Sideband thermocapillary instability of a thin film flowing down the outside of a thick walled cylinder with finite thermal conductivity

• Published in: International journal of non-linear mechanics 2019-03, Vol.109, p.15-23
• Main Author: Dávalos-Orozco, L.A.
• Format: Article
• Language: English
• Subjects: Flow stability; Fluid dynamics; Fluid flow; Heat conductivity; Heat transfer; Marangoni convection; Nonlinear sideband instability; Parameters; Reynolds number; Surface tension; Thermal conductivity; Thermocapillary convection; Thick wall with finite thermal conductivity; Thin films; Vertical cylinders; Vertical cylindrical thin liquid film; Wavelengths
• ISSN: 0020-7462; 1878-5638
• DOI: 10.1016/j.ijnonlinmec.2018.10.015

The sideband thermocapillary instability of a thin liquid film flowing down the outside of a hot vertical cylinder is investigated. The wall of the cylinder is thick and has finite thermal conductivity. In contrast to previous work, it is shown that the presence of a main flow represented by the Reynolds number promotes the linear axial instability mode as the most unstable one. Thermocapillarity excites the appearance of linear azimuthal modes but it is not able to make them the most unstable when the wavenumber is small but finite. Only when the wavenumber tends to zero the growth rate of the azimuthal modes is larger than that of the axial mode. It is found that the thickness and thermal conductivity of the wall have an important influence on the stability. Even though the linear axial mode is the most unstable one, azimuthal modes are observed in the experiment. Therefore, it is of interest here to investigate the nonlinear sideband instability of the flow to find out the parameters region where the first azimuthal mode is able to prevail. It was possible to group for the first time the Reynolds, surface tension and Marangoni numbers with wall effect in only one parameter. •Reynolds number promotes the linear axial mode m=0 as the most unstable one.•Thermocapillarity excites linear azimuthal modes m>1 but they are not the most unstable.•Nonlinear sideband results show the parameters region where mode m=0 is unstable against m=1.•Reynolds, surface tension and Marangoni numbers with wall thickness included in only one parameter.