DOI QR코드

DOI QR Code

Shape Oscillation and Detachment of Droplet on Vibrating Flat Surface

진동하는 평판 위의 액적의 형상 진동 및 제거 조건에 대한 연구

  • Received : 2013.11.16
  • Accepted : 2014.01.22
  • Published : 2014.04.01

Abstract

This study aimed to understand the mode characteristics of a droplet subject to periodic forced vibration and the detachment of a droplet placed on a plate surface. An surface was coated with Teflon to clearly observe the behavior of a droplet. The contact angle between the droplet and surface and the hysteresis were found to be approximately $115^{\circ}C$ and within $25^{\circ}C$, respectively. The coating process was performed in a clean room that had an environment with a low level of contaminants and impurities such as air dust, detergents, and particles. To predict the resonance frequency of a droplet, theoretical and experimental approaches were applied. Two high-speed cameras were configured to acquire side and top views and thus capture different characteristics of a droplet: the mode shape, the detachment, the separated secondary droplet, and the waggling motion. A comparison of the theoretical and experimental results shows no more than 18 discrepancies when predicting the resonance frequency. These differences seem to be caused by contact line friction, nonlinear wall adhesion, and the uncertainty of the experiment. For lower energy inputs, the contact line of the droplet was pinned and the oscillation pattern was axisymmetric. However, the contact line of the droplet was de-pinned as the oscillation became more vigorous with increased energy input. The size of each lobe at the resonance frequency is somewhat larger than that at the neighboring frequency. A droplet in mode 2, one of the primary mode frequencies, exhibits vertical periodic movement as well as detachment and secondary ejection from the main droplet.

본 연구는 주기적 강제 진동이 가해지는 표면의 액적 모드 특성과 표면에 놓인 액적의 제거에 대한 조건을 실험적으로 이해하는 것을 목적으로 하고 있다. 액적의 거동을 명확하게 관찰하기 위해 아크릴 표면에 Teflon 코팅을 진행하여 접촉각을 높였고, 히스테리시스는 25도 이내로 진행하여 액적의 거동이 보다 쉽게 진행되도록 하였다. 본 실험은 먼지가 적은 청정실에서 실험이 진행되었다. 제작된 소수성 표면에 놓인 액적의 실제 공진 주파수를 예측하기 위해 이론 및 실험적 해석을 통해 두 접근방법의 타당성을 파악하였으며, 두 개의 초고속카메라를 액적의 상면과 측면에 설치하여 2가지 측면에서 액적의 다양한 형상 변형 특성- 모드 형상, 분리, 미소 액적의 발생, 그리고 좌우 비틀림의 특성을 관찰하였다. 이론 값 비교결과 실제 공진 주파수 값들의 차이가 약 18% 이하로 관찰되었으며, 이러한 차이는 접촉선 마찰, 비선형 벽 고착, 실험의 불확실성 등에 가장 큰 영향을 받는 것으로 판단된다. 사용된 스피커에 상대적으로 낮은 전압을 인가할 경우 액적의 접촉선은 고정된 상태에서 좌우 대칭적인 액적 형상진동이 나타났다. 반면, 높은 전압을 인가할 경우 액적의 접촉선은 비고정된 상태가 되면서 더 활발한 형상 진동이 나타났다. 가진 주파수가 모드 주파수와 일치할 경우에는 액적의 로브 크기가 주변부 주파수 일 때 보다 비교적으로 컸으며, 같은 전압을 인가 할 경우, 표면에 놓인 액적의 미소 액적 발생 및 완전한 제거는 2차 모드에서만 진행되는 것을 실험을 통해 규명하였다.

Keywords

References

  1. Lord Rayleigh, 1890, "The Theory of Sound," Macmillan.
  2. Lord Rayleigh, 1879, "The Capillary Phenomena of Jets," Proc R Soc, Vol. 29, pp. 71-97. https://doi.org/10.1098/rspl.1879.0015
  3. Wilkes, E. D. and Basaran, O. A., 1997, "Forced Oscillations of Pendant (Sessile) Drops," Phys. Fluids, Vol. 9, pp. 1512-1528. https://doi.org/10.1063/1.869276
  4. Lundgren, T. S. and Mansour, N. N., 1988, "Oscillation of Drops in Zero Gravity with Weak Vicous Effects," J. Fluid, Vol. 194, pp. 479-510. https://doi.org/10.1017/S0022112088003076
  5. Rodot, H., Bisch, C. and Lasek, A., 1979, "Zero Gravity Simulation of Liquids in Contact with a Solid Surface," Acta Astronaut, Vol. 6, pp. 1083-1092. https://doi.org/10.1016/0094-5765(79)90057-2
  6. Daniel, S., Sircar, S., Gliem, J. and chaudhury, M. K., 2004, "Ratcheting Motion of Liquid Drops on Gradient Surfaces," Langmuir, Vol. 20, pp. 4085-4098. https://doi.org/10.1021/la036221a
  7. Daniel, S., Chaudhury, M. K. and De Gennes, P. G., 2005, "Vibration-Actuated Drop Motion on Surfaces for Batch Microfluidic Processes," Langmuir, Vol. 21, pp. 4240-4248. https://doi.org/10.1021/la046886s
  8. Dong, L., Chaudhury, A. and Chaudhury, M. K., 2006, "Lateral Vibration of a Water Drop and Its Motion on a Vibrating Surface," Eur. Phys. J. E, Vol. 21, pp. 231-242. https://doi.org/10.1140/epje/i2006-10063-7
  9. Noblin, X., Buguin, A. and Brochard-Wyart, F., 2009, "Vibration of Sessile Drops," Eur. Phys. J. Special Topics, Vol. 166, pp. 7-10. https://doi.org/10.1140/epjst/e2009-00869-y
  10. Brunet, P., Eggers, J. and Deegan, R. D., 2009, "Motion of a Drop Driven by Substrate Vibrations," Eur. Phys. J. Special Topics, Vol 166, pp. 11-14. https://doi.org/10.1140/epjst/e2009-00870-6
  11. Hong, F. J., Jiang, D. D. and Cheng, P., 2012, "Frequency-Dependent Resonance and Asymmetric Droplet Oscillation Under AC Electrowetting on Coplanar Electrodes," J. Micromech. Microeng, Vol. 22, pp. 1-9.
  12. Oh, J. M., Ko, S. H. and Kang, K. H., 2008, "Shape Oscillation of a Drop in AC Electowetting," Langmuir, Vol. 24, pp. 8379-8386. https://doi.org/10.1021/la8007359
  13. McHale, G., Elliott, S. J., Newton, M. I., Herbertson, D. L. and Esmer, K., 2009, "Evitation-Free Vibrated Droplets: Resonant Oscillations of Liquid Marbles," Langmuir, Vol. 25, pp. 529-533. https://doi.org/10.1021/la803016f
  14. Sadhal, S. S., Portonovo, S. A. and Jacob, N. C., 1996, "Transport Phenomena with Drops and Bubbles," Springer.
  15. Cho, S. K., Moon, H., and Kim. C. J., 2003, "Creating, Transporting, Cutting, and Merging Liquid Droplet by Electrowetting-Based Actuation for Digital Microfluidic Circuits," J. Microelectromech. Syst, Vol. 12, No. 1, pp. 70-80 https://doi.org/10.1109/JMEMS.2002.807467
  16. Hayes, R. A. and Feenstra, B. J., 2003, "Video-Speed Electronic Paper Based on Electorwetting," Nature, Vol. 425, pp. 383-385 https://doi.org/10.1038/nature01988
  17. Zhou, K., Heikenfeld, J., Dean, K. A., Howard, E. M. and Johnson, M. R., 2009, "A Full Description of a Simple and Scalable Fabrication Process for Electrowetting Displays," J. Micromech. Microeng, Vol. 12, No. 6, 065029
  18. Depaoli, D. W., Feng, J. Q., Basaran, O. A. and Scott, T. C., 1995, "Hysteresis in Forced Oscillations of Pendant Drops," Phys. Fluids, Vol. 7, pp. 1181-1183. https://doi.org/10.1063/1.868576
  19. Kim, H. Y., 2004, "Drop Fall-off from the Vibrating Ceiling," Phys. Fluids, Vol. 14, No. 2, pp. 474.
  20. Brunet, P., Eggers, J. and Deegan, R. D., 2007, "Vibration-Induced Climbing of Drops," Phys. Rev. Lett, Vol. 99, pp. 144501-1-4. https://doi.org/10.1103/PhysRevLett.99.144501
  21. Matsumoto, T., Fujii, H., Ueda, T., Kamai, M. and Nogi, K., 2005, "Measurement of Surface Tension of Molten Copper Using the Free-Fall Oscillating Drop Method," Meas. Sci. Technol, Vol. 16, pp. 432-437. https://doi.org/10.1088/0957-0233/16/2/014
  22. Yamakita, S., Matsui, Y. and Shiokawa, S., 1999, "New Method for Measurement of Contact Angle (Droplet Free Vibration Frequency Method)," Jpn. J. Appl. Phys, Vol. 38, pp. 3127-3130. https://doi.org/10.1143/JJAP.38.3127
  23. Strani, M. and Sabetta, F., 1984, "Free vibrations of a Drop in Partial Contact with a Solid Support," J. Fluid. Mech, Vol. 141, pp. 233-247. https://doi.org/10.1017/S0022112084000811
  24. Langley, K. R. and Sharp, J. S., 2010, "Microtextured Surfaces with Gradient Wetting Properties," Langmuir, Vol. 26, pp. 18349-18356 https://doi.org/10.1021/la1036212
  25. Lamb, H., 1932, "Hydrodynamics," Cambridge Univ. Press, pp. 461-463.
  26. Lee, S. M., Kang, I. S., 1999, "Three-Dimensional Analysis of the Steady-State Shape and Small Amplitude Oscillation of a Bubble in Uniform and Non-Uniform Electric Fields," J. Fluid. Mech, Vol. 384, pp. 59-91. https://doi.org/10.1017/S0022112098004133
  27. Oh, J. M., Kim, P. J. and Kang, I. S., 2001, "Chaotic Oscillation of a Bubble in a Weakly Viscous Dielectric Fluid Under Electric Fields," Phys. Fluids, Vol. 13, No. 10, pp. 2820-2830. https://doi.org/10.1063/1.1400135
  28. Kim, H. S., Kim, J. S., Kang, H. J., and Kim, S. R., 1999, "An Analysis of Stress Waves in Coated Elastic Half-Space Due to Water Drop Impact," Trans. Korean Soc. Mech. Eng. A, Vol. 23, No.8, pp.1417-1424.