Numerical study of Rayleigh fission of a charged viscous liquid drop

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

doi:10.1103/physrevfluids.2.113603

Cited by 17 publications

(41 citation statements)

References 30 publications

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“…The total surface charge is non-dimensionalized by γ a 3 e such that the non-dimensional Rayleigh charge is 8π. The electrostatic and Stokes equations are solved using the axisymmetric boundary integral method, using well-established methodologies (Deshmukh & Thaokar 2012;Lanauze et al 2015;Gawande et al 2017).…”

Section: Problem Formulationmentioning

confidence: 99%

“…Actual experimental images show a cone angle of 30 • , indicating significant viscous effects (Giglio et al 2008). Furthermore, the PC model was also used for predicting fractional charge loss of approximately 39 % (Gawande, Mayya & Thaokar 2017) assuming negligible mass loss.…”

Section: Introductionmentioning

confidence: 99%

“…In the Rayleigh breakup of a charged drop, the perfect conductor model fairly predicts the drop deformation until the formation of the cone (Betelú et al 2006;Giglio et al 2008;Gawande et al 2017;Singh et al 2019b). Up to this stage, the bulk charges are indeed zero.…”

Section: Introductionmentioning

confidence: 99%

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Jet and progeny formation in the Rayleigh breakup of a charged viscous drop

2019

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Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Jet and progeny formation in the Rayleigh breakup of a charged viscous drop

2019

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“…where J and K are the Stokeslet and Stresslet Green's functions for Stokes flow, and x 0 is located in regions 1 and 2 in (15) and (16), respectively. The first term on the right hand side of (15) is transformed into a surface integral by using the divergence free property of the Stokeslet, namely,…”

Section: A Integral Equationsmentioning

confidence: 99%

Deformation and stability of a viscous electrolyte drop in a uniform electric field

Wang

Siegel

2019

Phys. Rev. Fluids

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We study the deformation and breakup of an axisymmetric electrolyte drop which is freely suspended in an infinite dielectric medium and subjected to an imposed electric field. The electric potential in the drop phase is assumed small, so that its governing equation is approximated by a linearized Poisson-Boltzmann or modified Helmholtz equation (the Debye-Hückel regime). An accurate and efficient boundary integral method is developed to solve the low-Reynolds-number flow problem for the time-dependent drop deformation, in the case of arbitrary Debye layer thickness. Extensive numerical results are presented for the case when the viscosity of the drop and surrounding medium are comparable. Qualitative similarities are found between the evolution of a drop with a thick Debye layer (characterized by the parameter χ ≪ 1, which is an inverse dimensionless Debye layer thickness) and a perfect dielectric drop in an insulating medium. In this limit, a highly elongated steady state is obtained for sufficiently large imposed electric field, and the field inside the drop is found to be well approximated using slender body theory. In the opposite limit χ ≫ 1, when the Debye layer is thin, the drop behaves as a highly conducting drop, even for moderate permittivity ratio Q = ǫ 1 /ǫ 2 , where ǫ 1 , ǫ 2 is the dielectric permittivity of drop interior and exterior, respectively. For parameter values at which steady solutions no longer exist, we find three distinct types of unsteady solution or breakup modes. These are termed conical end formation, end splashing, and open end stretching. The second breakup mode, end splashing, resembles the breakup solution presented in a recent paper [R. B. Karyappa et al., J. Fluid Mech. 754, 550-589 (2014)]. We compute a phase diagram which illustrates the regions in parameter space in which the different breakup modes occur.

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“…The details of the mathematical formulation and numerical implementation can be found elsewhere. 15 The flow equations are solved in the Stokes flow limit while the Laplace equation is solved for the electric potential. The integral equation…”

Section: Numerical Simulationsmentioning

confidence: 99%

Effect of the Quadrupolar Trap Potential on the Rayleigh Instability and Breakup of a Levitated Charged Droplet

et al. 2019

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Rayleigh instability that results in the breakup of a charged droplet, levitated in a quadrupole trap, has been investigated in the literature, but only scarcely. We report here asymmetric breakup of a charged drop, levitated in a "loose trap", wherein, the droplet is stabilized at an off-center location in the trap. This aspect of levitation leads to an asymmetric breakup of the charged drop, predominantly in a direction opposite to that of gravity. In a first of its kind of study, we capture the successive events of the droplet deformation, breakup and relaxation of the drop after jet ejection using high speed imaging at a couple of hundred thousand frames per second. A pertinent question of the effect of the electrodynamic trap parameters such as applied voltage as well as physical parameters such as the size of the drop, gravity and conductivity on the characteristics of droplet breakup is also explored. A clear effect of the trap strength on the deformation (both symmetric and asymmetric) is observed. Moreover, the cone angle at the pole undergoing asymmetric breakup is almost independent of the applied field investigated in the experiments. All the experimental observations are compared with numerical simulations carried out using the boundary element method (BEM) in 1 arXiv:1908.03132v1 [physics.flu-dyn] 8 Aug 2019the Stokes flow limit. The BEM simulations are also extended to other experimentally achievable parameters. It is observed that the breakup is mostly field influenced, and not field induced. A plausible theory for the observations is reported, and a sensitive role of the sign of the charge on the droplet and the sign of the end cap potential, as well as the off-center location of the droplet in the trap.

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Numerical study of Rayleigh fission of a charged viscous liquid drop

Cited by 17 publications

References 30 publications

Jet and progeny formation in the Rayleigh breakup of a charged viscous drop

Jet and progeny formation in the Rayleigh breakup of a charged viscous drop

Deformation and stability of a viscous electrolyte drop in a uniform electric field

Effect of the Quadrupolar Trap Potential on the Rayleigh Instability and Breakup of a Levitated Charged Droplet

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