超重力环境下黏弹性软固体的Rayleigh-Taylor失稳

熊弘雷; 叶晗; 李科呈; 吕朝锋

doi:10.21656/1000-0887.460243

超重力环境下黏弹性软固体的Rayleigh-Taylor失稳

doi: 10.21656/1000-0887.460243

熊弘雷¹,
叶晗¹,
李科呈^1,2, ,,
吕朝锋^1,2,3

1. 宁波大学极端环境交叉力学研究中心，浙江宁波 315211;
2. 宁波大学冲击与安全工程教育部重点实验室，浙江宁波 315211;
3. 浙江大学建筑工程学院, 杭州 310058

基金项目:

国家自然科学基金（11925206

12402197）；浙江省自然科学基金（LQ24A020005）

详细信息

作者简介:
熊弘雷（2004—），男，硕士生；李科呈（1995—），男，副研究员，博士(通信作者. E-mail: likecheng@nbu.edu.cn)；吕朝锋（1978—），男，教授，博士，博士生导师(通信作者. E-mail: lucf@nbu.edu.cn).

通讯作者:
李科呈（1995—），男，副研究员，博士(通信作者. E-mail: likecheng@nbu.edu.cn)

中图分类号: O331
计量
- 文章访问数: 17
- HTML全文浏览量: 3
- PDF下载量: 5
- 被引次数: 0
出版历程
- 收稿日期: 2025-12-29
- 修回日期: 2026-02-11
- 网络出版日期: 2026-07-03
- 刊出日期: 2026-06-01

Rayleigh-Taylor Instability of Viscoelastic Soft Solids in Hypergravity

XIONG Honglei¹,
YE Han¹,
LI Kecheng^{1,2
, ,},
Lü Chaofeng^1,2,3

1. Center for Mechanics Plus Under Extreme Environments, Ningbo University, Ningbo, Zhejiang 315211, P.R. China;
2. Key Laboratory of Impact and Safety Engineering, Ministry of Education, Ningbo University, Ningbo, Zhejiang 315211, P.R. China;
3. College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, P.R. China

Funds:

The National Science Foundation of China(11925206

12402197)

摘要

摘要: 在超重力环境下，受限黏弹性软固体的自由表面可能发生RayleighTaylor失稳(RayleighTaylor instability,RTI)，其演化行为同时受到材料流变特性与几何约束的显著影响.本文以受限圆柱形黏弹性软固体为研究对象，基于线性黏弹性本构关系建立了自由表面扰动的线性稳定性分析框架，通过在频域中求解控制方程，推导得到了扰动增长率与波数之间的色散关系，从而系统刻画了超重力、表面张力、材料压缩性及黏性耗散等因素对失稳特征的影响机制.进一步考虑有限几何尺寸的作用，在柱坐标系下引入环向边界条件，将连续波数离散化，构建了适用于受限体系的失稳模态描述方法，明确了径厚比在失稳临界值与模态选择行为中的关键作用.在此基础上，结合有限元特征值分析与非线性数值模拟，对理论预测进行了验证，并用于探讨失稳模态与后期形貌演化之间的关联.本文的研究为分析超重力条件下受限黏弹性软固体的界面稳定性问题提供了一种系统的理论与数值研究思路，可为相关实验设计及软材料失稳形貌调控提供参考.
- Rayleigh-Taylor失稳 /
- 超重力 /
- 黏弹性 /
- 模态选择 /
- 软材料
Abstract: Under hypergravity conditions, the free surface of confined viscoelastic soft solids can become unstable due to Rayleigh-Taylor instability, with the evolution behavior governed by both material rheology and geometric confinement. The confined cylindrical viscoelastic soft solids were studied, and a linear stability analysis for free-surface perturbations was developed based on linear viscoelastic constitutive relations. The governing equations were formulated and solved in the frequency domain, to deduce the dispersion relation between the perturbation growth rate and the wavenumber. Then, the roles of hypergravity, surface tension, material compressibility and viscous dissipation were systematically investigated in the instability process. Finite geometric effects were incorporated through introduction of circumferential boundary conditions in a cylindrical coordinate system, to discretize the admissible wavenumbers and reveal the effects of finite confinement on the instability critical values and mode selections. Furthermore, the finite element method was used to verify the theoretical predictions and to investigate the relationship between instability modes and the subsequent evolutions of surface patterns. This study provides a coherent theoretical and numerical approach for analyzing interfacial stability in confined viscoelastic soft solids under hypergravity, and offers a guidance for experiment design and pattern control of soft materials.
- Rayleigh-Taylor instability /
- hypergravity /
- viscoelasticity /
- mode selection /
- soft material

HTML全文

参考文献(25)

FOYART G, RAMOS L, MORA S, et al. The fingering to fracturing transition in a transient gel[J]. Soft Matter,2013,9(32): 7775-7779.

[2]LIN S, COHEN T, ZHANG T, et al. Fringe instability in constrained soft elastic layers[J]. Soft Matter,2016,12(43): 8899-8906.

[3]DU Y K, L C F, LIU C S, et al. Prescribing patterns in growing tubular soft matter by initial residual stress[J]. Soft Matter,2019,15(42): 8468-8474.

[4]GRZELKA M, BOSTWICK J B, DANIELS K E. Capillary fracture of ultrasoft gels: variability and delayed nucleation[J]. Soft Matter,2017,13(16): 2962-2966.

[5]STYLE R W, BOLTYANSKIY R, CHE Y, et al. Universal deformation of soft substrates near a contact line and the direct measurement of solid surface stresses[J]. Physical Review Letters,2013,110(6): 066103.

[6]DERVAUX J, BEN AMAR M. Mechanical instabilities of gels[J]. Annual Review of Condensed Matter Physics,2012,3: 311-332.

[7]ANDREOTTI B, SNOEIJER J H. Statics and dynamics of soft wetting[J]. Annual Review of Fluid Mechanics,2020,52: 285-308.

[8]RAYLEIGH L. On the instability of a cylinder of viscous liquid under capillary force[J]. The London,Edinburgh,and Dublin Philosophical Magazine and Journal of Science,1892,34(207): 145-154.

[9]MORA S, PHOU T, FROMENTAL J M, et al. Gravity driven instability in elastic solid layers[J]. Physical Review Letters,2014,113(17): 178301.

[10]CHOU Y J, SHAO Y C. Numerical study of particle-induced Rayleigh-Taylor instability: effects of particle settling and entrainment[J]. Physics of Fluids,2016,28(4): 043302.

[11]LORENZ K T, EDWARDS M J, GLENDINNING S G, et al. Accessing ultrahigh-pressure, quasi-isentropic states of matter[J]. Physics of Plasmas,2005,12(5): 056309.

[12]GORCZYK W, VOGT K. Tectonics and melting in intra-continental settings[J]. Gondwana Research,2015,27(1): 196-208.

[13]BURROWS A. Supernova explosions in the universe[J]. Nature,2000,403(6771): 727-733.

[14]BEN AMAR M, JIA F. Anisotropic growth shapes intestinal tissues during embryogenesis[J]. Proceedings of the National Academy of Sciences of the United States of America,2013,110(26): 10525-10530.

[15]LEGOFF L, LECUIT T. Mechanical forces and growth in animal tissues[J]. Cold Spring Harbor Perspectives in Biology,2016,8(3): a019232.

[16]CHAKRABARTI A, MORA S, RICHARD F, et al. Selection of hexagonal buckling patterns by the elastic Rayleigh-Taylor instability[J]. Journal of the Mechanics and Physics of Solids,2018,121: 234-257.

[17]ZHENG Y, LAI Y, HU Y, et al. Rayleigh-Taylor instability in a confined elastic soft cylinder[J]. Journal of the Mechanics and Physics of Solids,2019,131: 221-229.

[18]RICCOBELLI D, CIARLETTA P. Rayleigh-Taylor instability in soft elastic layers[J]. Philosophical Transactions of the Royal Society A: Mathematical,Physical and Engineering Sciences,2017,375(2093): 20160421.

[19]TAMIM S I, BOSTWICK J B. A dynamic analysis of the Rayleigh-Taylor instability in soft solids[J]. Extreme Mechanics Letters,2020,40: 100940.

[20]PIRIZ S A, PIRIZ A R, TAHIR N A, et al. Magneto-Rayleigh-Taylor instability in an elastic-medium slab[J]. Physics of Fluids,2018,30(11): 111703.

[20]PIRIZ S A, PIRIZ A R, TAHIR N A. Letter: magneto-Rayleigh-Taylor instability in an elastic-medium slab[J]. Physics of Fluids,2018,30(11): 111703.

[21]BRUN P T. Shape formation in interfacial flows[J]. Physical Review Fluids,2024,9(11): 110501.

[22]CHRISTENSEN. Theory of Viscoelasticity[M]. New York: Academic Press, 1982.

[23]KARPITSCHKA S, DAS S, VAN GORCUM M, et al. Droplets move over viscoelastic substrates by surfing a ridge[J]. Nature Communications,2015,6: 7891.

[24]SWEENEY H, KERSWELL R R, MULLIN T. Rayleigh-Taylor instability in a finite cylinder: linear stability analysis and long-time fingering solutions[J]. Journal of Fluid Mechanics,2013,734: 338-362.

施引文献

资源附件(0)

访问统计