Experimental investigations of liquid falling films flowing under an inclined planar substrate

We report on detailed and systematic experiments of thin liquid films flowing as a result of the action of gravity under an inverted planar substrate. A measurement technique based on planar laser-induced fluorescence (PLIF) was developed and applied to a range of such flows in order to provide detailed space- and time-resolved film-height information. Specifically, the experimental campaign spanned three inclination angles (β=−15∘, −30∘, and −45∘, in all cases negative with respect to the vertical), two water-glycerol solutions (with Kapitza numbers of Ka=13.1 and 330), and flow Reynolds numbers covering the range Re=0.6–193. The collection optics were arranged so as to interrogate a spanwise section of the flow extending about 40mm symmetrically on either side the centerline of the film span (80mm in total), at a distance 330 mm downstream of the flow inlet. A range of flow regimes, typically characterized by strong three dimensionality and pronounced rivulet formation, were observed depending on the imposed inlet flow conditions. In the lower liquid Kapitza number Ka(=13.1) flows and depending on the flow Re, the free surface of the film was populated by smooth rivulets or regular sequences of solitary pulses that traveled over the rivulets. In the higher liquid Ka(=330) flows, rivulets were observed typically above Re≈30, depending also on the inclination angle, and grew in amplitude until quasi-two-dimensional fronts developed intermittently that were associated with distinct thin-film regions of varying length and frequency. These regions are of particular interest as they are expected to affect strongly the heat and mass transfer capabilities of these flows. The occurrence of the fronts was more pronounced, with higher wave frequencies, in film flows at smaller negative inclinations for the same flow Re. The rivulet amplitude was found to increase at larger inclinations for the same Re and showed a nonmonotonic trend with increasing Re, reaching a maximum that shifted to higher Re at larger inclinations. Furthermore, in flows that displayed pronounced rivulet formation [i.e., large (negative) β and higher Re], the local film-height standard deviation in regions corresponding to the rivulet crests and troughs was reduced compared to the film-height standard deviation calculated over the entire examined film region. The mean rivulet wavelength also increased at larger inclinations, peaking at 26 mm when Ka=330. Based on our experimental results and theoretical arguments, we hypothesize that the formation of rivulets can be attributed, at small β, to a secondary Rayleigh-Taylor instability mechanism that destabilizes the suspended two-dimensional wavefronts, and at larger β, to the primary Rayleigh-Taylor instability mechanism of a flat film coating the underside of the inclined plate