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Experimental and Modeling Studies on Solitary Wave Dynamics on Vertical and Inclined Film Flows

Cesar E. Meza Jr.1, Ramesh Raju Mudunuri, and Vemuri Balakotaiah2. (1) Chemical Engineering, University of Houston, 4800 Calhoun Rd., Houston, TX 77204, (2) Department of Chemical Engineering, University of Houston, 4800 Calhoun Ave., Houston, TX 77204-4004

We present modeling and experimental study of thin films falling down an inclined plane, along with new insights to wave behavior. Starting with the 2D Navier-Stokes equations, we derive a partial differential equation model involving the film thickness and flow rate, using the integral method. Besides the inclination angle, the system is governed by two other dimensionless parameters, the Reynolds number, Re and the Weber number, We. In order to study the nonlinear dynamics of thin film flows, we simulated pulsing experiments where the inlet flow rate was periodically excited with two or more frequencies. We compare the model simulations with experiments of Liu & Gollub (1994). For commensurate frequencies, the model captures the nonlinear generation of solitary waves though the interaction of periodic, non-solitary waves. For incommensurate frequencies, the model predictions are quantitatively consistent with experiments where the spacing between the weakly interacting solitary waves is found to be irregular. Experiments show that the speed and peak height of solitary waves, correlate linearly. We analyze the model in a steady traveling coordinate system and present a new class of solitary wave solutions that exist in the low-frequency limit. For these waves, the model predicts a slope of for the linear relation between peak height and celerity. The experimental slopes and those calculated using time simulations are between 1.7 and 2. Our measurements of naturally excited waves on a vertical 1.5 I.D acrylic tube, at distances of about 5.2m and 6.9m from the inlet, show that the dimensionless maximum wave amplitude and the R.M.S. deviation of the film thickness correlate inversely with the Weber number. The experiments consisted of using glycerin/water solutions varying from pure water to about 92 (% vol) glycerin yielding a viscosity range from 1cP to 250cP. The Kapitza number being inversely proportional to the fluid viscosity can be categorized into two groups which show different wave behaviors. Solutions with low Ka values (2 to about 200) exhibit behavior much different from the larger Ka (200 to 3700) fluids and seem to have smaller normalized asymptotic average maximum amplitude and R.M.S deviations values than the latter.