On a linear instability of a plane parallel couette flow of viscoelastic fluid

Городцов, В. А.; Leonov, A. I.

doi:10.1016/0021-8928(67)90156-6

Cited by 123 publications

(135 citation statements)

References 4 publications

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“…These equations are very similar to those for Couette flow of a UCM fluid [5]. In fact, the only difference is in the coefficient of the highest derivative, and the final term in Eqs.…”

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confidence: 58%

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Instability of channel flow of a shear-thinning White–Metzner fluid

Wilson

Rallison

1999

Journal of Non-Newtonian Fluid Mechanics

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We consider the inertialess planar channel flow of a White±Metzner (WM) fluid having a power-law viscosity with exponent n. The case n 1 corresponds to an upper-convected Maxwell (UCM) fluid. We explore the linear stability of such a flow to perturbations of wavelength k À1 . We find numerically that if n < n c % 0.3 there is an instability to disturbances having wavelength comparable with the channel width. For n close to n c , this is the only unstable disturbance. For even smaller n, several unstable modes appear, and very short waves become unstable and have the largest growth rate. If n exceeds n c , all disturbances are linearly stable. We consider asymptotically both the long-wave limit which is stable for all n, and the shortwave limit for which waves grow or decay at a finite rate independent of k for each n.The mechanism of this elastic shear-thinning instability is discussed. #

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“…These equations are very similar to those for Couette flow of a UCM fluid [5]. In fact, the only difference is in the coefficient of the highest derivative, and the final term in Eqs.…”

mentioning

confidence: 58%

“…In steady, simple shear it gives a viscosity G M ( and first normal stress difference G M ( 2 2 . If ( is constant, we recover the UCM model whose stability characteristics are well known [5], and this will provide a useful check on our computations. To explore shear-thinning possibilities we put…”

Section: Introductionmentioning

confidence: 99%

Instability of channel flow of a shear-thinning White–Metzner fluid

Wilson

Rallison

1999

Journal of Non-Newtonian Fluid Mechanics

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“…The eigenvalues from this group are "purely elastic" in the sense that they exist even in the limit Re = 0. The pair was discovered by Gorodtsov and Leonov (Gorodtsov and Leonov, 1967) for twodimensional purely elastic plane Couette flow and can be generalized to the 3-dimensional case:…”

Section: Resultsmentioning

confidence: 96%

“…The only results available are on the linear stability of these flows. For essentially all studied visco-elastic models, laminar plane Couette flow is linearly stable (Gorodtsov and Leonov, 1967, Renardy and Renardy, 1986, Renardy, 1992, Wilson et al, 1999 (note the exception (Grillet et al, 2002)). In the case of pipe flow, the linear stability was demonstrated numerically by Ho and Denn (Ho and Denn, 1978) for any value of the Weissenberg and Reynolds numbers.…”

Section: Introductionmentioning

confidence: 99%

Subcritical Instabilities in Plane Couette Flow of Visco-Elastic Fluids

Morozov

Saarloos

2005

Fluid Mechanics and Its Applications

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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.

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“…After substituting the Fourier modes for stress and velocity into Eqs. 1, 2 and 4, the subsequent equations can be reduced to a single equation in v z (n) (z) which has a general solution given by (GORODTSOV and LEONOV, 1967;SHANKAR and KUMAR, 2004) …”

Section: Small Perturbations To a Flat Fault Interfacementioning

confidence: 99%

Effect of Surface Morphology on the Dissipation During Shear and Slip Along a Rock–Rock Interface that Contains a Visco-elastic Core

Angheluta

Candela

Mathiesen

et al. 2011

Pure Appl. Geophys.

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Abstract-High resolution topography measurements of the Vuache-Sillingy fault (Alps, France) reveal a characteristic roughness of the fault zone. We investigate the effect of roughness on the rheology of a planar shear configuration by using a model system consisting of a visco-elastic layer embedded into a rigid solid. The model is discussed in the context of several geological cases: a damage fault zone, a fault smeared with a clay layer, and a shear zone with strain weakening. Using both analytical approaches and finite element simulations, we calculate to linear order the relation between wall roughness and the viscous dissipation in the fault zone as well as the average shear rate.

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On a linear instability of a plane parallel couette flow of viscoelastic fluid

Cited by 123 publications

References 4 publications

Instability of channel flow of a shear-thinning White–Metzner fluid

Instability of channel flow of a shear-thinning White–Metzner fluid

Subcritical Instabilities in Plane Couette Flow of Visco-Elastic Fluids

Effect of Surface Morphology on the Dissipation During Shear and Slip Along a Rock–Rock Interface that Contains a Visco-elastic Core

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