Thermal Marangoni instability of a thin film flowing down a thick wall deformed in the backside

The nonlinear instability of a thin liquid film flowing down a heated thick wall with deformations in the backside is investigated. Here it is assumed that the wall deformations are sinusoidal in space. Time dependent perturbations are imposed at the origin of the free surface of the film. It is found that the wall deformations have an important influence on the flow instability. Moreover, it is shown that the free surface has a large amplitude spatial response to the backside deformations of the wall. This response increases its amplitude considerably when decreasing the wall spatial wavelength down to the wavelength of the time dependent perturbations. At that point, numerical analysis reveals that the time dependent perturbations in some cases are almost impossible to observe on the free surface response. However, in other cases, their interaction produces large amplitude nonlinear wave modulations. Published by AIP Publishing.