Simple views on different problems in physics: from drag friction to tough biological materials

Abstract

We discuss the dynamics of bubbles and liquid drops in quasi two dimensions, i.e. in the Hele-Shaw cell, confirming different scaling laws for viscous drag friction, together with scaling laws for a number of related phenomena. Motivated by the study on viscous drag friction, we describe an experiment on drag friction in a granular medium, which reveals a length scale that diverges towards the jamming transition. These examples in the dynamics of viscous fluid and granular materials underscore the importance of the scaling concept in understanding physical phenomena, often vindicated by a clear data collapse by virtue of a corresponding scaling law. To demonstrate the universal usefulness of the strategy, we discuss another different example from the strength of biological materials. To stress a wide applicability of the scaling approach, we introduce the robustness of scaling laws and justify frequent emergence of the robustness.

Keywords:

• scaling laws
• drag friction
• jamming transition
• strength of biological materials

Acknowledgements

The author is most grateful to the late Pierre-Gilles de Gennes, Françoise Brochard and David Quéré for what the author has been given through discussions, articles and textbooks such as [4,5,35]. The author thanks Hisao Hayakawa and Satoshi Takada (both, Kyoto University) for discussions on granular drag friction.

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was partly supported by Grant-in-Aid for Scientific Research (A) No. [24244066] of JSPS, Japan, and by ImPACT Program of Council for Science, Technology and Innovation (Cabinet Office, Government of Japan).