of Applied Mathematics

Abstract

In numerical linear stability investigations, the rates of change of the kinetic and thermal energy of the perturbation flow are often used to identify the dominant mechanisms by which kinetic or thermal energy is exchanged between the basic and the perturbation flow. Extending the conventional energy analysis for a single-phase Boussinesq fluid, the energy budgets of arbitrary infinitesimal perturbations to the basic two-phase liquid–gas flow are derived for an axisymmetric thermocapillary bridge when the material parameters in both phases depend on the temperature. This allows identifying individual transport terms and assessing their contributions to the instability if the basic flow and the critical mode are evaluated at criticality. The full closed-form energy budgets of linear modes have been derived for thermocapillary two-phase flow taking into account the temperature dependence of all thermophysical parameters. The influence of different approximations to the temperature dependence on the linear stability boundary of the axisymmetric flow in thermocapillary liquid bridges is tested regarding their accuracy. The general mechanism of symmetry breaking turns out to be very robust.

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