(108f) Flow Reversal And Cellular Patterns In Vertically Falling Liquid Films

Numerical solutions of the two-dimensional Navier-Stokes equations are presented for vertically falling films with special attention to the region in front of large waves. Examination of the flow field underneath the waves show that, cells are formed near the peak of the waves and the flow field near the surface becomes disconnected to that near the wall. When a critical value of the wave amplitude is exceeded, wall eddy formation with flow reversal occurs near the minimum of large waves. Upon further increase of the wave amplitude, the wall eddy expands all the way to the free surface and the entire film is divided into cells with alternate down and up flows. For fluids with high Kapitza number (such as water) breathinf vortices that expand and shrink with time and oscillatory patterns are observed. Both stationary and oscillatory pattern formation is illustrated using parameter values corresponding to the experiments of Alekseenko et al. (1985) and the classical experiments of Kapitza and Kapitza (1949).