Anderson, D. M., McFadden, G. B. & Wheeler, A. A. 1998 Diffuse-interface methods in fluid mechanics. Annu. Rev. Fluid Mech. 30, 139–165.
Baygents, J. C. & Baldessari, F. 1998 Electrohydrodynamic instability in a thin fluid layer with an electrical conductivity gradient. Phys. Fluids 10, 301–311.
Canuto, C., Hussaini, M. Y., Quarteroni, A. & Zang, T. 1988 Spectral Methods in Fluid Dynamics. Springer.
Charles, M. E., Govier, G. W. & Hodgson, G. W. 1961 The horizontal pipeline flow of equal density oil-water mixtures. Can. J. Chem. Engng 39, 27–36.
Chen, C. H., Lin, H., Lele, S. K. & Santiago, J. G. 2005 Convective and absolute electrokinetic instability with conductivity gradients. J. Fluid Mech. 524, 263–303.
Craster, R. V. & Matar, O. K. 2005 Electrically induced pattern formation in thin leaky dielectric films. Phys. Fluids 17, 321041.
Dongarra, J. J., Straughan, B. & Walker, D. W. 1996 Chebyshev tau-QZ algorithm methods for calculating spectra of hydrodynamics stability problems. Appl. Num. Math. 22, 399–434.
Du, J., Fix, B., Glimm, J., Jia, X., Li, X., Li, Y. & Wu, L. 2005 A simple package for front tracking. J. Comput. Phys. 213 (2), 613–628.
El Moctar, A. O., Aubry, N. & Batton, J. 2003 Electro-hydrodynamic microfluidic mixer. Lab on a Chip 3, 273–280.
Glimm, J., Grove, J. W., Li, X. L., Shyue, K.-M., Zeng, Y. & Zhang, Q. 1995 Three dimensional front tracking. SIAM J. Sci. Comp. 19, 703–727.
Hagerdon, J. G., Martyn, N. S. & Douglas, J. F. 2004 Breakup of a fluid thread in a conned geometry: droplet-plug transition, perturbation sensitivity, and kinetic stabilization with connement. Phys. Rev. E 69, 056312.
Hirt, C. W. & Nichols, B. D. 1981 Volume of fluid (vof) method for the dynamics of free boundaries. J. Comput. Phys. 39, 201–225.
Hooper, A. P. 1989 The stability of two superposed viscous fluids in a channel. Phys. Fluids A 1 (7), 1133–1142.
Hooper, A. P. & Boyd, W. G. C. 1983 Shear-flow instability at the interface between two viscous fluids. J. Fluid Mech. 128, 507–528.
Jackson, J. D. 1962 Classical Electrodynamics. Wiley.
Landau, L. D. & Lifshitz, E. M. 1960 Electrodynamics of Continuous Media. Pergamon.
Lee, L. & LeVeque, R. J. 2003 An immersed interface method for incompressible Navier–Stokes equations. SIAM J. Numer. Anal. 25, 832–856.
LeVeque, R. J. & Li, Z. 1994 The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J. Numer. Anal. 13, 1019–1044.
Li, F., Ozen, O., Aubry, N., Papageorgiou, D. T. & Petropoulos, P. G. 2007 Linear stability of a two-fluid interface for electrohydrodynamic mixing. J. Fluid Mech. 583, 347–377.
Lin, H., Storey, B. D., Oddy, M. H., Chen, C. H. & Santiago, J. G. 2004 Instability of electrokinetic microchannel flows with conductivity gradients. Phys. Fluids 16, 1922–1935.
Lin, H. 2009 Electrokinetic instability in microchannel flows: a review. Mech. Res. Commun. 16, 1922–1935.
Mählmann, S. & Papageorgiou, D. T. 2009 Numerical study of electric field effects on the deformation of two-dimensional liquid drops in simple shear flow at arbitrary Reynolds number. J. Fluid Mech. 626, 367–393.
Melcher, J. R. & Schwarz, W. J. Jr. 1968 Interfacial relaxation overinstability in a tangential electric field. Phys. Fluids 11 (12), 2604–2616.
Melcher, J. R. & Smith, C. V. Jr. 1969 Electrohydrodynamic charge relaxation and interfacial perpendicular-field instability. Phys. Fluids 12 (4), 778–790.
Melcher, J. R. & Taylor, G. I. 1969 Electrohydrodynamics: A Review of the Role of Interfacial Shear Stresses. Annual Review of Fluid Mechanics 1, 111–146.
Navaneetham, G. & Posner, J. D. 2009 Electrokinetic instabilities of non-dilute colloidal suspensions. J. Fluid Mech. 619, 331–365.
Osher, S. & Sethian, J. 1988 Front propagating with curvature dependent speed: algorithms based on Hamilton–Jacobi formulations. J. Comput. Phys. 79, 12–49.
Ozen, O., Aubry, N., Papageorgiou, D. T. & Petropoulos, P. G. 2006 a Monodisperse drop formation in square microchannels. Phys. Rev. Letters 96 (14), 144501.
Ozen, O., Papageorgiou, D. T. & Petropoulos, P. G. 2006 b Nonlinear stability of a charged electrified viscous liquid film under the action of a horizontal electric field. Phys. Fluids 18 (4), 042102.
Papageorgiou, D. T. & Vanden-Broeck, J.-M. 2004 a Antisymmetric capillary waves in electrified fluid sheets. Eur. J. Appl. Maths 15 (6), 609–623.
Papageorgiou, D. T. & Vanden-Broeck, J.-M. 2004 b Large amplitude capillary waves in electrified fluid sheets. J. Fluid Mech. 508, 71–88.
Peskin, C. S. 1977 Numerical analysis of blood flow in the heart. J. Comput. Phys. 25, 220–252.
Peskin, C. S. 2002 The immersed boundary method. Acta Numerica 11, 1–39.
Posner, J. D. & Santiago, J. G. 2006 Convective instability of electrokinetic flows in a cross-shaped microchannel. J. Fluid Mech. 555, 1–42.
Pozrikidis, C. S. 2001 Interfacial dynamics for Stokes flow. J. Comput. Phys. 169, 250–301.
Renardy, Y. 1985 Couette flow of two fluids between concentric cylinders. J. Fluid Mech. 150, 381–394.
Renardy, Y. 1987 The thin layer effect and interfacial stability in a two-layer Couette flow with similar liquids. Phys. Fluids 30 (6), 1627–1637.
Saville, D. A. 1997 Electrohydrodyamics: the Taylor–Melcher dielectric model. Annu. Rev. Fluid Mech. 29, 27–64.
Shin, S. & Juric, D. 2002 Modeling three-dimensional multiphase flow using a level contour reconstruction method for front tracking without connectivity. J. Comput. Phys. 180, 427–470.
Song, H., Chen, D. L. & Ismagilov, R. F. 2006 Reactions in droplets in microfluidic channels. Angew. Chem. 45, 7336–7356.
Thaokar, R. M. & Kumaran, V. 2005 Electrohydrodynamic instability of the interface between two fluids confined in a channel. Phys. Fluids 17 (8), 84104–1.
Tomar, G., Gerlach, D., Biswas, G., Alleborn, N., Sharma, A., Durst, F., Welch, S. W. J. & Delgado, A. 2007 Two-phase electrohydrodynamic simulations using a volume-of-fluid approach. J. Comput. Phys. 227, 1267–1285.
Trefethen, L. N. 2000 Spectral Methods in MATLAB. SIAM.
Tseluiko, D., Blyth, M. G., Papageorgiou, D. T. & Vanden-Broeck, J. M. 2008 Effect of an electric field on film flow down a corrugated wall at zero Reynolds number. Phys. Fluids 20, 042103.
Uguz, A. K. & Aubry, N. 2008 Quantifying the linear stability of a flowing electrified two-fluid layer in a channel for fast electric times for normal and parallel electric fields. Phys. Fluids 20, 092103.
Uguz, A. K., Ozen, O. & Aubry, N. 2008 Electric field effect on a two-fluid interface instability in channel flow for fast electric times. Phys. Fluids 20, 031702.
Unverdi, O. & Tryggvason, G. 1992 A front-tracking method for viscous incompressible, multi-fluid flows. J. Comput. Phys. 100, 25–37.
Yiantsios, S. G., Brian, G. & Higgins, G. 1988 Linear stability of plane Poiseuille flow of two superposed fluids. Phys. Fluids 31 (11), 3225–3238.
Yih, C. S. 1967 Instability due to viscosity stratification. J. Fluid Mech. 27, 337–352.