Singularities on charged viscous droplets

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...

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Bibliographic Details
Published in:Physics of fluids (1994) 2006-05, Vol.18 (5), p.051706-051706-4
Main Authors: Betelú, S. I., Fontelos, M. A., Kindelán, U., Vantzos, O.
Format: Article
Language:English
Subjects:
Drops and bubbles
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Nonhomogeneous flows
Physics
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Summary: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 t 0 , and that the velocity at the tips blows up as ( t 0 − 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.
ISSN:1070-6631
1089-7666
DOI:10.1063/1.2204044