Gawande Neha, Mayya Y S, Thaokar Rochish
Department of Chemical Engineering, Indian Institute of Technology Bombay, Mumbai, 400076, India.
Eur Phys J E Soft Matter. 2022 May 13;45(5):47. doi: 10.1140/epje/s10189-022-00203-4.
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.
在过去利用交流四极阱中悬浮带电液滴的高速成像进行的实验中观察到的瑞利裂变过程的破裂路径，已显示出呈现几个形状和质心振荡周期，随后通过向上（即与重力方向相反）喷射射流进行不对称破裂。我们最近试图在斯托克斯流极限下使用边界积分模拟来解释这一现象，其中液滴的位置和端盖电极的极性是根据物理原理确定的，并且质心运动并未通过引用准静态条件进行一致估计。在这项工作中，我们使用基于边界元方法的数值计算来解释四极场中带电液滴向上破裂的实验观察结果，该计算考虑了利用四极电场电动悬浮的无粘性液滴。在数值方案中一致地计算了质心运动和端盖。模拟结果表明，重力引起的阱中液滴平衡位置的向下移动会导致叠加在液滴质心振荡上的显著大振幅形状振荡。这里一个重要的观察结果是，由于施加的四极场引起的形状振荡会导致足够的变形，这些变形成为低于瑞利极限时不稳定性开始的触发因素，从而允许亚临界不稳定性。阱内液滴的质心振荡跟随施加的频率，与施加的交流信号相位不同。因此，形状变形和液滴动态位置的综合作用导致不对称破裂，使得瑞利裂变通过在变形液滴北极处喷射射流向上发生。
