MEASUREMENTS OF THE PRIMARY INSTABILITIES OF FILM FLOWS

We present novel measurements of the primary instabilities of thin liq uid films flowing down an incline. A fluorescence imaging method allow s accurate measurements of film thickness h(x, y, t) in real time with a sensitivity of several microns, and laser beam deflection yields lo cal measurements with a sensitivity of less than one micron. We locate the instability with good accuracy despite the fact that it occurs (a symptotically) at zero wavenumber, and determine the critical Reynolds number R(c) for the onset of waves as a function of angle beta. The m easurements of R(c)(beta) are found to be in good agreement with calcu lations, as are the growth rates and wave velocities. We show experime ntally that the initial instability is convective and that the waves a re noise-sustained. This means that the waveform and its amplitude are strongly affected by external noise at the source. We investigate the role of noise by varying the level of periodic external forcing. The nonlinear evolution of the waves depends strongly on the initial waven umber (or the frequency f). A new phase boundary f(S)(R) is measured, which separates the regimes of saturated finite amplitude waves (at h igh f) from multipeaked solitary waves (at low f). This boundary proba bly corresponds approximately to the sign reversal of the third Landau coefficient in weakly nonlinear theory. Finally, we show that periodi c waves are unstable over a wide frequency band with respect to a conv ective subharmonic instability. This instability leads to disordered t wo-dimensional waves.