2019 EJRNL PP QIMING WANG 1.pdf
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Terbatas Ratnasari
» ITB
Terbatas Ratnasari
» ITB
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 to be 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 ? 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 ? 1, when the Debye layer is thin, the drop behaves as a
highly conducting drop, even for moderate permittivity ratio Q = 1/2, where 1, 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 (2014)]. We
compute a phase diagram which illustrates the regions in parameter space in which the
different breakup modes occur.