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.

中文翻译：

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重力作用下覆盖有限厚导热壁厚壁圆筒内部的薄膜的非线性边带热毛细管不稳定性

研究了在没有重力的情况下覆盖加热缸内部的液体薄膜的非线性边带热毛细管不稳定性。结果表明，对于牛顿流体，在小波数和大圆柱半径的近似情况下，波数为k _{m a x} > 0的轴向和所有方位模态具有相同的线性最大增长率，与先前的论文是关于圆柱体外流的。在这里，线性问题的不确定性可以通过非线性方式寻找参数范围，其中轴向模式占优势，并且相对于热毛细管不稳定性的第一方位角模式不稳定。