European Journal of Mechanics B/Fluids 26 (2007) 404–421 Interfacial capillary waves in the presence of electric fields Scott Grandison a , Demetrios T. Papageorgiou b,∗ , Jean-Marc Vanden-Broeck a a School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK b Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, University Heights, Newark, NJ 07102, USA Received 3 April 2006; received in revised form 14 June 2006; accepted 20 June 2006 Available online 8 September 2006 Abstract Large amplitude capillary waves on an inviscid, incompressible fluid layer of density ρ 1 bounded by a second inviscid, incom- pressible fluid of density ρ 2 are computed in the presence of a uniform electric field acting in a direction parallel to the undisturbed configuration. Periodic travelling waves of arbitrary amplitudes and wavelengths are calculated and the effect of the electric field is studied. The solutions extend the results of Papageorgiou and Vanden-Broeck [D.T. Papageorgiou, J.-M. Vanden-Broeck, Large- amplitude capillary waves in electrified fluid sheets, J. Fluid Mech. 508 (2004) 71–88; D.T. Papageorgiou, J.-M. Vanden-Broeck, Antisymmetric capillary waves in electrified fluid sheets, Eur. J. Appl. Math. 16 (2004) 609–623] where the case of ρ 2 = 0 was treated. Fully nonlinear solutions are computed using boundary integral equation methods. It is shown that there are both symmetric and antisymmetric waves and their characteristics are explored and compared. When there is a jump in the undisturbed horizontal velocities, the flow is susceptible to Kelvin–Helmholtz instability. It is shown analytically in the linear regime, that even in the absence of surface tension, the flow is stabilized by sufficiently large electric fields. In such situations two wave speeds are possible for given electric fields and we construct these branches numerically when the amplitudes are not infinitesimal, both in the absence and presence of surface tension.  2006 Elsevier Masson SAS. All rights reserved. Keywords: Electrohydrodynamics; Liquid sheets; Travelling waves; Boundary integral methods 1. Introduction Liquid sheets arise in many diverse physical and technological applications. Some of these include coating and curtain coating processes (as in, for example, photographic or magnetic membrane manufacture), where interfacial instabilities can affect the subsequent coating patterns and hence product quality (see Kistler and Schweizer [1] for a review). Liquid sheets are also used as liquid protector systems in inertial fusion energy reactor cavities—see Durbin et al. [2], [3] and the review by Abdel-Khalik and Yoda [4]. Another application is in float glass processes described by Warner [5,6]. An additional complication in liquid sheet dynamics is the possible rupture and formation of braids and droplets through primary and secondary instabilities. Such phenomena are mathematically challenging and find * Corresponding author. E-mail addresses: s.grandison@uea.ac.uk (S. Grandison), depapa@oak.njit.edu (D.T. Papageorgiou), j.vanden-broeck@uea.ac.uk (J.-M. Vanden-Broeck). 0997-7546/$ – see front matter  2006 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.euromechflu.2006.06.005