THE ROLE OF MARANGONI EFFECT ON THE NON-ISOTHERMAL FALLING FLUID FILM INSTABILITY

The Marangoni effect, caused by temperature-induced surface tension variations along an inclined/vertical plane, creates dynamic fluid film flows with roll waves. When an inclined plane is non-isothermally heated from below, gravity and thermocapillarity drive fluid flow, leading to strong nonlinear wave evolution along the film. Forcing at the inlet can amplify thermocapillarity, increasing flow instability and enhancing wave formation.

To analyze the nonlinear evolution of falling film flows, we use the non-isothermal model [Cellier & Ruyer-Quil, Int. J. Heat Mass Transf., 154, 2020]. This model allows adjustments to the Biot number Bi, Peclet number Pe, the plane inclination angle θ, Reynolds number Re, and Weber number We to attain desired values for the simulation.

The evolution of nonlinear waves changes for various Marangoni numbers Ma, comparing the effects of thermocapillarity and viscosity. Comparing the Ma = 0 case with experimental results [Liu & Gollub, Phys. Fluids 6, 1702—1712, 1994] shows good agreement with the base case without thermocapillarity. As Ma increases, fluid film thickness and wave height rise significantly, with a 10% increase at Ma = 10. Enhanced nonlinear wave formation is evident as Ma exceeds 5. The nonlinear evolution of the fluid film for large Peclet numbers is studied.