交变电场中Oldroyd B液滴的变形动力学
Deformation dynamics of Oldroyd B drop in alternating electric field
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中文总结 AI 辅助
本文结合渐近分析与Basilisk求解器的数值模拟，探究交变电场中Oldroyd-B液滴的变形动力学，识别六个电流体动力学区域，明确不同频率下变形模式与De、Ca_E的关系，为电流体应用提供理论依据。
中文摘要 AI 辅助
粘弹性液滴在交变电场中的变形与微流控、喷墨打印、液滴操控等电流体动力学应用相关。本文采用渐近分析与开源求解器Basilisk的直接数值模拟，研究中性浮力Oldroyd-B液滴在均匀交变电场中的动力学行为。针对悬浮于Oldroyd-B介质中的Oldroyd-B液滴，在轴对称斯托克斯流、两种流体均为漏介质的假设下，推导了小变形与弱弹性的解析解。根据电导率与介电常数的比值，识别出六个电流体动力学区域，各区域具有不同的变形模式、流动方向与非线性响应：部分区域呈现稳定的椭球变形，其余区域在超过临界电毛细管数后会发生尖端突出、多瓣或扁平分叉。在高、中、低三个频率区间，变形以施加电场频率的两倍振荡，其均值与振幅由电场频率和粘弹性决定。对于稳态电场下呈现长椭球变形的情况，液滴在高频时保持长椭球形，在中频时出现短暂的扁椭球偏移，在低频时在近球形与高度变形状态间发生大幅振荡；均值变形随De的变化呈现单调或非单调关系，具体取决于频率与电特性比值。对于稳态电场下呈现扁椭球变形的情况，液滴在高频时保持扁椭球形，在中频时产生凹痕，在低频且De与Ca_E足够大时发生分叉；均值变形随De单调增加。
英文摘要
The deformation of viscoelastic drops in alternating electric fields is relevant to electrohydrodynamic applications such as microfluidics, inkjet printing, and drop manipulation. We investigate the dynamics of a neutrally buoyant Oldroyd-B drop subjected to a uniform alternating electric field using asymptotic analysis and direct numerical simulations with the open-source solver Basilisk. An analytical solution is derived for small deformation and weak elasticity for an Oldroyd-B drop suspended in an Oldroyd-B medium, with both fluids modeled as leaky dielectrics under axisymmetric Stokes flow. Depending on the conductivity and permittivity ratios, six electrohydrodynamic regions are identified, characterized by distinct deformation modes, flow directions, and nonlinear responses; while some exhibit stable spheroidal deformation, others undergo pointed-tip, multi-lobed, or oblate breakup beyond a critical electric capillary number. Across high-, intermediate-, and low-frequency regimes, the deformation oscillates at twice the applied field frequency, with its mean and amplitude governed by the field frequency and viscoelasticity. For cases that produce prolate deformation under a steady field, the drop remains prolate at high frequency, exhibits brief oblate excursions at intermediate frequency, and undergoes large-amplitude oscillations between near-spherical and highly deformed states at low frequency. The mean deformation varies monotonically or non-monotonically with $De$, depending on frequency and electrical property ratios. For cases producing oblate deformation under a steady field, the drop remains oblate at high frequency, develops dimples at intermediate frequency, and breaks up at low frequency for sufficiently large $De$ and $Ca_E$; the mean deformation increases monotonically with $De$.
