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Numerical study of Rayleigh fission of a charged viscous liquid drop
Phys. Rev. Fluids 2, 113603 – Published 15 November, 2017
DOI: https://doi.org/10.1103/PhysRevFluids.2.113603
Abstract
It is well known that a spherical drop charged beyond its Rayleigh limit becomes unstable (when subjected to a small shape perturbation) and ejects a significant fraction of the original charge in the form of a jet. To understand the detailed mechanism of this process, we model a charged drop of a perfectly conducting viscous liquid numerically using the boundary-element method. It is found from the simulations that the drop progressively deforms into a conical shape with pointed ends just prior to breakup. For ethylene glycol droplets suspended in air, the drop attains an aspect ratio of 3.86 at its critical shape, close to the observed value of 3.85 in the experimental images available in the literature. As the numerical approach fails to predict charge ejection due to the occurrence of a singularity at this point, the charge loss fraction is estimated by determining how much minimum charge must be removed if the drop is to relax back to a spherical shape. In this manner, the charge loss due to Rayleigh fission (the difference between the original charge and the minimum charge removed) is estimated to be about 39%, which falls within the range of experimental data lying between 20% and 50%. The results on scaling laws, time scales of the process, and the role of various stresses on the dynamics of the drop are discussed.
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