Modeling and experimental studies of large amplitude waves on vertically falling films

Abstract

Experimental data on the amplitude of large waves on vertically falling films are presented over a wide range of fluid properties and flow rates. Attempts are made to correlate the amplitude of these naturally excited and saturated waves to the Weber ( We) and Kapitza numbers ( Ka), the two dimensionless groups characterizing the film. For viscous fluids (with 2 < Ka < 200 ), the wave amplitude increases with the reciprocal of the Weber number and saturates at values around 3 ( h max / h N ∼ 3 ) while the dependence on Ka is found to be weak. For less viscous fluids ( 200 < Ka < 3890 ), the waves are found to be much more dynamic with amplitudes saturating at much higher values of around 10. The film roughness, or more precisely, the standard deviation (r.m.s) of the film thickness is also found to be correlated with the reciprocal of the Weber number. Scaling arguments are used to explain the initial increase in wave amplitudes. A two-equation h– q model is used to study the spatio-temporal dynamics of waves on long domains with periodic inlet forcing. The model is used to examine the amplitude–celerity relation for three families of solitary waves: the slow moving γ 1 family, the fast moving γ 2 family and the very fast moving ‘tsunami ( Γ 2 ) family’ having Nusselt film as the substrate. It is found that the film profile at short distances depends on the forcing amplitude and frequency but once the wave amplitude exceeds a critical value, the amplitude–celerity relationship is linear for all solitary waves that exist on the film and is independent of the forcing frequency or amplitude. It is also found that for a fixed set of fluid properties and flow rate ( We and Ka), the Γ 2 wave has the largest amplitude and wavelength. Local bifurcation and computational results are used to explain the experimentally observed wave amplitudes on naturally excited films.