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Electric discharges due to the flow of charged organic liquids are a common ignition source for explosions in the chemical and process industry. Prevention of incidents requires knowledge of electric fields above the surface of charged liquids. Quantitative methods often estimate electric fields based on simplifying assumptions like homogeneous volumetric charge distribution and neglect of surface charge. More detailed electrohydrodynamic (EHD) models are only available for laminar flow regimes. This work presents a model for forced turbulent EHD flows of dielectric liquids based on Reynolds-averaged Navier-Stokes equations that predicts the electric field in the gas phase in good agreement with our experiments. We observe diminishing surface charge accumulation at the liquid surface with increasing flow velocities and thereby unify seemingly contradictory previous findings regarding the relevance of surface charge. The model can efficiently be applied to various industrial flow configurations and provide a central tool in preventing electrostatic hazards.

Inducing transport in electrolyte-filled nanopores with dc fields has led to influential applications ranging from nanosensors to DNA sequencing. Here we use the Poisson-Nernst-Planck and Navier-Stokes equations to show that unbiased ac fields can induce comparable directional flows in gated conical nanopores. This flow exclusively occurs at intermediate driving frequencies and hinges on the resonance of two competing timescales, representing space charge development at the ends and in the interior of the pore. We summarize the physics of resonant nanopumping in an analytical model that reproduces the results of numerical simulations. Our findings provide a generic route towards real-time controllable flow patterns, which might find applications in controlling the translocation of particles such as small molecules or nanocolloids.