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Rebounding hydrogel sphere water entry

Published online by Cambridge University Press:  13 June 2025

Xiaoyan Ye Open the ORCID record for Xiaoyan Ye [Opens in a new window] ,
Kaizhao Qin ,
Rui Yang Open the ORCID record for Rui Yang [Opens in a new window]  and
Joshua A. Dijksman Open the ORCID record for Joshua A. Dijksman [Opens in a new window]
Xiaoyan Ye*
Affiliation:
Key Laboratory of Mechanics on Disaster and Environment in Western China attached to the Ministry of Education of China, and Department of Mechanics and Engineering Science, School of Civil Engineering and Mechanics, Lanzhou University, Lanzhou, Gansu 730000, PR China
Kaizhao Qin
Affiliation:
Key Laboratory of Mechanics on Disaster and Environment in Western China attached to the Ministry of Education of China, and Department of Mechanics and Engineering Science, School of Civil Engineering and Mechanics, Lanzhou University, Lanzhou, Gansu 730000, PR China
Rui Yang
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
Joshua A. Dijksman
Affiliation:
Van der Waals-Zeeman Institute, Institute of Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
*
Corresponding author: Xiaoyan Ye, yexy@lzu.edu.cn
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Abstract

The interaction between elastic structures and fluid interfaces, known as ‘hydroelastic’ problems, presents unique challenges to classical frameworks established for rigid spheres and liquid droplets. In this work, we experimentally demonstrate an intriguing phenomenon where ultrasoft hydrogel spheres rebound from a water surface at high impact speeds, even when their density exceeds that of water. We further propose a theoretical force-balance model, incorporating energy redistribution and potential flow theory, to predict the critical impact speed for the transition from sinking to rebounding, as well as the temporal evolution of both spreading diameter and cavity expansion. Our findings extend the classical Weber- and Bond-number-dominated paradigms for rigid spheres and liquid droplets, demonstrating that hydrogel dynamics is controlled by a modified elastocapillary Mach number, with rebound achievable even for hydrophilic spheres. These findings improve the understanding of soft-impact hydrodynamics and offer design principles for applications in biomimetic robotics and energy-absorbing materials.

JFM classification

Aerodynamics: Flow-structure interactions Drops and Bubbles: Drops and Bubbles Non-Newtonian Flows: Viscoelasticity
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1013 , 25 June 2025 , A2
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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Supplementary material: File

Ye et al. supplementary material movie 1

A hydrogel sphere with diameter D0 = 4 mm and Young’s modulus Y = 150 Pa impacts a water surface at 1.5 m/s.
Download Ye et al. supplementary material movie 1(File)
File 7.2 MB
Supplementary material: File

Ye et al. supplementary material movie 2

A hydrogel sphere with diameter D0 = 4 mm and Young’s modulus Y = 150 Pa impacts a water surface at 2.5 m/s.
Download Ye et al. supplementary material movie 2(File)
File 7 MB
Supplementary material: File

Ye et al. supplementary material movie 3

A hydrogel sphere with diameter D0 = 4 mm and Young’s modulus Y = 150 Pa impacts a water surface at 3.5 m/s.
Download Ye et al. supplementary material movie 3(File)
File 7.3 MB
Supplementary material: File

Ye et al. supplementary material movie 4

A hydrogel sphere with diameter D0 = 4 mm and Young’s modulus Y = 150 Pa impacts a water surface at 4 m/s.
Download Ye et al. supplementary material movie 4(File)
File 7.4 MB