Abstract
The spontaneous migration of droplets on conical fibers is studied experimentally by depositing silicone oil droplets onto conical glass fibers. Their motion is recorded using optical microscopy and analyzed to extract the relevant geometrical parameters of the system. The speed of the droplet can be predicted as a function of geometry and the fluid properties using a simple theoretical model, which balances viscous dissipation against the surface tension driving force. The experimental data are found to be in good agreement with the model.
Graphic abstract
Similar content being viewed by others
Data Availability Statement
This manuscript has associated data in a data repository. [Authors’ comment: Please contact the corresponding author for data.]
References
Q. Wang, X. Yao, H. Liu, D. Quéré, L. Jiang, Proc. Natl. Acad. Sci. USA 112, 9247 (2015)
C. Duprat, S. Protiere, A. Beebe, H. Stone, Nature 482, 510 (2012)
Y. Zheng, H. Bai, Z. Huang, X. Tian, F.Q. Nie, Y. Zhao, J. Zhai, L. Jiang, Nature 463, 640 (2010)
A.R. Parker, C.R. Lawrence, Nature 414, 33 (2001)
Z. Pan, W.G. Pitt, Y. Zhang, N. Wu, Y. Tao, T.T. Truscott, Nat. Plants 2, 16076 (2016)
J. Ju, H. Bai, Y. Zheng, T. Zhao, R. Fang, L. Jiang, Nat. Commun. 3, 1247 (2012)
L. Guo, G. Tang, Int. J. Heat Mass Transf. 84, 198 (2015)
C. Luo, Langmuir 31, 11809 (2015)
F.T. Malik, R.M. Clement, D.T. Gethin, D. Beysens, R.E. Cohen, W. Krawszik, A.R. Parker, Bioinspir. Biomim. 10, 036005 (2015)
K. Li, J. Ju, Z. Xue, J. Ma, L. Feng, S. Gao, L. Jiang, Nat. Commun. 4, 2276 (2013)
J. Ju, K. Xiao, X. Yao, H. Bai, L. Jiang, Adv. Mater. 25, 5937 (2013)
X. Heng, M. Xiang, Z. Lu, C. Luo, A.C.S. Appl, Mater. Interfaces 6, 8032 (2014)
Y. Peng, Y. He, S. Yang, S. Ben, M. Cao, K. Li, K. Liu, L. Jiang, Adv. Funct. Mater. 25, 5967 (2015)
M. Cao, J. Ju, K. Li, S. Dou, K. Liu, L. Jiang, Adv. Funct. Mater. 24, 3235 (2014)
T. Xu, Y. Lin, M. Zhang, W. Shi, Y. Zheng, ACS Nano 10, 10681 (2016)
T.S. Chan, F. Yang, A. Carlson, J. Fluid Mech. 894, A26 (2020)
B. Carroll, J. Colloid Interface Sci. 57, 488 (1976)
B. Carroll, Langmuir 2, 248 (1986)
H. Bai, X. Tian, Y. Zheng, J. Ju, Y. Zhao, L. Jiang, Adv. Mater. 22, 5521 (2010)
Y. Hou, L. Gao, S. Feng, Y. Chen, Y. Xue, L. Jiang, Y. Zheng, Chem. Commun. 49, 5253 (2013)
A.L. Yarin, W. Liu, D.H. Reneker, J. Appl. Phys. 91, 4751 (2002)
Y. Chen, L. Wang, Y. Xue, L. Jiang, Y. Zheng, Sci. Rep. 3, 2927 (2013)
T. Gilet, D. Terwagne, N. Vandewalle, Appl. Phys. Lett. 95, 014106 (2009)
T. Gilet, D. Terwagne, N. Vandewalle, Eur. Phys. J. E. 31, 253 (2010)
I.L. Kliakhandler, S.H. Davis, S.G. Bankoff, J. Fluid Mech. 429, 381 (2001)
É. Lorenceau, D. Quéré, J. Fluid Mech. 510, 29 (2004)
S. Michielsen, J. Zhang, J. Du, H.J. Lee, Langmuir 27, 11867 (2011)
J.L. Liu, R. Xia, B.W. Li, X.Q. Feng, Chin. Phys. Lett. 24, 3210 (2007)
Y.E. Liang, H.K. Tsao, Y.J. Sheng, Langmuir 31, 1704 (2015)
X. Tan, T. Shi, Z. Tang, B. Sun, L. Du, Z. Peng, G. Liao, J. Bionic Eng. 13, 364 (2016)
M.E.R. Shanahan, Langmuir 27, 14919 (2011)
T.S. Chan, C. Pedersen, J. Koplik, A. Carlson, preprint (https://arxiv.org/abs/2008.03058)
E.Q. Li, S.T. Thoroddsen, Phys. Fluids 25, 052105 (2013)
C. Lv, C. Chen, Y.C. Chuang, F.G. Tseng, Y. Yin, F. Grey, Q. Zheng, Phys. Rev. Lett. 113, 026101 (2014)
J. McCarthy, D. Vella, A.A. Castrejón-Pita, Soft Matter 15, 9997 (2019)
M. Reyssat, L. Courbin, E. Reyssat, H.A. Stone, J. Fluid Mech. 615, 335 (2008)
P. Renvoisé, J. Bush, M. Prakash, D. Quéré, Europhys. Lett. 86, 64003 (2009)
J.W. Bush, F. Peaudecerf, M. Prakash, D. Quéré, Adv. Colloid Interface Sci. 161, 10 (2010)
Z. Wang, C.C. Chang, S.J. Hong, Y.J. Sheng, H.K. Tsao, Phys. Rev. E 87, 062401 (2013)
E. Reyssat, J. Fluid Mech. 748, 641 (2014)
É. Ruiz-Gutiérrez, C. Semprebon, G. McHale, R. Ledesma-Aguilar, J. Fluid Mech. 842, 26 (2018)
J. Bico, B. Roman, L. Moulin, A. Boudaoud, Nature 432, 690 (2004)
C. Duprat, J.M. Aristoff, H.A. Stone, J. Fluid Mech. 679, 641 (2011)
J.M. Aristoff, C. Duprat, H.A. Stone, Int. J. Non Linear Mech. 46, 648 (2011)
M. Taroni, D. Vella, J. Fluid Mech. 712, 273 (2012)
J. Bico, É. Reyssat, B. Roman, Annu. Rev. Fluid Mech. 50, 629 (2018)
S. Haefner, M. Benzaquen, O. Bäumchen, T. Salez, R. Peters, J.D. McGraw, K. Jacobs, E. Raphaël, K. Dalnoki-Veress, Nat. Commun. 6, 1 (2015)
P. de Gennes, F. Brochard-Wyart, D. Quéré, Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves (Springer, New York, 2003).
R.J. Roe, J. Colloid Interface Sci. 50, 70 (1975)
G. McHale, M. Newton, B. Carroll, Oil Gas Sci. Technol. 56, 47 (2001)
Acknowledgements
The authors are grateful to Michael Brook and Dan Chen for providing the silicone oils, and to Tak Shing Chan and Andreas Carlson for extensive discussions. The financial support by the Natural Science and Engineering Research Council of Canada is gratefully acknowledged.
Author information
Authors and Affiliations
Contributions
CF, RDS and KDV designed the research project, CF performed all experiments, all authors contributed to analyzing the data and developing the models, and CF wrote the first draft of the manuscript. All authors edited the manuscript to generate a final version and contributed to discussions.
Corresponding author
Rights and permissions
About this article
Cite this article
Fournier, C., Lee, C.L., Schulman, R.D. et al. Droplet migration on conical fibers. Eur. Phys. J. E 44, 12 (2021). https://doi.org/10.1140/epje/s10189-021-00014-z
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epje/s10189-021-00014-z