@article{GanchenkoMayurDemekhinetal.2015,
  author    = {Georgy S. Ganchenko and Manik Mayur and Evgeny A. Demekhin and Sakir Amiroudine},
  title     = {Electrokinetic instability of liquid micro- and nanofilms with a mobile charge},
  series   = {Physics of Fluids},
  volume    = {27},
  number    = {6},
  organization    = {American Institute of Physics},
  issn      = {0899-8213},
  doi       = {10.1063/1.4921779},
  pages     = {062002},
  year      = {2015},
  abstract  = {The instability of ultra-thin films of an electrolyte bordering a dielectric gas in an external tangential electric field is scrutinized. The solid wall is assumed to be either a conducting or charged dielectric surface. The problem has a steady one-dimensional solution. The theoretical results for a plug-like velocity profile are successfully compared with available experimental data. The linear stability of the steady-state flow is investigated analytically and numerically. Asymptotic long-wave expansion has a triple-zero singularity for a dielectric wall and a quadruple-zero singularity for a conducting wall, and four (for a conducting wall) or three (for a charged dielectric wall) different eigenfunctions. For infinitely small wave numbers, these eigenfunctions have a clear physical meaning: perturbations of the film thickness, of the surface charge, of the bulk conductivity, and of the bulk charge. The numerical analysis provides an important result: the appearance of a strong short-wave instability. At increasing Debye numbers, the short-wave instability region becomes isolated and eventually disappears. For infinitely large Weber numbers, the long-wave instability disappears, while the short-wave instability persists. The linear stability analysis is complemented by a nonlinear direct numerical simulation. The perturbations evolve into coherent structures; for a relatively small external electric field, these are large-amplitude surface solitary pulses, while for a sufficiently strong electric field, these are short-wave inner coherent structures, which do not disturb the surface.},
  language  = {en}
}