Primary instability and subsequent dynamics of liquid film flow along periodic corrugations

Abstract

This work is an experimental study of gravity-driven liquid film flowalong corrugated substrates. Thin liquid films appear in importantindustrial, environmental and biomedical flows. The modifications,resulting from the substitution of the flat substrate on which the filmflows by one with topography, are presently not well understood. Inparticular, there is little experimental evidence about the effect ofperiodic corrugations on the primary instability of the flow, and therelevant theoretical predictions appears contradictory. This problemis of significant interest, because of the potential for instability controlin such flows through the development of appropriately tailoredsubstrates.Systematic experiments were performed with water-glycerol solutions,in two flow facilities spanning a wide range of inclination angles. Substrateswith different shapes (sinusoidal and rectangular) and variouswavelengths and amplitudes were examined. The temporal variationof liquid film thickness was measured by conductance probes at multiplelocations along the flow. A photographic technique was developedto record the spatial variation of the free surface in the streamwisedirection. Using these techniques, the primary instability thresholdwas reliably determined, and the characteristics of traveling waves inthe unstable regime were recorded.A major finding of the thesis is that, for intermediate and high inclinations,steep enough corrugations trigger a new instability modeof finite wavelength, while they delay significantly the occurrence ofthe classical, convective, long-wave instability. The new mode is ashort, traveling wave, which is highly regular and persistently twodimensional,and appears to be a global mode. Transition from longtoshort-wave instability is observed to occur with increasing inclinationangle, and the exact location of the transition varies with thecorrugation shape. The parametric effects of liquid viscosity and ofcorrugation wavelength and amplitude are examined, and the importantspecial case of a vertical wall is investigated using a cylindricalflow geometry. Finally, an unexpected oscillatory instability is documented,specific to steep, rectangular substrates, which appears andintensifies when decreasing the liquid flow rate. It is speculated thatthis counter-intuitive behaviour is related to the specific separationcharacteristics of the rectangular substrate, and is triggered when thebackflow velocity exceeds a percentage of the forward stream.