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Updated: Apr 16, 2026

Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
Marangoni instability of a liquid film flow with viscous dissipation
Michele Celli1, Antonio Barletta1, Leonardo S de B Alves2
1Department of Industrial Engineering, Alma Mater Studiorum Università di Bologna, Viale Risorgimento 2, 40136 Bologna, Italy.
Abstract:
A linear stability analysis of a thin liquid film flowing over a plate is performed. The plate is considered as impermeable and adiabatic. The upper surface of the film is assumed to be a free boundary with a non-negligible surface tension, characterized by a Robin thermal boundary condition. The thermoconvective instability is generated by the interplay between the heating due to viscous dissipation and the temperature-dependent surface tension at the free boundary. A basic parallel flow, arbitrarily oriented, is assumed and the basic temperature profile is determined analytically. In order to investigate the linear stability of the system, the normal mode method is employed. A system of ordinary differential equations defining an eigenvalue problem is thus obtained. The case of longitudinal rolls, where the base flow velocity is parallel to the axis rolls, is solved both analytically and numerically. Other possible inclinations of the base flow are investigated by means of a numerical procedure based on combining the Runge-Kutta and the shooting methods.
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