A low-dimensional approach to nonlinear plane-Couette flow of viscoelastic fluids

Ashrafi, Nariman; Khayat, Roger E.

doi:10.1063/1.870313

Cited by 20 publications

(35 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is tempting to speculate that the numerical instability observed by Atalik and Keunings is a manifestation of the underlying physical instability. Ashrafi and Khayat (Ashrafi and Khayat, 2000) have developed a low-dimensional Galerkin projection for the Johnson-Segalman fluid, and have shown that one-dimensional disturbances in x-direction become unstable. There as well, one cannot draw a conclusion about the resulting state in view of the special form of the perturbation and the very small number of modes included.…”

Section: Discussionmentioning

confidence: 99%

Subcritical Instabilities in Plane Couette Flow of Visco-Elastic Fluids

Morozov

Saarloos

2005

Fluid Mechanics and Its Applications

View full text Add to dashboard Cite

A non-linear stability analysis of plane Couette flow of the Upper-Convected Maxwell model is performed. The amplitude equation describing time-evolution of a finite-size perturbation is derived. It is shown that above the critical Weissenberg number, a perturbation in the form of an eigenfunction of the linearized equations of motion becomes subcritically unstable, and the threshold value for the amplitude of the perturbation decreases as the Weissenberg number increases.

show abstract

Section: Discussionmentioning

confidence: 99%

Subcritical Instabilities in Plane Couette Flow of Visco-Elastic Fluids

Morozov

Saarloos

2005

Fluid Mechanics and Its Applications

View full text Add to dashboard Cite

show abstract

“…A summary of problem formulation is given for the channel ow of a Johnson-Segalman (JS) uid. Details of formulation and solution procedure as well as additional results are given elsewhere [11]. Only one-dimensional ow is considered.…”

Section: Problem Formulation and Solution For Channel Flowmentioning

confidence: 99%

“…These techniques have been explored by Khayat [12] for various non-linear and non-Newtonian problems in hydrodynamic stability. In this paper, only a summary of methodology and results relevant to fully developed PCF are reported, leaving the details to Reference [11].…”

Section: Introductionmentioning

confidence: 99%

“…The more interesting response of transient blade coating is expected to emerge when nonlinear channel ow is considered. The JS equation is ideal in this case as it leads to multiple nonlinear proÿles in the critical range of Weissenberg numbers [10,11]. These proÿles, along with the stability and bifurcation diagrams, have been extensively investigated recently [11].…”

Section: Introductionmentioning

confidence: 99%

“…The JS equation is ideal in this case as it leads to multiple nonlinear proÿles in the critical range of Weissenberg numbers [10,11]. These proÿles, along with the stability and bifurcation diagrams, have been extensively investigated recently [11]. The method of solution was based on the Galerkin projection method and low-order dynamical systems.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A pseudo‐viscoelastic approach for transient polymeric flow exiting a channel

Khayat

Ashrafi

2003

Numerical Methods in Fluids

View full text Add to dashboard Cite

SUMMARYThe in uence of elasticity of a uid exiting a channel is examined on transient coating downstream. A hybrid spectral=boundary element approach is proposed to solve the problem. The ow inside the channel is assumed to be fully developed. A viscoelastic instability of one-dimensional plane Couette ow is ÿrst determined for a large class of Oldroyd uids with added viscosity, which typically represent polymer solutions composed of a Newtonian solvent and a polymeric solute. The Johnson -Segalman equation is used as the constitutive model. The velocity proÿle inside the channel is taken as the exit proÿle for the emerging free-surface ow. The ow is assumed to be Newtonian as it emerges from the channel. An estimate of the magnitude of the rate-of-strain tensor components in the free-surface region reveals that they are generally smaller than the shear rate inside the channel. The evolution of the ow front is simulated using the boundary element method. For the channel ow, the problem is reduced to a nonlinear dynamical system using the Galerkin projection method. Stability analysis indicates that the channel velocity may be linear or non-linear depending on the range of the Weissenberg number. The evolution of the coating ow at the exit is examined for steady as well as transient (monotonic and oscillatory) channel ow. It is found that adverse ow can exist as a result of uid elasticity, which can hinder the process of blade coating.

show abstract

Numerical study of concentrated fluid–particle suspension flow in a wavy channel

Mukhopadhyay

Usha

Tulapurkara

2008

Numerical Methods in Fluids

View full text Add to dashboard Cite

SUMMARYThe particle migration effects and fluid-particle interactions occurring in the flow of highly concentrated fluid-particle suspension in a spatially modulated channel have been investigated numerically using a finite volume method. The mathematical model is based on the momentum and continuity equations for the suspension flow and a constitutive equation accounting for the effects of shear-induced particle migration in concentrated suspensions. The model couples a Newtonian stress/shear rate relationship with a shear-induced migration model of the suspended particles in which the local effective viscosity is dependent on the local volume fraction of solids. The numerical procedure employs finite volume method and the formulation is based on diffuse-flux model. Semi-implicit method for pressure linked equations has been used to solve the resulting governing equations along with appropriate boundary conditions. The numerical results are validated with the analytical expressions for concentrated suspension flow in a plane channel. The results demonstrate strong particle migration towards the centre of the channel and an increasing blunting of velocity profiles with increase in initial particle concentration. In the case of a stenosed channel, the particle concentration is lowest at the site of maximum constriction, whereas a strong accumulation of particles is observed in the recirculation zone downstream of the stenosis. The numerical procedure applied to investigate the effects of concentrated suspension flow in a wavy passage shows that the solid particles migrate from regions of high shear rate to low shear rate with low velocities and this phenomenon is strongly influenced by Reynolds numbers and initial particle concentration.

show abstract

A low-dimensional approach to nonlinear plane-Couette flow of viscoelastic fluids

Cited by 20 publications

References 42 publications

Subcritical Instabilities in Plane Couette Flow of Visco-Elastic Fluids

Subcritical Instabilities in Plane Couette Flow of Visco-Elastic Fluids

A pseudo‐viscoelastic approach for transient polymeric flow exiting a channel

Numerical study of concentrated fluid–particle suspension flow in a wavy channel

Contact Info

Product

Resources

About