Small deformation theory for two leaky dielectric drops in a uniform electric field
Small deformation theory for two leaky dielectric drops in a uniform electric field
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均匀电场中两个漏电滴的小变形理论
DOI：
10.1098/rspa.2019.0517
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
M. Zabarankin
中科院分区：
文献类型：
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作者：
M. Zabarankin
提出了两个不同的球形液滴自由悬浮在环境流体中并受到均匀电场的小变形理论。假设三相是漏电（微导电）粘性不可压缩流体，并且忽略惯性和表面电荷对流的非线性效应。液滴的变形形状相对于表征电应力和表面张力之间的平衡的电毛细管数是线性化的。当两个液滴相距足够远时，泰勒的小变形理论可以预测它们的变形形状 - 根据泰勒的判别函数，液滴可能会变成长长形、扁圆形或保持球形。当两滴彼此靠近时，除了变成扁长形/扁圆形外，它们还开始平移并形成鸡蛋形状。 （由于没有净电荷，两个液滴的质心保持静止。）每种变形“模式”的程度取决于液滴中心之间的距离以及液滴与环境流体的电导率、介电常数和粘度之比。两滴小变形理论的预测与基于边界积分方程方法的两滴动力学模拟的现有结果完全一致。此外，虽然以前的工作只观察到两个相同液滴的三种类型的行为——液滴可能变成扁长形或扁圆形并相互靠近，或者变成扁圆形并彼此远离——小变形理论预测，当液滴与环境流体电导率之比是倒数且液滴与环境流体粘度比足够大时，不同的液滴实际上可能会变成扁圆形并彼此远离。所提出的理论还可以轻松地对不同液滴变形模式之间的相互作用产生分析洞察，并可用于指导选择两滴动力学模拟的相机电特性。
A small deformation theory for two non-identical spherical drops freely suspended in an ambient fluid and subjected to a uniform electric field is presented. The three phases are assumed to be leaky dielectric (slightly conducting) viscous incompressible fluids and the nonlinear effects of inertia and surface charge convection are neglected. The deformed shapes of the drops are linearized with respect to the electric capillary number that characterizes the balance between the electric stress and the surface tension. When the two drops are sufficiently far apart, their deformed shapes are predicted by Taylor’s small deformation theory—depending on Taylor’s discriminating function, the drops may become prolate, oblate or remain spherical. When the two drops get closer to each other, in addition to becoming prolate/oblate, they start translating and developing an egg shape. (Since there is no net charge, the centre of mass of the two drops remains stationary.) The extent of each of these ‘modes’ of deformation depends on the distance between the drops’ centres and on drop-to-ambient fluid ratios of electric conductivities, dielectric constants and viscosities. The predictions of the small deformation theory for two drops perfectly agree with the existing results of two-drop dynamics simulation based on a boundary-integral equation approach. Moreover, while previous works observed only three types of behaviour for two identical drops—the drops may either become prolate or oblate and move towards each other or become prolate and move away from each other—the small deformation theory predicts that non-identical drops may, in fact, become oblate and move away from each other when the drop-to-ambient fluid conductivity ratios are reciprocal and the drop-to-ambient fluid viscosity ratios are sufficiently large. The presented theory also readily yields an analytical insight into the interplay among different modes of drop deformation and can be used to guide the selection of the phases’ electromechanical properties for two-drop dynamics simulations.