Effect of conductivity on the mechanism of charge ejection in Rayleigh breakup of a charged drop

Gawande, Neha; Mayya, Y. S.; Thaokar, Rochish

doi:10.1016/j.elstat.2022.103720

Cited by 2 publications

(1 citation statement)

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“…(2008, 2013) first proposed a scaling law for the radius of ejected droplets and the charge quantity in EHD tip streaming. Subsequently, Gawande, Mayya & Thaokar (2019, 2022) investigated the effect of electrical conductivity on the breakup mechanisms for prolate deformation of droplets. Sengupta et al.…”

Section: Introductionmentioning

confidence: 99%

Lattice Boltzmann modelling and study of droplet equatorial streaming in an electric field

Wang,

Lei,

Yang

et al. 2024

J. Fluid Mech.

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In 2017, Brosseau & Vlahovska (Phys. Rev. Lett, vol. 119, no. 3, 2017, p. 034501) found that, in a strong electric field, a weakly conductive, low-viscosity droplet immersed in a highly conductive, high-viscosity medium formed a lens shape, and liquid rings continuously detached from its equatorial plane and subsequently broke up into satellite droplets. This fascinating multiphase electrohydrodynamic (EHD) phenomenon is known as droplet equatorial streaming. In this paper, based on the unified lattice Boltzmann method framework proposed by Luo et al. (Phil. Trans. R. Soc. A Math. Phys. Engng Sci, vol. 379, no. 2208, 2021, p. 20200397), a novel lattice Boltzmann (LB) model is constructed for multiphase EHD by coupling the Allen–Cahn type of multiphase LB model and two new LB equations to solve the Poisson equation of the electric field and the conservation equation of the surface charge. Using the proposed LB model, we successfully reproduced, for the first time, the complete process of droplet equatorial streaming, including the continuous ejection and breakup of liquid rings on the equatorial plane. In addition, it is found that, under conditions of high electric field strength or significant electrical conductivity contrast, droplets exhibit fingering equatorial streaming that was unknown before. A power-law relationship is discovered for droplet total charge evolution and a theoretical model is then proposed to describe the droplet radius and height over time. The breakup of liquid rings is found to be dominated by capillary instability, while the breakup of liquid fingers is governed by the end-pinching mechanism. Finally, a phase diagram is constructed for fingering equatorial streaming and ring equatorial streaming, and a criterion equation is established for the phase boundary.

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