Stability and dynamics of thin film flow on a rotating cylinder

The study of thin liquid films flowing along vertical cylinders has gained significant attention due to their rich dynamics and various industrial applications. In this work, we investigate the influence of rotation on the dynamics of a falling liquid film along the outside or inside of a rotating vertical cylinder. We explore various setups, including slippery cylinder surfaces and thermal effects. The interplay between gravity-driven film flow and cylinder rotation, in the presence of wall slippage or thermal effects, introduces complex fluid dynamics. We perform linear stability analysis and extend it beyond the linear regime. Additionally, we propose a combination of these physical effects to explain the traveling wave solution and further investigate the stability of this solution. Numerical simulations and theoretical analysis are employed to understand the intricate dynamics and heat transfer characteristics of this system. The findings offer insights into optimizing industrial applications involving heat and mass transfer or slippery cylinder surfaces. Stability analysis and numerical simulations agree well with theoretical observations.