Numerical simulation of droplet motion on glass surface driven by ultrasonic travelling wave
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摘要:
针对液滴铺展和移动的动力学行为在工业生产和微流控芯片等领域有着重要作用，提出了一种基于超声行波理论的弹性体平板驱动模型，利用压电陶瓷的逆压电效应在弹性体玻璃产生超声行波从而驱动液滴运动。借助多物理场软件COMSOL建立液滴模型，首先进行行波分析，验证了驱动液滴的可行性。在0~60 ms中，液滴在超声行波的驱动下进行收缩-铺展的正弦振荡运动。然后通过液滴内部流场结构分析发现，当液滴半径铺展到最大后开始收缩时，液滴与基底接触面处的速度首先发生变化，表明液滴内部速度场的变化对接触线是否发生移动有着重要作用。液滴内部流场存在一个类似于椭圆形的漩涡，说明液滴运动不是单纯由于收缩-铺展而引起的平动，而是滚动着朝前运动。最后分别探讨了液滴移动速度与驱动电压、驱动频率以及动力黏度的关系，结果表明液滴移动速度受动力黏度影响较为显著。
Abstract:Aimed at the situations of the spreading and moving dynamics behavior of the droplet that plays an important role in industrial production and microfluidic chips, an elastic planar model based on the theory of ultrasonic travelling wave was proposed. The droplet on the elastic glass surface was driven by ultrasonic travelling wave generated by the inverse piezoelectric effect of piezoelectric ceramic. The droplet model was built with multi-physics field software COMSOL. Firstly, through the analysis of the ultrasonic travelling wave, the feasibility of the model was verified. During the period of 0 to 60 ms, the droplet behaves a shrinking-spreading sinusoidal oscillation motion driven by ultrasonic travelling wave. Then, the internal flow structure inside the droplet was also investigated. When the droplet radius spreads to the maximum and begins to shrink, the velocity inside the contact surface between the droplet and the substrate changes first. It shows that the change of the velocity field inside the droplet plays an important role in the motion of the contact line. There is a similar elliptic vortex in the flow field inside the droplet, which illustrates that the droplet motion is not a simple translation induced by shrinking-spreading, but a forward movement with rolling. Finally, we studied the dependency of the moving velocity of the droplet on the parameters (driving voltage, driving frequency and dynamic viscosity) via simulations. The results show that the moving velocity of the droplet is significantly influenced by the dynamic viscosity.
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Key words:
- ultrasonic travelling wave /
- droplet /
- contact line motion /
- droplet oscillations /
- piezoelectric
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图 1 液滴在水平固体表面上的接触角与表面张力
Figure 1. Contact angle and surface tensions of a droplet on horizontal solid surface
图 2 弹性体平板模型产生超声行波
Figure 2. Elastic planar model used to generate ultrasonic travelling wave
图 11 液滴移动速度随驱动电压的变化
Figure 11. Variation of droplet moving velocity with driving voltage
图 12 液滴移动速度随驱动频率的变化
Figure 12. Variation of droplet moving velocity with driving frequency
图 13 压电振子的阻抗频率响应曲线
Figure 13. Impedance frequency response curve of piezoelectric vibrator
图 14 液滴移动速度随动力黏度的变化
Figure 14. Variation of moving velocity of droplet with dynamic viscosity
表 1 几何模型的结构参数
Table 1. Structure parameters of geometric model
类型 长度/mm 厚度/mm 玻璃平板 150 3 压电陶瓷 5π/4 1 
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表 2 玻璃的材料参数
Table 2. Material parameters of glass
参数 弹性模量/Pa 密度/(kg·m-3) 泊松比 数值 7×1010 2 210 0.24
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表 3 质点的瞬时位移
Table 3. Instantaneous displacement of particle
时间/ms x方向位移/nm z方向位移/nm 30.085880 3.654254 35.945566 30.086332 37.307580 42.905864 30.086784 56.858371 35.665642 30.087236 55.340976 17.141958 30.087688 33.690540 -5.537054 30.088140 0.086644 -24.081458 30.088592 -33.196754 -32.023728 30.089044 -54.042325 -26.239285 30.089496 -54.650676 -7.623552 30.089948 -34.476498 18.330271 30.090400 -0.687655 42.223590
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