Theoretical and experimental study of capillary bridges between two parallel planes

Abstract

Based on the solution of Young-Laplace equation using an inverse problem method for unknown capillary pressure, the exact parameterisation of the convex meridional profile of capillary bridges between two planar surfaces is presented in this paper. Mainly, two shapes of liquid bridges are discussed: nodoid and unduloid. In each case, from a set of observable data, we determine the exact parameterisation of the capillary bridges and their associated geometrical properties. The capillary pressure is recovered without direct measurements. The comparisons between the theory and the experiment demonstrate the accuracy of the analytical calculations.

Keywords:

• Capillary bridge
• capillary force
• Young-Laplace equation
• experimental measurement
• constant mean curvature

Acknowledgments

The authors would like to express their sincere gratitude to Stephan Devic, Boleslaw Mielniczuk and Moulay Saïd El Youssoufi from University of Montpellier as well as Bruno Peraudeau and Mathieu Lemaire from University of La Rochelle for their great assistance in the installation of experimental apparatus.

Notes

1 In particular case of identical planes, since $y_{c1}=y_{c2}=y_c$ and ${\theta }_1={\theta }_2,$ the compatibility condition is automatically satisfied and not required.

2 Telecentric light-rays reduce unwanted reflexion, telecentric lens avoid image distortion.

3 In optics, Depth of Field (DoF) is the distance where an object is sharp in the captured photo.

Additional information

Funding

The described research was funded in part by the French National Center for Space Studies (CNES) and the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No. 832405 (ICARUS).