On stabilizing effect of elasticity in the Rayleigh–Taylor problem of stratified viscoelastic fluids

<p style='text-indent:20px;'>It is well-known that viscoelasticity is a material property that exhibits both viscous and elastic characteristics with deformation. In particular, an elastic fluid strains when it is stretched and quickly returns to its original state once the stress is removed. In this review, we first introduce some mathematical results, which exhibit the stabilizing effect of elasticity on the motion of viscoelastic fluids. Then we further briefly introduce similar stabilizing effect in the elastic fluids.</p>

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

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2019.04.014 ◽

2019 ◽

Vol 476 (2) ◽

pp. 773-800 ◽

Cited By ~ 1

Author(s):

Zhidan Tan ◽

Weiwei Wang

Keyword(s):

Viscoelastic Fluids ◽

Bounded Domains ◽

Taylor Problem

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Effect of Inertia on the Stability of Film Casting of Viscoelastic Fluids

Fluids Engineering ◽

10.1115/imece2006-16070 ◽

2006 ◽

Author(s):

R. German ◽

R. E. Khayat

Keyword(s):

Stability Analysis ◽

Linear Stability Analysis ◽

Rheological Model ◽

Draw Ratio ◽

Viscoelastic Fluids ◽

Deborah Number ◽

Two Dimensional ◽

Film Casting ◽

Stabilizing Effect ◽

The Stability

The influence of inertia on the stability of isothermal film casting of viscoelastic fluids is examined using a Phan-Thien and Tanner rheological model. The linear stability analysis for two-dimensional disturbances is carried out. The numerical results indicate that the flow can have single or double critical draw ratio depending on the model parameter. While in the former case the flow is stable below and unstable above a critical draw ratio, in the latter case the flow is stable below the lower and above the upper critical draw ratio and unstable between the two values. The inertia is found to have a stabilizing effect on the flow. It is also found that there is a region of Deborah number, where the inertia has a stronger stabilizing effect on stability of flow than elsewhere.

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

Boundary Value Problems ◽

10.1186/s13661-019-1271-4 ◽

2019 ◽

Vol 2019 (1) ◽

Author(s):

Xingrui Ma ◽

Xianzhu Xiong

Keyword(s):

Surface Tension ◽

Growth Rate ◽

Viscoelastic Fluids ◽

Internal Surface ◽

Linear Stage ◽

Unstable Solution ◽

Instability Condition ◽

Taylor Problem ◽

Rt Instability ◽

Effect Of Surface

Abstract 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 $\vartheta _{c}$ ϑ c ). Moreover, for this instability condition, the largest growth rate $\varLambda _{\vartheta }$ Λ ϑ decreases from a positive constant to 0, when ϑ increases from 0 to $\vartheta _{c}$ 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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