Amplitudes of three-dimensional waves in a nonisothermal falling liquid film

The amplitudes of three-dimensional (3D) waves in a water film flowing down a vertical plate with a local heater have been measured. Thermocapillary forces that arise on heating lead to the formation of rivulets separated by thin-layer troughs, with 3D waves propagating over the crests of rivulets. The film thickness and 3D wave amplitudes on the heater grow with increasing heat flux density and distance downstream the flow, but the relative wave amplitude remains unchanged. In the heated regions between rivulets, the relative amplitude of waves increases with decreasing average thickness (or local Reynolds number). Analysis of results obtained for large Reynolds numbers showed that the relative amplitudes of waves in the regions between rivulets at high heat flux densities are much greater than those for small Reynolds numbers in isothermal falling films.