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Richtmyer–Meshkov instability at gas/viscoelastic interfaces

Published online by Cambridge University Press:  10 December 2025

Yongrui Deng ,
Rui Sun ,
Juchun Ding Open the ORCID record for Juchun Ding [Opens in a new window] ,
Zhangbo Zhou Open the ORCID record for Zhangbo Zhou [Opens in a new window]  and
Xisheng Luo Open the ORCID record for Xisheng Luo [Opens in a new window]
Yongrui Deng
Affiliation:
State Key Laboratory of High Temperature Gas Dynamics, School of Engineering Science, University of Science and Technology of China, Hefei 230026, PR China
Rui Sun
Affiliation:
State Key Laboratory of High Temperature Gas Dynamics, School of Engineering Science, University of Science and Technology of China, Hefei 230026, PR China
Juchun Ding*
Affiliation:
State Key Laboratory of High Temperature Gas Dynamics, School of Engineering Science, University of Science and Technology of China, Hefei 230026, PR China Laoshan Laboratory, Qingdao 266237, PR China
Zhangbo Zhou
Affiliation:
State Key Laboratory of High Temperature Gas Dynamics, School of Engineering Science, University of Science and Technology of China, Hefei 230026, PR China
Xisheng Luo
Affiliation:
State Key Laboratory of High Temperature Gas Dynamics, School of Engineering Science, University of Science and Technology of China, Hefei 230026, PR China
*
Corresponding author: Juchun Ding, djc@ustc.edu.cn
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Abstract

This work investigates the Richtmyer–Meshkov instability (RMI) at gas/viscoelastic interfaces with an initial single-mode perturbation both experimentally and theoretically. By systematically varying the compositions and concentrations of hydrogels, a series of viscoelastic materials with tuneable mechanical properties is created, spanning from highly viscous to predominantly elastic. Following shock impact, the interface exhibits two distinct types of perturbations: small-amplitude, short-wavelength perturbations inherited from initial single-mode condition, and large-amplitude, long-wavelength perturbations arising from viscous effects. For hydrogels with high loss factors, viscosity dominates the interface dynamics, leading to pronounced V-shaped deformation of the entire interface accompanied by a rapid decay of the initial single-mode perturbation. In contrast, for hydrogels with low loss factors, elasticity plays a prominent role, leading to sustained oscillations of the single-mode perturbation. By employing the Maxwell model to simultaneously incorporate both viscous and elastic effects, a comprehensive linear theory for RMI at gas/viscoelastic interfaces is developed, which shows good agreement with experimental results in the early stages. Although deviations arise at later times due to factors such as the shear-thickening feature of hydrogels and three-dimensional effects, the model well reproduces the oscillation behaviour of single-mode perturbations. In particular, it effectively captures the trend that increasing elasticity reduces both oscillation period and amplitude, providing key insights into the role of material properties in interface dynamics.

JFM classification

Compressible Flows: Shock waves Interfacial Flows (free surface): Interfacial Flows (free surface)

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JFM Papers
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Journal of Fluid Mechanics , Volume 1025 , 25 December 2025 , A1
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© The Author(s), 2025. Published by Cambridge University Press

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Supplementary material: File

Deng et al. supplementary movie 1

Evolution of the single-mode air/hydrogel interface accelerated by a planar shock for case 1.
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Supplementary material: File

Deng et al. supplementary movie 2

Evolution of the single-mode air/hydrogel interface accelerated by a planar shock for case 4.
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Deng et al. supplementary movie 3

Evolution of the single-mode air/hydrogel interface accelerated by a planar shock for case 5.
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