Eur. Phys. J. E (2016) 39: 106
https://doi.org/10.1140/epje/i2016-16106-6

Tips and Tricks

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

¹ Physics of Fluids group, Department of Science and Technology, Mesa+ Institute, and J. M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500, AE Enschede, The Netherlands
² Soft Matter & Interfaces Group, School of Engineering, RMIT University, VIC 3001, Melbourne, Australia
³ Center for Combustion Energy & Department of Thermal Engineering, Tsinghua University, Beijing, China
⁴ Max Planck Institute for Dynamics and Self-Organization, 37077, Göttingen, Germany

^* e-mail: h.tan@utwente.nl
^** e-mail: xuehua.zhang@rmit.edu.au
^*** e-mail: d.lohse@utwente.nl

Received: 6 September 2016
Accepted: 14 October 2016
Published online: 15 November 2016

Abstract

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.