Deformation characteristics of droplet generated by Rayleigh jet breakup

Abstract

This article investigated the effects of driving and jet parameters on the deformation characteristics of the droplet generated by a Rayleigh jet breakup for the first time. The deformation characteristics of the droplet include its oscillation amplitude and oscillation period. The driving parameters are the dimensionless wavenumber and the initial amplitude of the perturbation. The jet parameters are non-dimensionalized as the Ohnesorge number. The non-dimensional Navier–Stokes equations were numerically solved to simulate the spatial instability of the jet breakup and obtain the complete oscillation process of the droplet. An equivalent oscillation amplitude was formulated based on the hydrodynamic similarity principle and energy method to explain the source of the oscillation of the droplet. The dependence of the oscillation amplitude was explained for the first time by analyzing the growth of the various harmonics of the perturbation derived from the Fourier expansion of axial velocity distribution. The results show that the higher harmonics caused by the non-linearity of the jet breakup have a certain influence on the dependence of the oscillation amplitude. The dependence of the oscillation period was formulated according to the linear solution of the problem of oscillating droplets.

Bag film breakup of droplets in uniform airflows

“…figure 7( b ) in Hu et al. 2021), matching the perturbation shape of the second Rayleigh mode, which then excites oscillation modulated by capillary effects. In the meantime, the other parts of the ligament do not pinch off to form a series of fragments at once, but first break up into several elongated debris, and then split into large primary and small satellite drops via the well-known end-pinching mechanism (Castrejón-Pita, Castrejón-Pita & Hutchings 2012; Pal et al.…”

“…This arises from the coupled effects of reduction of bag film area (hence smaller chance for formation of 'node' fragments, as observed in figure 20l) and breakup of long viscous ligaments into smaller fragments, and implies a reduction in the average fragment size which will be discussed in more details further below. Finally, figure 21(d) suggests that increasing the Oh value causes the fragment speed to become more evenly distributed across different fragment sizes, which is probably due to the combined effects of viscous damping of the internal axial velocity distributions of pre-breakup ligaments (Hu et al 2021), and the ambient airflow becoming much less turbulent as its viscosity also increases under a fixed viscosity ratio μ * .…”

“…It can be seen from figure 13(a) that significant cross-sectional diameter variations have developed on the ligament before the onset of its breakup, which can be viewed as the result of the nonlinear development of the RP instability (Pal et al 2021). Afterwards, the ligament shrinks to form sharp tips and then breaks up on multiple sites, as shown in figure 13(b), and forms a primary drop which continues to undergo periodic prolate-oblate shape oscillations resembling droplets produced by breaking Rayleigh jets (Hu et al 2021), as highlighted in the red boxes in figures 13(b)-13(h). This is because the pinch-off of the stretching ligament induces an inner velocity field within the detaching droplet that drives it in the oblate direction (see e.g.…”

“…Afterwards, the ligament shrinks to form sharp tips and then breaks up on multiple sites, as shown in figure 13( b ), and forms a primary drop which continues to undergo periodic prolate–oblate shape oscillations resembling droplets produced by breaking Rayleigh jets (Hu et al. 2021), as highlighted in the red boxes in figures 13( b )–13( h ). This is because the pinch-off of the stretching ligament induces an inner velocity field within the detaching droplet that drives it in the oblate direction (see e.g.…”

Piezoelectric High Temperature Liquid Droplet Spraying Component

“…集成电路是当今信息社会的基石，也是人类工业文明的集大成者。而用于制备芯片的光刻技术则是 集成电路领域的核心技术。为满足人工智能、云计算、大数据等领域对处理器越来越高的算力需求，芯 片制程不断下探，从 28 nm 到 14 nm，再到全面迈向 7 nm 及以下节点 [1][2][3] 。在芯片制造过程中，制程尺 寸越小，制造精度就越高，传统的深紫外(λ = 193 nm)光刻技术已经无法满足这些要求。EUV 光刻使用波 长更短、能量更高的 EUV 光(λ = 13.5 nm)作为曝光光源，可以实现更高的分辨率和更小的制程尺寸。因 此，EUV 光刻已成为实现更小制程节点的首选技术 [4][5] 。 EUV 光源是 EUV 光刻系统中重要的组成部分，高功率、稳定的光源为整体系统的稳定工作奠定基 础。EUV 光源主要通过放电等离子体和激光等离子体获得，其中激光等离子体 EUV 光源由于其功率可 拓展、极紫外辐射收集效率高等特性，是当前量产光刻机用高功率 EUV 光源的解决方案之一 [6][7] 。激光 等离子体采用高功率短脉冲激光轰击锡液滴流靶，产生等离子体以辐射 EUV 光。均匀、稳定、小尺寸的 高频锡液滴靶是获取高质量 EUV 光源的关键 [7][8] 。 基于逆压电效应的压电式高温液滴喷射元件是获取高质量锡液滴靶的首选方案，其核心功能元件耐 高温微细压电陶瓷管的典型特点是耐高温(＞240 ℃)、高性能(压电系数 d33＞350 pC/N)、大长径比(长径 比＞20)和薄壁(0.2~0.8 mm)。其中，微细压电陶瓷管的精细制备是关键技术难点。中国科学院上海硅酸 盐研究所压电陶瓷材料与器件研究团队基于自主研制的 PZT 高温压电陶瓷材料，突破了微细压电陶瓷管 的成型、烧结、加工、极化、性能测试等一系列核心技术，成功研制出耐 250 ℃高温的微细压电陶瓷管， 同心度、线性度等均达到了国外同类产品水平，分别如图 1(a, b)所示。基于射流断裂原理 [9] ，通过电压驱 动微细压电陶瓷管产生的径向振动对射流产生周期性扰动，形成了均匀、稳定的锡液滴靶。 在此基础上，联合中国科学院上海光学精密研究所 EUV 光源团队，解决了压电式高温锡液滴喷射元 件的密封组装与高温真空气密性等关键问题，实现了压电式高温锡液滴喷射元件的自主制备，如图…”