Journal of Fluid Mechanics

Measurements of the primary instabilities of film flows

Jun  Liu a1, Jonathan D.  Paul a1 and J. P.  Gollub a1
a1 Department of Physics, Haverford College, Haverford, PA 19041, USA and Department of Physics, University of Pennsylvania, Philadelphia, PA 19104, USA

Article author query
liu j   [Google Scholar] 
paul jd   [Google Scholar] 
gollub jp   [Google Scholar] 


We present novel measurements of the primary instabilities of thin liquid films flowing down an incline. A fluorescence imaging method allows accurate measurements of film thickness h(x, y, t) in real time with a sensitivity of several microns, and laser beam deflection yields local measurements with a sensitivity of less than one micron. We locate the instability with good accuracy despite the fact that it occurs (asymptotically) at zero wavenumber, and determine the critical Reynolds number Rc for the onset of waves as a function of angle β. The measurements of Rc(β) are found to be in good agreement with calculations, as are the growth rates and wave velocities. We show experimentally that the initial instability is convective and that the waves are noisesustained. 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 wavenumber (or the frequency f). A new phase boundary f*s(R) is measured, which separates the regimes of saturated finite amplitude waves (at high f) from multipeaked solitary waves (at low f). This boundary probably corresponds approximately to the sign reversal of the third Landau coefficient in weakly nonlinear theory. Finally, we show that periodic waves are unstable over a wide frequency band with respect to a convective subharmonic instability. This instability leads to disordered two-dimensional waves.

(Published Online April 26 2006)
(Received July 17 1992)
(Revised November 3 1992)