Electrohydrodynamic effects in the leveling of coatings Aruna Ramkrishnan, Satish Kumar n Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, USA HIGHLIGHTS  Effect of electric charge on leveling of thin-film coatings is modeled.  Both homogeneous and heterogeneous charge distributions are considered.  Simple heuristics are proposed for determining when leveling occurs. article info Article history: Received 19 April 2013 Received in revised form 7 June 2013 Accepted 10 June 2013 Available online 26 June 2013 Keywords: Electrohydrodynamics Fluid mechanics Interfacial tension Leveling Mathematical modeling Transport processes abstract Electrostatic charges that accumulate on substrates and at liquid–air interfaces in various coating processes can drive liquid flows that lead to defects. To better understand this phenomenon, we model the leveling of thin liquid films subject to electrohydrodynamic forces. We consider cases of homo- geneous and heterogeneous substrate charge distributions and contamination of the film surface by free charge. The liquid is assumed to be Newtonian, both perfect dielectric and leaky dielectric materials are considered, and lubrication theory is employed. Linear stability analysis and nonlinear simulations reveal different leveling criteria for small- and large-amplitude perturbations to the film surface. Heterogeneous charge distributions on the substrate are found to lead to steady curved interface shapes. Using asymptotic methods, we develop analytical expressions to predict these shapes, and consequently, the magnitude of coating defects. We also employ transient nonlinear simulations track the leveling of disturbances created by contamination of the film surface by free charge. The results of our study enable us to propose simple heuristics for determining the conditions under which coatings subject to electrohydrodynamic forces will level. & 2013 Elsevier Ltd. All rights reserved. 1. Introduction Coating is the process of laying out a uniform thin liquid film onto a substrate. In many coating applications, generating a smooth defect-free surface is crucial for improved product perfor- mance. Properties like high gloss, mechanical stability, and elec- trochemical performance are dependent on coating uniformity (Desjumaux et al., 1998; Glatter and Bousfield, 1997; Orchard, 1963; Phair et al., 2009; Schwartz et al., 1996; Xiang and Bousfield, 2000). To get a smooth coating, interfacial defects should level before the liquid coating dries (Iyer and Bousfield, 1996; Tsai et al., 2010). Detailed studies of leveling of disturbances in coatings have been carried out and these take into account the effects of surface tension, gravity, viscosity, elasticity, drying, non-Newtonian rheol- ogy, Marangoni flows, and other phenomena (Bousfield, 1991; Iyer and Bousfield, 1996; Keunings and Bousfield, 1987; Kheshgi and Scriven, 1988; Orchard, 1963; Tsai et al., 2010; Wulf et al., 2000). A significant source of defects in liquid coatings is electrostatic charge, which can build up on dielectric webs during web handling processes involving friction between the web and rollers, separation of surfaces, stretching of webs, and modification of surface properties by exposure to ionized gas. Electrostatic poten- tial differences on the order of tens to hundreds of volts can be created by static charge on non-conductive webs which may take days or weeks to dissipate (Gutoff and Cohen, 1995). Static charges can be damaging to liquid coatings because they pose a spark ignition hazard, attract dust particles, and create defects or rupture coatings through electrohydrodynamic interaction with the liquid (Jendrejack et al., 2010, 2011a,b). A second source of defects is sparking in coating processes, which may cause free charges to jump onto the liquid surface and travel in the coating, creating localized disturbances which may or may not level. It would be valuable to have models that predict the leveling behavior of liquid coatings in the presence of electrostatic charges in order to provide guidelines to design robust coatings. However, to the best of our knowledge, such models have not been developed. Most related studies focus on how electric fields can be used to create surface patterns in thin liquid films. Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ces Chemical Engineering Science 0009-2509/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ces.2013.06.024 n Corresponding author. Tel.: +1 612 625 2558; fax: +1 612 626 7246. E-mail address: kumar030@umn.edu (S. Kumar). Chemical Engineering Science 101 (2013) 785–799