Measurements of the primary instabilities of film flows

Abstract

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.

Nonlinear evolution of nonuniformly heated falling liquid films

“…In the limiting case of a vertical plate (␤ϭ /2) the stabilizing hydrostatic pressure vanishes and the interface is always unstable, i.e., for all film thicknesses. Experiments performed by Liu et al 8,9 for this situation are in good agreement with the critical Reynolds number, growth rates and wave velocities resulting from linear stability analysis.…”

Critical inclination for absolute/convective instability transition in inverted falling films

“…Owing to an inherent unstable flow above a critical inclination angle, falling films are characterized by a wavy and distorted topology exhibiting different types of vortices in the trough 4 and the crest 5 of the wave. These instabilities are always of convective type 3 , such that surface perturbations grow in space (in flow direction) and not locally in time, which is confirmed by experiments 6 . For the inverse case of a film flowing down the bottom side of an inclined plate, the flow should also be of convective type if the inclination angle is close to the vertical.…”

Validity domain of the Benney equation including the Marangoni effect for closed and open flows

“…This is due to the fact that in time-dependent simulations, using periodic boundary conditions, the amount of liquid leaving the domain downstream is reinjected upstream. However, the open flow condition is more appropriate to the experimental situation of a flow on an inclined plate when a periodic forcing is imposed at the inlet (Kapitza & Kapitza 1949;Liu et al 1993;Liu & Gollub 1994). Indeed, Ruyer-Quil & Manneville (2000) found satisfactory agreement with the phase speeds of two-dimensional travelling-wave solutions from Kapitza's experiments using the open flow condition, whereas the closed flow condition resulted in deviations of up to 15%.…”

“…In experiments, the control parameter that determines the Nusselt film thicknessh N is the specific volumetric flow rateq N (Kapitza & Kapitza 1949;Liu et al 1993;Kabov et al 2002). We denote its dimensionless form by q N =q N /ν.…”