STABILITY OF THIN LIQUID FILMS FALLING DOWN ISOTHERMAL AND NONISOTHERMAL WALLS

Luis Antonio Davalos-Orozco
2013 Interfacial Phenomena and Heat Transfer  
This paper reviews important results found in the past years on thin films falling down isothermal and nonisothermal walls. The discussion on isothermal flows is presented as the basis and background for the study of nonisothermal flows. Different model equations are presented and their approximations are discussed. Both linear and nonlinear results are surveyed on uniform and nonuniform heating of the wall. Also a review is given of the effect the curvature of the wall has on flows down
more » ... n flows down vertical cylinders. KEY WORDS: thin films down walls, thermocapillarity, thermal Marangoni, model equations, nonuniform heating, flows down cylinders Davis (1987) reviews results of thermocapillary problems with temperature gradient perpendicular to the liquid layer and for horizontal temperature gradient. An extensive survey has also been done by Zeytounian (1998) , who includes very thin layers which are only susceptible to Marangoni convection and not very thin layers that are sensitive to both buoyancy and Marangoni convection. He also presents results of layers flowing down walls. Velarde et al. (2001) and Velarde and Vignes-Adler (2002) give a discussion on the effect of surface deformation and natural convection on thermocapillary nonlinear surface waves. Kalliadasis (2007) analyzes the problem of heated thin films, comparing all the models obtained to date in order to improve the approximation and derive equations that agree completely with the linear results of the Orr-Sommerfeld equation. A review of thermocapillary phenomena with important applications in microelectronics is given by Kabov (2010) . This paper presents results of a great number of experiments of films heated locally and driven by surface shear (due to gas flow over the free surface). The problems of wetting and rupture of the film are discussed when the film is subjected to different thermal and surface shear conditions. Wetting is discussed in de Gennes (1985) from a physico-chemical point of view. Davis (2000) gives a review of interface phenomena including thin films. The case of ultrathin films, with the problem of rupture, is included. O'Brien and Schwartz (2002) discuss the basis of the approximations used to describe thin films analytically. Besides, they include a review of wetting and dewetting in very thin films where the disjoining pressure is effective. Thiele (2007) examines critically, from the point of view of structure formation, the problems of dewetting depending on the characteristics of the substrate. He also presents the effects of themocapillarity. Bonn et al. (2009) review the recent results on wetting and spreading of drops, important in the spin-coating process. The issue of micro-and nanofluidics is discussed along with the effects produced by the three-phase contact line. Craster and Matar's (2009) survey includes wetting and dewetting of thin films under the influence of heat and surfactants. The effect of substrate properties, like topography, compliance, and rotation, are also reviewed. A full review on the flow on fibers has been done by Quéré (1999). He describes phenomena when the radius of the cylinder is small and throttling effects are important on the stability. A number of books have been published which describe theoretical and experimental results. Hewitt and Hall-Taylor (1970) discuss theoretical and experimental results of two-phase flows which occur inside tubes. Also, they present phenomena related with core-annular flows where one of the phases may also include another phase. The isothermal flow is reviewed by Alekseenko et al. (1994), who published a monograph on thin films where the integral boundary layer equations are used in the theoretical discussion. The theory is compared with experimental results which are presented throughout the book. Chang and Demekhin (2002) present the linear theory before discussing the nonlinearity of surface phenomena of thin films flowing down walls. The analysis follows with equations which are derived from balance approximations of the linear and nonlinear terms of the Navier-Stokes equations by means of a small parameter. Ajaev (2012) presents a review of models of thin films and problems related with coating flows and films flowing down walls with fingering. He includes the effects of electric forces, surfactants, structured substrates, and phase change. Some books survey thermocapillary flow. The problem of Marangoni convection is extensively discussed in the book by Colinet et al. (2001). They include linear and nonlinear phenomena in one and two layers with surface deformation. Similar problems are reviewed in Nepomnyashchy et al. (2002) but they also include phenomena of drops on heated substrates or subjected to the effects of a surfactant. Birich et al. (2003) survey, among other usual things, the parametric excitation of Marangoni convection, the suppression of Rayleigh-Taylor instability with high frequency oscillations, and multilayer problems. The book by Kalliadasis et al. (2012) analyzes the flow of films falling down walls under isothermal and nonisothermal conditions. Of particular interest are the discussions on the different approximations already done to model thin films, as are the lubrication approximation and the integral boundary layer approximation equations, their success and problems in describing experimental results for different parameter ranges. They compare the model equations with those obtained by the new weighted residual method put forward by Ruyer-Quil, and Manneville and improved by Scheid, Ruyer-Quil and Manneville. Blossey (2012) gives a survey of dewetting, which is very important in coating problems. Relevant applications need the use of non-Newtonian fluids. Therefore, this book is devoted to reviewing the theory and experiments on polymeric flows and in particular viscoelastic flows. This paper is devoted to reviewing the flow of thin films flowing down walls including thermocapillary flows. Here, the literature published in more recent years is surveyed along with important classical literature. The goal is
doi:10.1615/interfacphenomheattransfer.2013006655 fatcat:2xvlmzcifvhh7niw5qsy4qiiie