(192f) Experimental and Modeling Studies on Solitary Wave Dynamics on Vertical and Inclined Film Flows

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.