Nonlinear Sideband Thermocapillary Instability of a Thin Film Coating the Inside of a Thick Walled Cylinder with Finite Thermal Conductivity in the Absence of Gravity

The nonlinear sideband thermocapillary instability of a thin liquid film coating the inside of a heated cylinder in the absence of gravity is investigated. It is shown that for a newtonian fluid and under the approximation of small wavenumber and large radius of the cylinder, the axial and all azimuthal modes with wavenumber k(max) > 0 have the same linear maximum growth rate, in the same way as in a previous papers for flow outside the cylinder. Here, this indeterminacy of the linear problem is resolved nonlinearly looking for the parameters' range where the axial mode prevails and where it is unstable against the first azimuthal mode of thermocapillary instability.