Nonlinear instabilities of falling films on a heated vertical plane with gas absorption

The nonlinear instability and dynamics of nonisothermal falling films with simultaneous absorption from a gas phase are studied theoretically. The study is based on a long wave analysis of equations of motion, energy and mass. The resulting long wave evolution equation describing the film thickness is solved by a Fourier collocation technique. The effects and interactions of flows resulting from gravity, surface tension, thermocapillarity and solutal Marangoni effect are elucidated by considering the following cases: (1) isothermal film; (2) nonisothermal film with purely conductive heat transfer, as well as combined conductive and convective heat transfer; and (3) nonisothermal film with solute absorption. Conditions are identified for equilibration of the wave, wave breaking and for the formation of dry spots. Also, phase diagrams representing the stable and unstable regions are presented for the above cases.