Abstract

The breakup pathway of the Rayleigh fission process observed in the past experiments carried out using high-speed imaging of a charged drop levitated in an AC quadrupole trap has shown to exhibit several cycles of shape and center-of-mass oscillations followed by asymmetric breakup by ejecting a jet in the upward direction (i.e., opposite to the direction of gravity). We recently attempted to explain this using boundary integral simulations in the Stokes flow limit, wherein the position of the droplet and the polarity of the end cap electrodes were assigned using physical arguments, and the center-of-mass motion was not estimated consistently invoking quasi-static conditions. In this work, we explain the experimental observation of upward breakup of charged droplets in a quadrupolar field, using numerical calculations based on the boundary element method considering inviscid droplets levitated electrodynamically using quadrupole electric fields. The center-of-mass motion and the end cap are consistently calculated in the numerical scheme. The simulations show that the gravity-induced downward shift in the equilibrium position of the drop in the trap causes significant, large-amplitude shape oscillations superimposed over the center-of-mass oscillations of the drop. An important observation here is that the shape oscillations due to the applied quadrupole fields result in sufficient deformations that act as triggers for the onset of the instability below the Rayleigh limit, thereby admitting a subcritical instability. The center-of-mass oscillations of the droplet within the trap, which follow the applied frequency, are out of phase with the applied AC signal. Thus the combined effect of shape deformations and dynamic position of the drop leads to an asymmetric breakup such that the Rayleigh fission occurs upward via the ejection of a jet at the north pole of the deformed drop.

Graphical abstract

中文翻译：

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平移-变形耦合对电动悬浮带电液滴瑞利不稳定性的影响

摘要

在过去的实验中观察到的瑞利裂变过程的分裂路径是使用悬浮在交流四极阱中的带电液滴的高速成像进行的，显示出几个周期的形状和质心振荡，然后是不对称分裂以向上的方向（即与重力方向相反）喷射射流。我们最近尝试使用斯托克斯流动极限中的边界积分模拟来解释这一点，其中液滴的位置和端盖电极的极性是使用物理参数分配的，并且质心运动没有被一致地调用准-静态条件。在这项工作中，我们解释了在四极场中带电液滴向上分裂的实验观察，使用基于边界元法的数值计算，考虑使用四极电场电动悬浮的无粘性液滴。质心运动和端盖在数值方案中一致计算。模拟表明，重力引起的陷阱中液滴平衡位置的向下移动会导致显着的大振幅形状振荡叠加在液滴的质心振荡上。这里的一个重要观察是，由于施加的四极场导致的形状振荡导致足够的变形，这些变形充当了瑞利极限以下不稳定性开始的触发因素，从而允许亚临界不稳定性。陷阱内液滴的质心振荡，遵循所施加的频率，与施加的交流信号异相。因此，液滴的形状变形和动态位置的综合影响导致不对称分裂，从而瑞利裂变通过在变形液滴的北极喷射射流而向上发生。

图形概要