J. Fluid Mech. (2013), vol. 718, pp. 304–320. c  Cambridge University Press 2013 304 doi:10.1017/jfm.2012.612 Experimental evidence for a short-wave global mode in film flow along periodic corrugations Z. Cao 1 , M. Vlachogiannis 1,2 and V. Bontozoglou 1, † 1 Department of Mechanical Engineering, University of Thessaly, GR-38334 Volos, Greece 2 Technological Educational Institute of Larissa, GR-41110 Larissa, Greece (Received 28 March 2012; revised 19 October 2012; accepted 6 December 2012) 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 two- dimensional, 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. Key words: thin films, waves/free-surface flows 1. Introduction The flow of thin liquid films is important in a variety of applications, in particular coating processes (Qu´ er´ e 1999; Weinstein & Ruschak 2004), heat and mass transfer equipment (de Santos, Melli & Scriven 1991; Valluri et al. 2005; Helbig et al. 2009), environmental flows (Balmforth & Liu 2004) and biomedical flows (Bull & Grotberg 2003). Various aspects of film flow have been reviewed extensively (Oron, Davis & Bankoff 1997; Chang & Demekhin 2002; Craster & Matar 2009). The modifications imposed on the flow by walls that are not flat has recently attracted the attention of many researchers. The available literature may be schematically categorized around two complementary cases: (i) the reaction of film flow to an isolated topographical feature, such as a step, a protrusion or an intrusion (Kalliadasis & Homsy 2001; Gaskell et al. 2004; Bontozoglou & Serifi 2008); and (ii) the reaction to a wall consisting of periodic corrugations. The present contribution deals with the latter case from the experimental point of view. Gravity-driven films along a periodic wall were initially studied in the special case of creeping flow (Wang 1981; Pozrikidis 1988; Shetty & Cerro 1993). The effect † Email address for correspondence: bont@mie.uth.gr