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In order to further explore the oscillation mechanism of constrained droplets in microgravity and extend the application and management of space fluid, the small-amplitude self-excited oscillation processes of droplets that are pinned on a confined substrate are investigated. The substrate has a 5 mm diameter contact circle, which is implemented through the use of a drop tower and high-speed photography technology. Oscillation is a recovery procedure for droplet configuration in microgravity with the confined effect at the boundary, making the contact line and diameter unchanged throughout the entire process. A self-excited oscillation could be divided into two stages: a morphological change process and a small-amplitude damping attenuation oscillation. The first stage is a morphological change process, where the heights of high and low oscillations rise gradually, which in turn correspond to the variation of gravity. And the deformation rate is inversely proportional to the droplet size. The second stage is the small-amplitude damping attenuation oscillation around the equilibrium position until it reaches the final steady state in microgravity. At this stage, the frequency is nearly constant and the attenuation of amplitude represents an exponential damping, like the free oscillation of isolated viscous droplets. The pinning contact line makes the oscillation waveform deviate from sine curve and in the process there exists a period when the heights keep constant at some positions, such as the highest, lowest and others. Studies confirm the hypothesis that the oscillation occurs with the similar second-order mode of free drop when the height fluctuates, and the third-order mode when the height is immobile. This is in agreement with the spectral analysis. Furthermore, when the liquid volume varies within this experimental system, the pinning constraint with fixed contact area on the confined substrate can generate droplets with various static contact angles and undisturbed radii. The deformation stage and oscillation mode of the droplets remains stable, although the concrete courses differ in some ways. In the case of bigger drops, the phenomenon of height unchanging should be in the middle position and vanishes with time. However, the smaller one shows no signs for this condition, and the waveform remains consistent all around. In the second stage, the amplitude decay damping rate and non-dimensional frequency of small droplet are higher.
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Keywords:
- microgravity /
- confined substrate /
- self-excited oscillation /
- droplet volume
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[2] Lamb H 1932 Hydrodynamics (London: Cambridge University)
[3] Apfel R E, Tian Y, Jankovsky J, Shi T, Chen X, Holt R G, Trinh E, Croonquist A, Thornton K C, Sacco A Jr., Coleman C, Leslie F W, Matthiesen D H 1997 Phys. Rev. Lett. 78 1912
[4] Busse F H 1984 J. Fluid Mech. 142 1
[5] Patzek T W, Basaran O A, Benner R E, Scriven L E 1995 J. Comput. Phys. 116 3
[6] Miller C A, Scriven L E 1968 J. Fluid Mech. 32 417
[7] Basaran O A, Scott T C, Byers C H 1989 AIChE J. 35 1263
[8] Tsamopoulos J A, Brown R A 1983 J. Fluid Mech. 127 519
[9] Patzek T W, Benner R E, Basaran O A, Scriven L E 1991 J. Comput. Phys. 97 489
[10] Noblin X, Buguin A, Brochard W F 2004 Eur. Phys. J. E 14 395
[11] Zhou J C, Geng X G, Lin K J, Zhang Y J, Zhang D Y 2014 Acta Phys. Sin. 63 216801(in Chinese) [周建臣, 耿兴国, 林可君, 张永建, 臧渡洋 2014 物理学报 63 216801]
[12] Jiang C G, Shi L T, Zhou P, Wu C W 2011 Chin. Sci. Bull. 56 3082
[13] Mukherjee S, Johnson W L, Rhim W K 2005 Appl. Phys. Lett. 86 014104
[14] Franses E I, Basaran O A, Chang C H 1996 Curr. Opin. Colloid Interface Sci. 1 296
[15] Basaran O A, Depaoli D W 1994 Phys. Fluids 6 2923
[16] James A J, Vukasinovic B, Smith M K, Glezer A 2003 J. Fluid Mech. 476 1
[17] James A J, Vukasinovic B, Smith M K, Glezer A 2003 J. Fluid Mech. 476 29
[18] Daniel S, Chaudhury M K, De Gennes P G 2005 Langmuir 21 4240
[19] Celestini F, Kofman R 2006 Phys. Rev. E 73 041602
[20] Fujii H, Matsumoto T, Nogi K 2000 Acta Mater. 48 2933
[21] Liang R, Chen Z 2009 Microgravity Sci. Technol. 21 247
[22] Bisch C, Lasek A, Rodot H 1982 J. Mec. Theor. Appl 1 165
[23] Basaran O A, DePaoli D W 1994 Phys. Fluids 6 2923
[24] Lopez C A, Hirsa A H 2008 Nat. Photon. 2 610
[25] Jonas A, Karadag Y, Tasaltin N, Kucukkara I, Kiraz A 2011 Langmuir 27 2150
[26] Rodot H, Bisch C, Lasek A 1979 Acta Astronaut. 6 1083
[27] Strani M, Sabetta F 1984 J. Fluid. Mech. 141 223
[28] Strani M, Sabetta F 1988 J. Fluid. Mech. 189 397
[29] Siekmann J, Schilling U 1989 Appl. Microgravity Technol. 2 17
[30] Olgac U, Izbassarov D 2013 Comput. Fluids 77 152
[31] Bostwick J B, Steen P H 2009 Phys. Fluids 21 032108
[32] Theisen E A, Vogel M J, Lopez C A, Hirsa A H, Steen P H 2007 J. Fluid Mech. 580 495
[33] Ramalingam S, Ramkrishna D, Basaran O A 2012 Phys. Fluids 24 082102
[34] Zhu Z Q, Wang Y, Liu Q S, Xie J C 2012 Microgravity Sci. Technol. 24 181
[35] Zhu Z Q, Brutin D, Liu Q S, Wang Y, Mourembles A, Xie J C, Tadrist L 2010 Microgravity Sci. Technol. 22 339
[36] Wu S, Li W B, Shi F, Jiang S C, Lan D, Wang Y R 2015 Acta Phys. Sin. 64 96101(in Chinese) [吴赛, 李伟斌, 石峰, 蒋世春, 蓝鼎, 王育人 2015 物理学报 64 96101]
[37] Zhang W B 2013 Ph. D. Dissertation (Beijing: Institute of Physics, Chinese Academy of Sciences) (in Chinese) [张文彬 2013 博士学位论文(北京: 中国科学院物理研究所)] 2150
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[1] Rayleigh J 1879 Proc. R. So. London 29 71
[2] Lamb H 1932 Hydrodynamics (London: Cambridge University)
[3] Apfel R E, Tian Y, Jankovsky J, Shi T, Chen X, Holt R G, Trinh E, Croonquist A, Thornton K C, Sacco A Jr., Coleman C, Leslie F W, Matthiesen D H 1997 Phys. Rev. Lett. 78 1912
[4] Busse F H 1984 J. Fluid Mech. 142 1
[5] Patzek T W, Basaran O A, Benner R E, Scriven L E 1995 J. Comput. Phys. 116 3
[6] Miller C A, Scriven L E 1968 J. Fluid Mech. 32 417
[7] Basaran O A, Scott T C, Byers C H 1989 AIChE J. 35 1263
[8] Tsamopoulos J A, Brown R A 1983 J. Fluid Mech. 127 519
[9] Patzek T W, Benner R E, Basaran O A, Scriven L E 1991 J. Comput. Phys. 97 489
[10] Noblin X, Buguin A, Brochard W F 2004 Eur. Phys. J. E 14 395
[11] Zhou J C, Geng X G, Lin K J, Zhang Y J, Zhang D Y 2014 Acta Phys. Sin. 63 216801(in Chinese) [周建臣, 耿兴国, 林可君, 张永建, 臧渡洋 2014 物理学报 63 216801]
[12] Jiang C G, Shi L T, Zhou P, Wu C W 2011 Chin. Sci. Bull. 56 3082
[13] Mukherjee S, Johnson W L, Rhim W K 2005 Appl. Phys. Lett. 86 014104
[14] Franses E I, Basaran O A, Chang C H 1996 Curr. Opin. Colloid Interface Sci. 1 296
[15] Basaran O A, Depaoli D W 1994 Phys. Fluids 6 2923
[16] James A J, Vukasinovic B, Smith M K, Glezer A 2003 J. Fluid Mech. 476 1
[17] James A J, Vukasinovic B, Smith M K, Glezer A 2003 J. Fluid Mech. 476 29
[18] Daniel S, Chaudhury M K, De Gennes P G 2005 Langmuir 21 4240
[19] Celestini F, Kofman R 2006 Phys. Rev. E 73 041602
[20] Fujii H, Matsumoto T, Nogi K 2000 Acta Mater. 48 2933
[21] Liang R, Chen Z 2009 Microgravity Sci. Technol. 21 247
[22] Bisch C, Lasek A, Rodot H 1982 J. Mec. Theor. Appl 1 165
[23] Basaran O A, DePaoli D W 1994 Phys. Fluids 6 2923
[24] Lopez C A, Hirsa A H 2008 Nat. Photon. 2 610
[25] Jonas A, Karadag Y, Tasaltin N, Kucukkara I, Kiraz A 2011 Langmuir 27 2150
[26] Rodot H, Bisch C, Lasek A 1979 Acta Astronaut. 6 1083
[27] Strani M, Sabetta F 1984 J. Fluid. Mech. 141 223
[28] Strani M, Sabetta F 1988 J. Fluid. Mech. 189 397
[29] Siekmann J, Schilling U 1989 Appl. Microgravity Technol. 2 17
[30] Olgac U, Izbassarov D 2013 Comput. Fluids 77 152
[31] Bostwick J B, Steen P H 2009 Phys. Fluids 21 032108
[32] Theisen E A, Vogel M J, Lopez C A, Hirsa A H, Steen P H 2007 J. Fluid Mech. 580 495
[33] Ramalingam S, Ramkrishna D, Basaran O A 2012 Phys. Fluids 24 082102
[34] Zhu Z Q, Wang Y, Liu Q S, Xie J C 2012 Microgravity Sci. Technol. 24 181
[35] Zhu Z Q, Brutin D, Liu Q S, Wang Y, Mourembles A, Xie J C, Tadrist L 2010 Microgravity Sci. Technol. 22 339
[36] Wu S, Li W B, Shi F, Jiang S C, Lan D, Wang Y R 2015 Acta Phys. Sin. 64 96101(in Chinese) [吴赛, 李伟斌, 石峰, 蒋世春, 蓝鼎, 王育人 2015 物理学报 64 96101]
[37] Zhang W B 2013 Ph. D. Dissertation (Beijing: Institute of Physics, Chinese Academy of Sciences) (in Chinese) [张文彬 2013 博士学位论文(北京: 中国科学院物理研究所)] 2150
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