﻿ 超声激励薄液膜Faraday波形成机理<sup>*</sup>
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Formation mechanism of Faraday wave on thin liquid film excited by ultrasonic vibration
GAO Guofu, LI Kang, LI Yu, XIANG Daohui, ZHAO Bo
School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo 454000, China
Received: 2018-12-02; Accepted: 2018-12-29; Published online: 2019-03-08 11:48
Foundation item: National Natural Science Foundation of China (51575453)
Corresponding author. GAO Guofu, E-mail: gaogf@hpu.edu.cn
Abstract: Aimed at the Faraday wave formed by 35 kHz ultrasonic excitation on thin liquid film, the formation mechanism of Faraday wave was explored by experiments and finite element simulation. The two-phase flow calculation model under ultrasonic excitation was established. The finite element simulation of the formation process of Faraday wave was carried out by CFD method. The formation mechanism of Faraday wave was discussed by analyzing the phase diagram and streamline diagram. The vibration frequency of Faraday wave was about 1/2 of the drive frequency. The existence of liquid inertia resulted in a constantly varying phase difference between the ultrasonic excitation and the liquid surface wave, and the phase difference variation period was about two ultrasonic excitation periods. Through the 35 kHz ultrasonic excitation experiment on thin liquid film, a well-arranged Faraday wave array pattern was observed on the surface of the thin liquid film. By measuring the wavelength of the Faraday wave, it was deduced that the surface wave frequency obtained by the experiment was about 1/2 of the ultrasonic frequency, and consistent with the results of finite element simulation.
Keywords: Faraday wave     ultrasonic excitation     thin liquid film     computational fluid dynamics (CFD)     formation mechanism

1 CFD有限元仿真分析

1.1 计算模型

 (1)

 图 1 计算模型 Fig. 1 Calculation model

 (2)

 (3)

1.2 仿真结果与分析

 图 2 超声激励频率35kHz、超声激励振幅8μm条件下不同时刻的Faraday波相图 Fig. 2 Phase diagram of Faraday wave at different moments under ultrasonic excitation frequency 35kHz and ultrasonic excitation amplitude 8μm

 图 3 超声激励频率35kHz条件下不同超声激励振幅的Faraday波相图 Fig. 3 Phase diagram of Faraday wave under different ultrasonic excitation amplitudes at ultrasonic excitation frequency 35kHz

 图 4 超声激励频率35kHz、超声激励振幅8μm条件下1.9×10-4s时刻的Faraday波相图 Fig. 4 Phase diagram of Faraday wave at 1.9×10-4s under ultrasonic excitation frequency 35kHz and ultrasonic excitation amplitude 8μm

 序号 横向坐标/μm 波长/μm 1 58.26 122.9 2 181.2 105.7 3 286.9 103.7 4 390.6 103.7 5 494.3 99.9 6 594.2 101.9 7 696.1 115.2 8 811.3 124.9 9 936.2

 图 5 一个超声激励周期Faraday波的流线图 Fig. 5 Streamline diagram of Faraday wave in an ultrasonic excitation period

1) 远离薄液膜的空气域速度方向始终和超声激励(液膜底面)的速度方向保持一致，薄液膜附近空气域的速度方向有偏差，此部分空气域速度变化较快，液体域速度存在滞后现象。

2) 超声激励竖直向下的速度逐渐减小转向为竖直向上并增大到最大值的过程中(图 5(a)(b)(f))，波峰左侧空气域和流体域的速度矢量组成一个顺时针闭环，波峰右侧空气域和流体域的速度矢量组成一个逆时针闭环。表面波波峰和波谷先短暂增加然后衰减至液膜表面基本为平面，空气抑制表面波增长。

3) 超声激励竖直向上的速度由最大值逐渐减小转向并增加到竖直向下最大值的过程中(图 5(c)~(e))，波峰左侧空气域和流体域的速度矢量组成一个逆时针闭环，波峰右侧空气域和流体域的速度矢量组成一个顺时针闭环，空气促进波峰波谷增长。

4) 图 5x=0.5mm处表面波在(a)中为波峰，在(f)中为波谷，即一个超声激励周期约为液膜表面波运动周期的1/2，超声激励与表面波运动存在不断变化的相位差，一个相位差变化周期约为2个超声激励周期。图 6所示为图 5x=0.5mm处表面波与超声激励的相位变化，图中η为位移量。

 图 6 Faraday波和超声激励相位差 Fig. 6 Phase difference between Faraday wave and ultrasonic excitation wave

2 实验分析

 图 7 实验装置平台 Fig. 7 Experimental device platform

 图 8 表面驻波阵列 Fig. 8 Surface standing wave array

3 结论

1) 通过CFD有限元仿真分析，同一超声激励频率下，当超声激励振幅超过临界值α时，经历数个超声激励周期后，薄液膜表面激发形成Faraday波。随超声激励振幅增加，Faraday波振幅增大，当超声激励振幅超过临界值β时，会产生超声雾化现象。此外，表面波波长不随超声激励振幅的改变而改变。

2) 通过对一个超声激励周期表面波流线图分析，在超声激励竖直向下的速度逐渐减小转向为竖直向上且不断增加到最大值的过程中，波峰处存在速度矢量闭环，空气抑制表面波的增长；当超声激励竖直向上的速度由最大值逐渐减小并转向增大到竖直向下最大值的过程中，波峰处存在速度矢量闭环，空气促进表面波的生长。液膜表面的表面波是在外部周期性激励下由空气与液体相互作用形成的。表面波波峰或波谷与超声激励存在不断变化的相位差，一个相位差变化周期约为2个超声激励周期。

3) 超声振动激励薄液膜表面形成Faraday波，实验测量的Faraday波波长与理论计算值相比较，得出35kHz超声激励形成Faraday波的振动频率约为超声激励频率的1/2，与CFD有限元仿真分析结果一致。

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#### 文章信息

GAO Guofu, LI Kang, LI Yu, XIANG Daohui, ZHAO Bo

Formation mechanism of Faraday wave on thin liquid film excited by ultrasonic vibration

Journal of Beijing University of Aeronautics and Astronsutics, 2019, 45(8): 1582-1588
http://dx.doi.org/10.13700/j.bh.1001-5965.2018.0710