Bouncing droplets of water

Michael Tsynkov; Isabel Chang; Ava Khoudary; Matt Greenwolfe

doi:10.3934/cac.2025014

Article Contents

December 2025, Volume 6, 19-31. Doi: 10.3934/cac.2025014

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Bouncing droplets of water

1.
Green Hope High School, Cary, NC 27519, USA
2.
University of Chicago, Chicago, IL 60637, USA
3.
Cary Academy, Cary, NC 27513, USA

^*Corresponding author: Michael Tsynkov
^*Corresponding author: Michael Tsynkov

Received: May 2025

Revised: June 2025

Published online: June 23, 2025

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Abstract

Understanding the mechanisms behind a drop of water spinning after bouncing on a hydrophobic surface with a hydrophilic pattern can be of interest for various applications, e.g., in engineering or biology. We studied this phenomenon both theoretically and experimentally. On the theoretical side, we analyzed the relationship between the droplet shape and its rotation speed under surface tension, assuming certain symmetries of the shape: a flattened cylinder, an oblate spheroid, and a rudimentary derivation for a general body of revolution. Our experimental setup consisted of soot atop glass slides for the hydrophobic surface and hydrophilic pattern. Despite a lack of accurate control of both pattern reproducibility and the experimental environment, we were able to experimentally corroborate our theory that uses surface tension to predict the relation between the shape and angular velocity of the droplet after bouncing off a hydrophobic surface with a given hydrophilic pattern.

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Mathematics Subject Classification: Primary: 76U99, 76B45, 76-05.

Citation:

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Figure 1. Cross-section of a finite-thickness disk with a rounded edge

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Figure 2. Camera used

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Figure 3. Lighting setup

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Figure 4. Droplet falling onto glass pane

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Figure 5. Angular velocity vs. $ a $ of study [4] and our measured data

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Figure 6. Angular velocity vs. $ a $ for two methods of evaluation

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Figure 7. Shape of the spinning droplet due to a four-pronged etched pattern

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Figure 8. Etched patterns: two-pronged (8a), three-pronged (8b), and four-pronged (8c)

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Figure 9. Angular velocity vs. $ a $ for two-pronged etched pattern (blue color) and four-pronged etched pattern (yellow color with black error bars)

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Figure 10. Angular velocity vs. $ a $ for three-pronged etched pattern (purple color) and four-pronged etched pattern (yellow color with black error bars)

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References

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