Exact solution for the electric field associated with charge caps on a leaky dielectric droplet at high electric Reynolds number
File(s)
Published version
Author(s)
Crowdy, Darren
Type
Journal Article
Abstract
In a recent paper [Peng et al., Phys. Rev. Fluids 9, 083701 (2024)], the phenomenon of electric charge cap formation on the surface of a leaky dielectric droplet in an electric
field was identified. The surface charge caps, which form at the droplet poles when charge relaxation is faster inside the droplet phase than in the ambient, are stagnant and perfectly conducting. Using asymptotic methods, a nonstandard, inhomogeneous, mixed boundary value problem satisfied by the droplet field potential in this high electric Reynolds number limit was derived by Peng et al. and then solved numerically. The present article gives
an exact solution to that mixed boundary value problem. This solution resolves fully the square-root singularities in the potential at the edges of the electric caps that can cause convergence difficulties in numerical schemes. Knowledge of the solution in analytical form is valuable because it feeds into a nonlinear problem for the coupled hydrodynamics. Moreover, the theoretical approach here is potentially extendible to finding the fields associated with electric charge cap formation in other settings
field was identified. The surface charge caps, which form at the droplet poles when charge relaxation is faster inside the droplet phase than in the ambient, are stagnant and perfectly conducting. Using asymptotic methods, a nonstandard, inhomogeneous, mixed boundary value problem satisfied by the droplet field potential in this high electric Reynolds number limit was derived by Peng et al. and then solved numerically. The present article gives
an exact solution to that mixed boundary value problem. This solution resolves fully the square-root singularities in the potential at the edges of the electric caps that can cause convergence difficulties in numerical schemes. Knowledge of the solution in analytical form is valuable because it feeds into a nonlinear problem for the coupled hydrodynamics. Moreover, the theoretical approach here is potentially extendible to finding the fields associated with electric charge cap formation in other settings
Date Issued
2026-03-01
Date Acceptance
2026-01-14
Citation
Physical Review Fluids, 2026, 11 (3)
ISSN
2469-990X
Publisher
American Physical Society
Journal / Book Title
Physical Review Fluids
Volume
11
Issue
3
Copyright Statement
© Open Access. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
License URL
Identifier
10.1103/4zsn-fd3r
Publication Status
Published
Article Number
034902
Date Publish Online
2026-03-09