2005/12/20 by S. I. Betelu, S. Betelú, Marco A. Fontelos +5 · 52 citations
Chemistry · Engineering · Mathematics · Physics and Astronomy · #Boundary value problem #Characterization and Applications of Magnetic Nanoparticles #Charge (physics) #Classical mechanics #Conical surface #Electric charge #Electrohydrodynamics and Fluid Dynamics #Flow (mathematics) #Geometry #Gravitational singularity #Instability #Mass Spectrometry Techniques and Applications #Mechanics #Nonlinear system #Physics #Quantum mechanics #Rayleigh–Taylor instability #Singularity #Stokes flow #Viscous liquid #math-ph #math.MP #msc:76d27 #msc:76d45
paper · pdf · doi:10.1063/1.2204044
published in Physics of Fluids 18(5) (American Institute of Physics) · 9 pages, 6 figures
arxiv created 2005/12/20 · openalex publication_date 2006/05/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the evolution of charged droplets of a conducting viscous liquid. The flow is driven by electrostatic repulsion and capillarity. These droplets are known to be linearly unstable when the electric charge is above the Rayleigh critical value. Here, we investigate the nonlinear evolution that develops after the linear regime. Using a boundary element method, we find that a perturbed sphere with critical charge evolves into a fusiform shape with conical tips at time t0, and that the velocity at the tips blows up as (t0−t)α, with α close to −1∕2. In the neighborhood of the singularity, the shape of the surface is self-similar, and the asymptotic angle of the tips is smaller than the opening angle in Taylor cones.