2024/03/21 by Gunnar G. Peng, Peng, Gunnar G., Rodolfo Brandão +5 · 1 citation
Engineering · #Aerosol Filtration and Electrostatic Precipitation #Electrohydrodynamics and Fluid Dynamics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Power Transformer Diagnostics and Insulation
paper · pdf · doi:10.48550/arxiv.2403.14876
openalex publication_date 2024/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We illuminate effects of surface-charge convection intrinsic to leaky-dielectric electrohydrodynamics by analyzing the symmetric steady state of a circular drop in an external field at arbitrary electric Reynolds number ReE. In formulating the problem, we identify an exact factorization that reduces the number of dimensionless parameters from four -- ReE and the conductivity, permittivity and viscosity ratios -- to two: a modified electric Reynolds number \widetildeRe and a charging parameter \varpi. In the case \varpi<0, where charge relaxation in the drop phase is slower than in the suspending phase, and, as a consequence, the interface polarizes antiparallel to the external field, we find that above a critical \widetildeRe value the solution exhibits a blowup singularity such that the surface-charge density diverges antisymmetrically with the -1/3 power of distance from the equator. We use local analysis to uncover the structure of that blowup singularity, wherein surface charges are convected by a locally induced flow towards the equator where they annihilate. To study the blowup regime, we devise a numerical scheme encoding that local structure where the blowup prefactor is determined by a global charging -- annihilation balance. We also employ asymptotic analysis to construct a universal problem governing the blowup solutions in the regime \widetildeRe≫1, far beyond the blowup threshold. In the case \varpi>0, where charge relaxation is faster in the drop phase and the interface polarizes parallel to the external field, we numerically observe and asymptotically characterize the formation at large \widetildeRe of stagnant, perfectly conducting surface-charge caps about the drop poles.