Experimental evidence for a short-wave global mode in film flow along periodic corrugations

Abstract

The primary instability of liquid film flow along periodically corrugated substrates is studied experimentally. Two different wall shapes, of the same wavelength and height, are tested for a wide range of inclinations. It is found that, beyond a specific inclination, a new instability mode occurs before the classical, convective, long-wave one. This is a short, travelling wave, which is highly regular and persistently twodimensional, and appears to be a global mode. The exact shape of the corrugations has a leading-order effect on the inclination at which the new mode appears and on its wavelength at inception. Compared with the behaviour of film flow on a flat substrate, the presently tested periodic walls are found to delay very significantly, but each one to a different extent, the onset of the primary instability. This delay increases with inclination, and presents a distinct discontinuity when transition from the long-to the short-wave mode takes place.

Stability of a film flowing down an inclined corrugated plate: The direct Navier-Stokes computations and Floquet theory

“…27 Trifonov 28 and Luo and Pozrikidis 29 computed film flow down a three-dimensional periodic wall. More complicated doubly periodic wavy regimes of flow down a corrugated surface were studied numerically by Trifonov 30,31 and experimentally by Cao et al 32 and Reck and Aksel. 33 Using both the integral approach and the Navier-Stokes equations, Trifonov 24,34 considered the linear stability of the viscous film falling down a vertical plate with the sinusoidal corrugations.…”

“…D'Alessio et al, 40 using the weighted residual integral equations, studied the effect of surface tension and found that the corrugations may destabilize the flow at some parameters and the primary instability takes place at Re < Re f lat . Cao et al 32 studied experimentally the primary instability for two shapes of corrugations -sinusoidal and orthogonal. They concluded that both the shape of corrugations and the inclination angle are important for the critical Reynolds number of the instability.…”

Does the topography’s specific shape matter in general for the stability of film flows?

“…We speculate that an increase of the tip's width changes the flow's free surface and concomitant the flow's free surface stability. First indications were reported by Cao et al 54 who found that for tips of the width λ b /2, the critical Reynolds number differs from the one of a flow over the corresponding sinusoidal topography.…”

“…Recent studies by Cao et al 54 and Pollak and Aksel 52 compared the linear stability of gravitydriven films flowing over different topography shapes. Cao et al 54 observed that the critical Reynolds number of film flows over a sinusoidal topography differs from the critical Reynolds number for a rectangular topography of the same amplitude and wavelength.…”

“…Cao et al 54 observed that the critical Reynolds number of film flows over a sinusoidal topography differs from the critical Reynolds number for a rectangular topography of the same amplitude and wavelength. Contrary to this, Pollak and Aksel 52 found a similar stability behavior of a film flow for two different topographies.…”