Variation of average coordination number with liquid fraction for two-dimensional foams with finite contact angle

ABSTRACT

We present Surface Evolver computer simulations for two-dimensional (2d) foams in which the contact angle at which liquid films and Plateau borders meet is non-zero. We determine the average coordination number Z of bubbles over a wide range of finite contact angles θ and liquid fractions ϕ. We find a linear scaling of Z for values of ϕ between about 0.07 and 0.15, corroborating previous data obtained for the case of zero contact angle. The results highlight the importance of attractive bubble interactions for 2d foams.

KEYWORDS:

• Bubbles
• foams
• films

Acknowledgments

This work is supported by the National Natural Science Foundation of China (No. 51706173), China Postdoctoral Science Foundation (No. 2017M613131), Foundation of China Scholarship Council, Shaanxi Province Postdoctoral Science Foundation (No. 2017BSHEDZZ43), Science Foundation Ireland (SFI) (grant number 13/IA/1926) and the European Space Agency project ‘Soft Matter Dynamics’ (contracts 4000115113 and 4000129502). We would like to thank K. Brakke for sharing and supporting the Surface Evolver software. We also thank the reviewers for their suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (No. 51706173), China Postdoctoral Science Foundation (No. 2017M613131), Foundation of China Scholarship Council and Shaanxi Province Postdoctoral Science Foundation (No. 2017BSHEDZZ43). Further support was supported by a research grant from Science Foundation Ireland (SFI) (grant number 13/IA/1926). We would like to thank K. Brakke for sharing and supporting the Surface Evolver software. SH and SC acknowledge funding from the European Space Agency for the ‘Soft Matter Dynamics’ projects, contracts 4000115113 and 4000129502.