3D spherical-cap fitting procedure for (truncated) sessile nano- and micro-droplets & -bubbles

  • Huanshu Tan
  • Shuhua Peng
  • Chao Sun
  • Xuehua Zhang
  • Detlef Lohse
Tips and Tricks


In the study of nanobubbles, nanodroplets or nanolenses immobilised on a substrate, a cross-section of a spherical cap is widely applied to extract geometrical information from atomic force microscopy (AFM) topographic images. In this paper, we have developed a comprehensive 3D spherical-cap fitting procedure (3D-SCFP) to extract morphologic characteristics of complete or truncated spherical caps from AFM images. Our procedure integrates several advanced digital image analysis techniques to construct a 3D spherical-cap model, from which the geometrical parameters of the nanostructures are extracted automatically by a simple algorithm. The procedure takes into account all valid data points in the construction of the 3D spherical-cap model to achieve high fidelity in morphology analysis. We compare our 3D fitting procedure with the commonly used 2D cross-sectional profile fitting method to determine the contact angle of a complete spherical cap and a truncated spherical cap. The results from 3D-SCFP are consistent and accurate, while 2D fitting is unavoidably arbitrary in the selection of the cross-section and has a much lower number of data points on which the fitting can be based, which in addition is biased to the top of the spherical cap. We expect that the developed 3D spherical-cap fitting procedure will find many applications in imaging analysis.

Graphical abstract


Tips and Tricks 

Supplementary material (619 kb)
Supplementary material


  1. 1.
    Detlef Lohse, Xuehua Zhang, Rev. Mod. Phys. 87, 981 (2015)ADSCrossRefGoogle Scholar
  2. 2.
    S. Lou, Z. Ouyang, Y. Zhang, X. Li, J. Hu, M. Li, F. Yang, J. Vac. Sci. Technol. B 18, 2573 (2000)CrossRefGoogle Scholar
  3. 3.
    N. Ishida, T. Inoue, M. Miyahara, K. Higashitani, Langmuir 16, 6377 (2000)CrossRefGoogle Scholar
  4. 4.
    Xuehua Zhang, William Ducker, Langmuir 23, 12478 (2007)CrossRefGoogle Scholar
  5. 5.
    D. Lohse, X. Zhang, Phys. Rev. E 91, 031003(R) (2015)ADSCrossRefGoogle Scholar
  6. 6.
    Sean R. German, Xi Wu, Hongjie An, Vincent S.J. Craig, Tony L. Mega, Xuehua Zhang, ACS Nano 8, 6193 (2014)CrossRefGoogle Scholar
  7. 7.
    Rongguang Wang, Li Cong, Mitsuo Kido, Appl. Surf. Sci. 191, 74 (2002)ADSCrossRefGoogle Scholar
  8. 8.
    X.H. Zhang, N. Maeda, V.S.J. Craig, Langmuir 22, 5025 (2006)CrossRefGoogle Scholar
  9. 9.
    X.H. Zhang, A. Quinn, W.A. Ducker, Langmuir 24, 4756 (2008)CrossRefGoogle Scholar
  10. 10.
    A.C. Simonsen, P.L. Hansen, B. Klösgen, J. Colloid Interface Sci. 273, 291 (2004)CrossRefGoogle Scholar
  11. 11.
    Md. Hemayet Uddin, Sin Ying Tan, Raymond R. Dagastine, Langmuir 27, 2536 (2011)CrossRefGoogle Scholar
  12. 12.
    Xingya Wang, Binyu Zhao, Wangguo Ma, Ying Wang, Xingyu Gao, Renzhong Tai, Xingfei Zhou, Lijuan Zhang, ChemPhysChem 16, 1003 (2015)CrossRefGoogle Scholar
  13. 13.
    Lijuan Zhang, Chunlei Wang, Renzhong Tai, Jun Hu, Haiping Fang, ChemPhysChem 13, 2188 (2012)CrossRefGoogle Scholar
  14. 14.
    Chenglong Xu, Shuhua Peng, Greg O. Qiao, V. Gutowski, D. Lohse, Xuehua Zhang, Soft Matter 10, 7857 (2014)ADSCrossRefGoogle Scholar
  15. 15.
    Shuhua Peng, Detlef Lohse, Xuehua Zhang, ACS Nano 9, 11916 (2015)CrossRefGoogle Scholar
  16. 16.
    J. Yang, J. Duan, D. Fornasiero, J. Ralston, J. Phys. Chem. B 107, 6139 (2003)CrossRefGoogle Scholar
  17. 17.
    F. Mugele, T. Becker, R. Nikopoulos, M. Kohonen, S. Herminghaus, J. Adhes. Sci. Technol. 16, 951 (2002)CrossRefGoogle Scholar
  18. 18.
    Antonio Méndez-Vilas, Ana Belén Jódar-Reyes, María Luisa González-Martín, Small 5, 1366 (2009)CrossRefGoogle Scholar
  19. 19.
    B.M. Borkent, S. de Beer, F. Mugele, D. Lohse, Langmuir 26, 260 (2010)CrossRefGoogle Scholar
  20. 20.
    B. Song, W. Walczyk, H. Schönherr, Langmuir 27, 8223 (2011)CrossRefGoogle Scholar
  21. 21.
    R. Garcia, R. Perez, Surf. Sci. Rep. 47, 197 (2002)ADSCrossRefGoogle Scholar
  22. 22.
    Anoop Chengara, Alex D. Nikolov, Darsh T. Wasan, Andrij Trokhymchuk, Douglas Henderson, J. Colloid Interface Sci. 280, 192 (2004)CrossRefGoogle Scholar
  23. 23.
    David N. Sibley, Andreas Nold, Nikos Savva, Serafim Kalliadasis, J. Eng. Math. 94, 19 (2014)CrossRefGoogle Scholar
  24. 24.
    Shuhua Peng, Ivan Dević, Huanshu Tan, Detlef Lohse, Xuehua Zhang, Langmuir 32, 5744 (2016)CrossRefGoogle Scholar
  25. 25.
    Varghese Mathai, Vivek N. Prakash, Jon Brons, Chao Sun, Detlef Lohse, Phys. Rev. Lett. 115, 124501 (2015)ADSCrossRefGoogle Scholar
  26. 26.
    Vivek N. Prakash, Yoshiyuki Tagawa, Enrico Calzavarini, Julián Martínez Mercado, Federico Toschi, Detlef Lohse, Chao Sun, New J. Phys. 14, 105017 (2012)CrossRefGoogle Scholar
  27. 27.
    Dana H. Ballard, Pattern Recognition 13, 111 (1981)CrossRefGoogle Scholar
  28. 28.
    Erik Reinhard, Wolfgang Heidrich, Paul Debevec, Sumanta Pattanaik, Greg Ward, Karol Myszkowski, High Dynamic Range Imaging: Acquisition, Display, and Image-Based Lighting (Morgan Kaufmann, 2010)Google Scholar
  29. 29.
    M.J.E. Najafabadi, H. Pourghassem, in Intelligent Computation and Bio-Medical Instrumentation (ICBMI), 2011 International Conference on, (IEEE, 2011) pp. 60--63Google Scholar
  30. 30.
    E. Roy Davies, Computer and Machine Vision: Theory, Algorithms, Practicalities (Academic Press, 2012)Google Scholar
  31. 31.
    Daniel Bonn, Jens Eggers, Joseph Indekeu, Jacques Meunier, Etienne Rolley, Rev. Mod. Phys. 81, 739 (2009)ADSCrossRefGoogle Scholar
  32. 32.
    J.M. Stauber, S.K. Wilson, B.R. Duffy, K. Sefiane, J. Fluid Mech. 744, R2 (2014)ADSCrossRefGoogle Scholar
  33. 33.
    C.W. Extrand, Sung In Moon, Langmuir 28, 7775 (2012)CrossRefGoogle Scholar
  34. 34.
    Ying Zhang, Dominique Chatain, Shelley L. Anna, Stephen Garoff, J. Colloid Interface Sci. 462, 88 (2016)CrossRefGoogle Scholar
  35. 35.
    Michael J. Neeson, Rico F. Tabor, Franz Grieser, Raymond R. Dagastine, Derek Y.C. Chan, Soft Matter 8, 11042 (2012)ADSCrossRefGoogle Scholar
  36. 36.
    L. Mahadevan, M. Adda-Bedia, Y. Pomeau, J. Fluid Mech. 451, 411 (2002)ADSMathSciNetCrossRefGoogle Scholar
  37. 37.
    Jan Guzowski, Piotr Garstecki, Phys. Rev. Lett. 114, 188302 (2015)CrossRefGoogle Scholar
  38. 38.
    Daniela J. Kraft, Wessel S. Vlug, Carlos M. van Kats, Alfons van Blaaderen, Arnout Imhof, Willem K. Kegel, J. Am. Chem. Soc. 131, 1182 (2009)CrossRefGoogle Scholar
  39. 39.
    Daniela J. Kraft, Jan Hilhorst, Maria A.P. Heinen, Mathijs J. Hoogenraad, Bob Luigjes, Willem K. Kegel, J. Phys. Chem. B 115, 7175 (2011)CrossRefGoogle Scholar
  40. 40.
    Kyoo-Chul Park, Philseok Kim, Alison Grinthal, Neil He, David Fox, James C. Weaver, Joanna Aizenberg, Nature 531, 78 (2016)ADSCrossRefGoogle Scholar
  41. 41.
    Sanjay S. Latthe, Chiaki Terashima, Kazuya Nakata, Akira Fujishima, Molecules 19, 4256 (2014)CrossRefGoogle Scholar
  42. 42.
    Ma Qian, Jie Ma, J. Chem. Phys. 130, 214709 (2009)ADSCrossRefGoogle Scholar
  43. 43.
    Hans J. Ensikat, Petra Ditsche-Kuru, Christoph Neinhuis, Wilhelm Barthlott, Beilstein J. Nanotechnol. 2, 152 (2011)CrossRefGoogle Scholar
  44. 44.
    Bin Liu, Yaning He, Yin Fan, Xiaogong Wang, Macromol. Rapid Commun. 27, 1859 (2006)CrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Huanshu Tan
    • 1
  • Shuhua Peng
    • 2
  • Chao Sun
    • 3
    • 1
  • Xuehua Zhang
    • 2
    • 1
  • Detlef Lohse
    • 1
    • 4
  1. 1.Physics of Fluids group, Department of Science and Technology, Mesa+ Institute, and J. M. Burgers Centre for Fluid DynamicsUniversity of TwenteAE EnschedeThe Netherlands
  2. 2.Soft Matter & Interfaces Group, School of EngineeringRMIT UniversityMelbourneAustralia
  3. 3.Center for Combustion Energy & Department of Thermal EngineeringTsinghua UniversityBeijingChina
  4. 4.Max Planck Institute for Dynamics and Self-OrganizationGöttingenGermany

Personalised recommendations