Singularities on charged viscous droplets

摘要: We study the evolution of charged droplets a conducting viscous liquid. The flow is driven by electrostatic repulsion and capillarity. These are known to be linearly unstable when electric charge above Rayleigh critical value. Here, we investigate nonlinear that develops after linear regime. Using boundary element method, find perturbed sphere with evolves into fusiform shape conical tips at time t0, velocity blows up as (t0−t)α, α close −1∕2. In neighborhood singularity, surface self-similar, asymptotic angle smaller than opening in Taylor cones.