Instability solutions for the Rayleigh–Taylor problem of non-homogeneous viscoelastic fluids in bounded domains

Tan, Zhidan; Wang, Weiwei

doi:10.1016/j.jmaa.2019.04.014

Cited by 5 publications

(2 citation statements)

References 46 publications

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“…Initially, the Rayleigh–Taylor instability was recognized as a phenomenon occurring at the interface of a Newtonian liquid and a gas or two Newtonian liquids. Numerous theoretical studies have appeared over the decades to discuss the Rayleigh–Taylor instability in viscoelastic liquids. − Recently, a new feature of the instabilitythe existence of a steady-state pattern of deformationswas identified by several research groups that experimentally characterized the Rayleigh–Taylor instability in elastic solids. ,, In addition, several groups have developed theoretical models of the Rayleigh–Taylor instability in viscoelastic solids. , However, to the best of our knowledge, there has not yet been experimental research specific to the Rayleigh–Taylor instability in viscoelastic solids, which is the goal of this paper.…”

Section: Introductionmentioning

confidence: 99%

Rayleigh–Taylor Instability in Soft Viscoelastic Solids

Slutzky,

Hwang,

Stone

et al. 2023

Langmuir

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We present an experimental characterization of the gravity-driven Rayleigh−Taylor instability in viscoelastic solids. The instability creates periodic patterns on the free surface of the soft solids that are distinct from the previously studied elastic Rayleigh−Taylor instability. The experimental results are supported by the linear stability analysis reported here. We identify the dependence of the steady-state pattern of deformations on the gel's geometry, complex shear modulus, and surface tension. This study provides quantitative measures applicable to the design of tunable surface textures, soft machines, and 3D structures.

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Section: Introductionmentioning

confidence: 99%

Rayleigh–Taylor Instability in Soft Viscoelastic Solids

Slutzky,

Hwang,

Stone

et al. 2023

Langmuir

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“…In the last decades, it has been also widely investigated how the RT instability evolves under the effects of other physical factors, such as elasticity [4,11,27,29,42,46], rotation [3,6,45], internal surface tension [9,16,24,48], magnetic fields [5, 17, 19-23, 25, 26], and so on. We also refer to the other related mathematical problems [1, 12, 13, 30, 32-34, 36, 38, 41].…”

Section: Introductionmentioning

confidence: 99%

On effect of surface tension in the Rayleigh–Taylor problem of stratified viscoelastic fluids

Xiong

2019

Bound Value Probl

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In this article, we investigate the effect of surface tension in the Rayleigh-Taylor (RT) problem of stratified incompressible viscoelastic fluids. We prove that there exists an unstable solution to the linearized stratified RT problem with a largest growth rate Λ under the instability condition (i.e., the surface tension coefficient ϑ is less than a threshold ϑ c). Moreover, for this instability condition, the largest growth rate Λ ϑ decreases from a positive constant to 0, when ϑ increases from 0 to ϑ c , which mathematically verifies that the internal surface tension can constrain the growth of the RT instability during the linear stage.

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