Deformation and stability of a viscous electrolyte drop in a uniform electric field
Deformation and stability of a viscous electrolyte drop in a uniform electric field
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均匀电场中粘性电解质滴的变形与稳定性
DOI：
10.1103/physrevfluids.4.053702
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发表时间：
2018-07
影响因子：
2.7
通讯作者：
Siegel Michael
中科院分区：
文献类型：
--
作者：
Wang Qiming;Ma Manman;Siegel Michael
本文研究了轴对称电解质液滴在外加电场作用下自由悬浮在无限介质中的变形和破裂。假设液滴相的电势很小，因此其控制方程近似为线性化的泊松-玻尔兹曼方程或修正的亥姆霍兹方程（debye - h<s:1> ckel体系）。提出了一种精确、高效的边界积分方法，用于求解任意德拜层厚度下随时间变化的水滴变形的低雷诺数流动问题。当液滴和周围介质的粘度相当时，给出了广泛的数值结果。在绝缘介质中，具有厚德拜层（以参数$\chi\ll 1$表征，这是一个逆无因次德拜层厚度）的液滴的演化与完美的介电液滴之间存在定性相似性。在此极限下，当施加的电场足够大时，得到了高度拉长的稳态，并用细长体理论很好地近似了液滴内部的场。在相反的极限$\chi\gg 1$，当Debye层很薄时，液滴表现为高导电性液滴，即使介电常数比适中$Q=\epsilon_1/\epsilon_2$，其中$\epsilon_1, \epsilon_2$分别为液滴内部和外部的介电常数。对于不再存在定常解的参数值，我们发现了三种不同类型的非定常解或破裂模式。这些被称为锥形末端形成，末端飞溅和开放端拉伸。第二种分离模式，末端飞溅，类似于最近一篇论文[R。张建军，张建军，张建军，等。液压与气动系统设计[j].液压与气动，2014,(4)。我们计算了一个相图，说明了参数空间中发生不同分裂模式的区域。
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-H\"{u}ckel 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 $\chi\ll 1$, 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 $\chi\gg 1$, when the Debye layer is thin, the drop behaves as a highly conducting drop, even for moderate permittivity ratio $Q=\epsilon_1/\epsilon_2$, where $\epsilon_1, \epsilon_2$ 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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影响因子：
4.6
作者：
Qiming Wang;M. Siegel;M. Booty
通讯作者：
Qiming Wang;M. Siegel;M. Booty
DOI：
--
发表时间：
2000
期刊：
--
影响因子：
--
作者：
J. Ong
通讯作者：
J. Ong
DOI：
10.1063/1.38956
发表时间：
2008-06
期刊：
--
影响因子：
--
作者：
J. Baygents;D. Saville
通讯作者：
J. Baygents;D. Saville
影响因子：
27.7
作者：
MELCHER, JR;TAYLOR, GI
通讯作者：
TAYLOR, GI
影响因子：
4.6
作者：
Fontelos, M. A.;Kindelan, U.;Vantzos, O.
通讯作者：
Vantzos, O.