Breakup of a conducting drop in a uniform electric field

Abstract

A conducting drop suspended in a viscous dielectric and subjected to a uniform DC electric field deforms to a steady-state shape when the electric stress and the viscous stress balance. Beyond a critical electric capillary number $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathit{Ca}$, which is the ratio of the electric to the capillary stress, a drop undergoes breakup. Although the steady-state deformation is independent of the viscosity ratio $\lambda $ of the drop and the medium phase, the breakup itself is dependent upon $\lambda $ and $\mathit{Ca}$. We perform a detailed experimental and numerical analysis of the axisymmetric shape prior to breakup (ASPB), which explains that there are three different kinds of ASPB modes: the formation of lobes, pointed ends and non-pointed ends. The axisymmetric shapes undergo transformation into the non-axisymmetric shape at breakup (NASB) before disintegrating. It is found that the lobes, pointed ends and non-pointed ends observed in ASPB give way to NASB modes of charged lobes disintegration, regular jets (which can undergo a whipping instability) and open jets, respectively. A detailed experimental and numerical analysis of the ASPB modes is conducted that explains the origin of the experimentally observed NASB modes. Several interesting features are reported for each of the three axisymmetric and non-axisymmetric modes when a drop undergoes breakup.

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

“…For parameter values at which steady solutions no longer exist, we find three distinct types of unsteady solution or breakup modes, which are termed conical end formation, end splashing, and open end stretching (see Section IV B for examples of these breakup modes). Similar breakup phenomena have been previously reported in simulations of perfect conductor, perfect dielectric, and leaky dielectric models [11,15,28,51]. However, there are some important differences in the results here.…”

“…Numerical computations based on a boundary integral formulation for the problem of freely suspended drops in an electric field have been popular due to their high accuracy and relative simplicity [11,14,28,31,[48][49][50][51][52]. When the electric potential is governed by Laplace's equation, there is an analytical expression for the axisymmetric version of the Green's function, i.e., the azimuthal part of the surface integral can be done analytically.…”

Investigation on Transient Oscillation of Droplet Deformation before Conical Breakup under Alternating Current Electric Field

“…Thereafter, the droplet retracted to ellipsoidal shape and oscillated at steady frequency which was about as twice as electric field. It is a bit similar to Karyappa's observation that lobes in ASPB and charged lobe disintegration mode in NASB 13 . However, some differences can be found between the two breakup modes: (1) According to Karyappa's report 13 , for the breakup under the DC electric field, a dimple forms at the electrode-facing pole of the first lobe, and then the dimple grows creating a crater of the sort 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 with an outer ring.…”

Effect of a Surrounding Liquid Environment on the Electrical Disruption of Pendant Droplets

“…19 The applied electric eld is known to strongly aect the dynamics of the drop 20 and, as expected, dierent behaviors are observed for applied potentials below and above a threshold value, that is, subcritical and supercritical regimes, respectively. Karyappa et al 21 Theoretical approach…”