The instability of a two-dimensional moving contact line is studied for a thin liquid film flowing down an inclined plane, leading to the formation of rivulets. A fluorescent imaging method was developed to facilitate accurate measurement of the spacing between rivulets, tip velocity, three-dimensional shape and dynamic contact line. A fluid circulation system produced steady films at constant volumetric flux, in contrast to time-varying films at constant total volume, as in previous measurements. Comparisons are made with the existing data for constant-volume films, and with theoretical predictions for the wavelength of the rivulets formed at constant inlet flow rate. Data were also obtained for rivulet shapes, tip speeds and contact angles as functions of the angle of inclination of the plate and liquid Reynolds number.

Section I describes steps taken to optimize the pulse shape and dynamic range from a 56 AVP photomultiplier. Section II discusses a model for the response of a photomultiplier. The parameters used in this model are obtained from direct measurements on a 56 AVP photomultiplier. Monte Carlo methods, as well as analytic techniques, are used to predict quantities such as distribution of triggering times, pulse shapes, etc. It is found, for example, that in the resolution of small time differences the predictions using the Monte Carlo method and the analytic treatment are in good agreement. The time resolution as predicted by the model is compared to experiment.

Fluorescent dye dissolved in a liquid flow was used to outline liquid-gas free boundaries and, with digital imaging, to observe quantitatively surface wave propagation and pattern formation, as well as contact-line velocity and contact angle in thin film flows on horizontal and inclined substrates. Using the relatively inexpensive system described here, a fluid depth measurement with a precision of ±0.02 mm is obtained routinely in flows of several millimeters depth over an area of approximately one square meter, and essentially unlimited continuous time spans. Dynamic contact angles are measured, for the first time, on liquid fronts with significant three-dimensional curvature such as rivulets draining down an inclined plate at any speed or global location. Procedures to normalize results quantitatively for any nonuniformities of the incident illumination are given. Estimates of the contribution to the experimental error by other effects, such as variations in dye concentration and temperature, and image digital register capacity, are also discussed. Illustrative results for two fluids and several dyes are given. Refinements to decrease the local error further to ±0.005 mm or less are described.

Thin films of oil flowing down a nearly-vertical plate were subjected to a strong normal electrostatic field. Steady-state height profiles were measured by fluorescence imaging. For electrode potentials less than that required to produce an instability, the two-dimensional response of the interface was <1%. Calculations of the fluid height coupled with the electric field solution were identical to uncoupled calculations for electric fields below the stability threshold. Pressure profiles under the film and three-dimensional effects are also discussed.