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Many industrial technologies, such as condensation cooling and fuel cells, require solid-liquid separation. Electrowetting is a very effective method of inducing droplets to detach from hydrophobic surfaces, and it is very convenient to control. The jumping of droplets excited by an electric field depends on the conversion of surface energy into kinetic energy and other forms of energy. At present, there is still a lack of in-depth research on this process. In this study, a high-speed camera is used to capture the jumping motion of a droplet on a hydrophobic surface under the actuation of electrowetting, and the threshold voltage that causes the droplet to detach is estimated based on the changes in contact angle and droplet shape. A self-written Matlab program is used to analyze and calculate the various forms of energy in the process of droplets detaching and subsequent bouncing. The results show that there is an obvious coupling relationship between the kinetic energy and potential energy of the droplet’s center of mass during the flight of the droplet from the surface. The vibrational kinetic energy and surface potential energy also show a certain coupling relationship during the flight phase. The internal dissipation caused by the viscosity of the droplet increases with the droplet oscillation amplitude increasing, and decays with time. Because it can cause the droplet to oscillate and deform and create more surface energy, AC pulses are more efficient than direct current in the droplet bounce. By revealing the energy conversion and dissipation mechanism in the process of droplet jumping driven by electrowetting, a theoretical reference is provided for the application of this technology in solid-liquid separation and three-dimensional digital microfluidics.
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Keywords:
- electrowetting /
- jumping /
- energy /
- conversion /
- dissipation
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图 1 实验装置示意图. 左边是实验装置, 右边是共面电极的设计图, 黑色为驱动电极, 白色为参照电极
Figure 1. Schematic diagram of the experimental setup. The left is the experimental setup, the right is the design diagram of the coplanar electrode, the black is the driving electrode and the white is the reference electrode.
图 2 250 V直流电压激励下液滴的变形和弹跳, 从左至右分别为液滴在激励前, 激励中和激励移除以后的状态
Figure 2. The deformation and bouncing of the droplet under the excitation of 250 V DC voltage, from left to right are the states of the droplet before excitation, during excitation and after excitation removal.
图 3 电润湿激励下的液滴变形和弹跳, 从左向右每帧间隔为1 ms
Figure 3. Droplet deformation and jumping under electrowetting excitation, the interval between two adjacent images is 1 ms.
图 4 无量纲化的液滴弹跳高度(蓝色)和形变因子(红色)随400 V交流正弦波(10 kHz)脉冲长度的变化, 绿色直线代表直流激励下的弹跳高度
Figure 4. The dimensionless droplet jumping height (blue) and deformation factor (red) as a function of 400 V sine wave (10 kHz) pulse duration. The green straight line represents the bounce height under DC actuation.
图 5 液滴在电润湿作用下界面能(空心圆圈)以及移除电压以后的界面能(实心方块), Rb 代表液滴球缺的底面半径. 两条曲线上相同的Rb对应的两点具有同样的形状, 同一条曲线上不同的点具有相同的固-液界面张力
${\gamma }_{\rm SL}$ . 注意液滴的界面能和底面半径均经过了无量纲处理Figure 5. The interfacial energies of the droplet under electrowetting (open circles) and after removing the voltage (solid squares), the X-axis represents the base radius of the droplet. The same abscissa (Rb) represents the same droplet shape, and different points on the same curve have the same solid-liquid interfacial tension. Note that both the interfacial energy and base radius of the droplet are dimensionless.
图 6 液滴质心高度和表面积在液滴弹跳过程中随时间的变化
Figure 6. Variation of droplet centroid height and surface area with time during droplet bouncing.
图 7 液滴在弹跳过程中质心能量随时间的变化, 其中液滴质心的动能(红色)和势能(蓝色)是分别结合实验数据利用方程(10)和(11)计算得出, 质心的质心总能量(黑色)是以上两部分的总和
Figure 7. Variation of the droplet centroid energy with time during the bouncing process. The kinetic energy (red) and potential energy (blue) of the droplet are calculated using Eqs. (10) and (11) based on experimental data, respectively, and the total energy (black) of the centroid is the sum.
图 8 液滴的振动能量转化图谱, 其中振动动能(粉色)和振动势能(蓝绿)分别是结合实验数据利用方程(13)和(15)计算得出, 液滴的振动总能量(紫色)是以上两部分之和
Figure 8. Vibrational energy conversion spectrum of droplet. The vibrational kinetic energy (pink) and vibrational potential energy (blue-green) are calculated using Eqs. (13) and (15) based on experimental data, respectively. The total vibrational energy (purple) of the droplet is the sum.
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[1] 毕菲菲, 郭亚丽, 沈胜强, 陈 觉先, 李熠桥 2012 物理学报 61 184702
Google Scholar
Bi F F, Guo Y L, Shen S Q, Chen J X, Li Z J 2012 Acta Phys. Sin. 61 184702
Google Scholar
[2] Lin S, Zhao B, Zou S, Guo J, Wei Z, Chen L 2018 J. Colloid Interf. Sci. 516 86
Google Scholar
[3] Schutzius T M, Jung S, Maitra T, Graeber G, Köhme M, Poulikakos D 2015 Nature 527 82
Google Scholar
[4] Palan V, Shepard W S 2006 J. Power Sources 159 1061
Google Scholar
[5] 姚朝晖, 钟麟彧 2016 第九届全国流体力学学术会议论文摘要集 中国南京 2016年10月21—23日
Yao Z H, Zhong L Y 2016 Abstract Collection of Papers of the 9 th National Conference on Fluid Mechanics Nanjing, China, October 21–23, 2016 (in Chinese)
[6] Boreyko J B, Chen C H 2010 Phys. Fluids 22 091110
Google Scholar
[7] Enright R, Miljkovic N, Sprittles J, Nolan K, Mitchell R, Wang E N 2014 ACS Nano 8 10352
Google Scholar
[8] Li X, Jiang Y, Jiang Z, Li Y, Wen C, Lian J 2019 Appl. Surf. Sci. 492 349
Google Scholar
[9] Pinchasik B E, Wang H, Möhwald H, Asanuma H 2016 Adv. Mater. Inter. 3 1600722
Google Scholar
[10] Baratian D, Dey R, Hoek H, Ende D V D, Mugele, F 2018 Phys. Rev. Lett. 120 214502
Google Scholar
[11] Lee S J, Lee S, and Kang K H 2011 J. Visual. 14 259
Google Scholar
[12] Raman K A, Jaiman R K, Lee T S, Low H T 2016 Int. J. Heat Mass Tran. 99 805
Google Scholar
[13] Wang Z, Ende D V D, Pit A M, Lagraauw R, Wijnperlé D, Mugele F 2017 Soft Matter. 13 4856
Google Scholar
[14] Hong J, Kim Y K, Won D J, Kim J, Lee, S J 2015 Sci. Rep. 5 1
[15] Mugele F, Baret J C 2005 J. Phys. Cond. Matter 17 R705
Google Scholar
[16] Vallet M, Berge B, Vovelle L 1996 Polymer 37 2465
Google Scholar
[17] Cho S K, Moon H, Kim C J 2003 J. Microelectromechanical Sys. 12 70
Google Scholar
[18] Li J, Kim C J 2020 Lab Chip 20 1705
Google Scholar
[19] Zhang K X, Li Z, Chen S 2019 Phys. Fluids 31 081703
Google Scholar
[20] Vo Q, Tran T 2019 Phys. Rev. Lett. 123 024502
Google Scholar
[21] Wang Q G, Xu M, Wan C, Gu J P, Hu N, Lyu J F, Yao W 2020 Langmuir 36 8152
Google Scholar
[22] Burkhart C T, Maki K L, Schertzer M J 2020 Langmuir 36 8129
Google Scholar
[23] Torkkeli, A 2003 Ph. D. Dissertation (Helsinki: VTT Technical Research Centre of Finland)
[24] Yi U C, Kim C J 2006 J. Micromech. Microeng. 16 2053
Google Scholar
[25] Cavalli A, Preston D J, Tio E, Martin D W, Miljkovic N, Wang E N, Miljkovic F, Bush J W M 2016 Phys. Fluids 28 866
[26] 周建臣, 耿兴国, 林可君, 张永建, 臧渡洋 2014 物理学报 63 216801
Google Scholar
Zhou J C, Geng X G, Lin K J, Zhang Y J, Zang D Y 2014 Acta Phys. Sin. 63 216801
Google Scholar
[27] Oh J M, Ko S H, Kang K H 2008 Langmuir 24 8379
Google Scholar
[28] Lee J, Park J K, Hong J, Lee S J, Kang K H, Hwang H J 2014 Phys. Rev. E 90 033017
Google Scholar
[29] Moláček J, Bush J W M 2012 Phys. Fluids 24 127103
Google Scholar
[30] Thoraval M J, Thoroddsen S T 2013 Phys. Rev. E 88 061001
Google Scholar
[31] De Ruiter J, Lagraauw R, Van Den Ende D, Mugele F 2015 Nat. Phys. 11 48
Google Scholar
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