Traveling wave solution of a thermoviscous liquid film on a vertical cylinder

A liquid film coating a cylindrical substrate is unstable to interfacial disturbances governed by Rayleigh-Plateau instability. These initial disturbances grow in time and beyond saturation, develop into a train of traveling waves, wherein the droplets of equal amplitude form at periodic intervals moving downstream at the same speed. Our study focuses on these traveling waves formed by a thermoviscous fluid falling on the outside surface of a vertical cylinder. We treat these traveling waves as a steady state film profile in a moving reference frame. The effects of Bond number, Marangoni number, thermoviscosity number and Biot number have been studied on the film profile and traveling wave speed. Smaller values of Bond number result in larger amplitudes and wave speeds. For a finite value of Biot number, an increase in thermoviscosity number is found to decrease the wave speed and increase the wave amplitude. Furthermore, the effect of Biot number is found to be dependent on the thermoviscosity number and can also result in non-monotonic variation in the wave amplitude.