Modeling and experimental studies of wave evolution on free falling viscous films

A new simplified model is developed for describing the characteristics of f ree falling wavy liquid films. The model consists of a set of three partial differential equations (in x and t) for the local film thickness, volumetr ic flow rate, and wall shear stress. It is shown that the new model is a su bstantial improvement over all existing simplified models of wavy films suc h as the long wave equation, the Nakaya model (extended third-order long wa ve equation), the Shkadov model, and the Kapitza boundary layer model. Thes e prior models predict nonphysical negative wall shear stress when the wave amplitude is large and cannot explain the experimentally observed relation ship between the maximum wave amplitude and the Reynolds (Re) and Kapitza ( Ka) or Weber (We) numbers. In contrast, the present model yields physically meaningful results and quantitative predictions of large amplitude waves. Local bifurcation analysis of the model for small Re gives the following an alytical relations for the velocity (Ce) and maximum amplitude of the solit ary waves: h(max)-1=0.132 Re-5/3 Ka(-1)=1/6(3-Ce)=1.925 We(-1). Experimenta l studies of free falling viscous films were conducted using water-glycerin solutions for Reynolds numbers in the range of 2-20 and Kapitza numbers in the range of 6-22. Comparison of the experimental data on wave amplitudes with analytical correlations shows excellent agreement. Numerical simulatio ns of the wave profiles generated from the simplified model also match clos ely with the experimentally observed wave profiles. (C) 2000 American Insti tute of Physics. [S1070-6631(00)00609-7].