LAUSR

Abstract 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.