Stability of traveling waves of a thermoviscous liquid film down the outer surface of a cylinder

The stability of a traveling wave on the outside of a heated solid vertical cylinder is considered. The axisymmetric traveling wave becomes unstable and leads to the formation of asymmetric droplets over the cylinder. Eigenvalue analysis indicates that at smaller wavenumbers, the gravity mode exists, and a thermocapillary mode also exists but at larger wavenumbers. Patterns generated using nonlinear analysis show that the selected mode is governed by the geometric confinement in the azimuthal direction. Interesting nonlinear patterns are obtained due to an interesting interplay between the gravity mode and thermocapillary mode.