Nonmonotonic Constitutive Laws and the Formation  of Shear-Banded Flows

Spenley, N. A.; Yuan, Xue‐Feng; Cates, Michael E.

doi:10.1051/jp2:1996197

Cited by 133 publications

(138 citation statements)

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“…Changes in the conformational diffusion constant from δ A = 0.005 to δ A = 0.01, do not effectively change the plateau of the steady state shear stress, but do slightly decrease the overshoot in the steady state flow curve at the start of the plateau. The presence of a small overshoot in the apparent equilibrium flow curve as well as path-dependent equilibrium flow curves are features commonly observed in experiments with micellar solutions [42][43][44] and in calculations using the Johnson-Segalman model [22] as well as another "toy" nonlinear model [45].…”

Section: Start Up Of Steady Shear Flowmentioning

confidence: 68%

Modeling the inhomogeneous response and formation of shear bands in steady and transient flows of entangled liquids

Zhou¹,

Vasquez²,

Cook³

et al. 2008

Journal of Rheology

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We simulate the spatial and temporal evolution of inhomogeneous flow fields in viscometric devices such as cylindrical Couette cells. The computations focus on a class of two species elastic network models which are prototypes for a model which can capture, in a self-consistent manner, the creation and destruction of elastically-active network segments as well as diffusive coupling between the microstructural conformations and the local state of stress in regions with large spatial gradients of local deformation. For each of these models, the 'flow curve' of stress and apparent shear rate resulting from an assumption of homogeneous deformation is non-monotonic and linear stability analysis shows that the region of non-monotonic response is unstable. Steady-state calculations of the full inhomogeneous flow field lead to localized shear bands that grow linearly in extent across the gap as the apparent shear rate is incremented. Time-dependent calculations in step strain experiments and in start up of steady shear flow show that the velocity profile in the gap and the total stress measured at the bounding surfaces are coupled and evolve in a complex non-monotonic manner as the shear bands develop. These spatio-temporal dynamics are consistent with time-resolved particle imaging velocimetry measurements in both concentrated solutions of monodisperse entangled polymers and in wormlike micellar solutions. The computational results have a number of implications for experimental observations of 'apparent' or 'gap-averaged' quantities in nearly-viscometric devices, and lead to plateaus or 'yield-like' transitions in the steady flow curve and deviations from the Lodge-Meissner relation in non-ideal step shearing deformations.

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Section: Start Up Of Steady Shear Flowmentioning

confidence: 68%

Modeling the inhomogeneous response and formation of shear bands in steady and transient flows of entangled liquids

Zhou¹,

Vasquez²,

Cook³

et al. 2008

Journal of Rheology

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“…In this paper we will use a slightly more general form that is also capable of incorporating the model introduced by Yuan [31], in which the term added is a negative multiple of the Laplacian of the rate of strain. The theoretical framework just described has been developed largely in the context of one dimensional (1D) studies that consider only the flow gradient direction, normal to the interface between the bands [21,32,33]. Clearly, such studies assume from the outset that the interface between the bands is perfectly flat and they predict (with few exceptions: [34,35]) time-independent banded states.…”

Section: Introductionmentioning

confidence: 99%

Linear instability of planar shear banded flow of both diffusive and non-diffusive Johnson–Segalman fluids

Wilson

Fielding

2006

Journal of Non-Newtonian Fluid Mechanics

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We consider the linear stability of shear banded planar Couette flow of the JohnsonSegalman fluid, with and without the addition of stress diffusion to regularise the equations. In particular, we investigate the linear stability of an initially onedimensional "base" flow, with a flat interface between the bands, to two-dimensional perturbations representing undulations along the interface. We demonstrate analytically that, for the linear stability problem, the limit in which diffusion tends to zero is mathematically equivalent to a pure (non-diffusive) Johnson-Segalman model with a material interface between the shear bands, provided the wavelength of perturbations being considered is long relative to the (short) diffusion lengthscale.For no diffusion, we find that the flow is unstable to long waves for almost all arrangements of the two shear bands. In particular, for any set of fluid parameters and shear stress there is some arrangement of shear bands that shows this instability. Typically the stable arrangements of bands are those in which one of the two bands is very thin. Weak diffusion provides a small stabilising effect, rendering extremely long waves marginally stable. However, the basic long-wave instability mechanism is not affected by this, and where there would be instability as wavenumber k → 0 in the absence of diffusion, we observe instability for moderate to long waves even with diffusion. This paper is the first full analytical investigation into an instability first documented in the numerical study of [1]. Authors prior to that work have either happened to choose parameters where long waves are stable or used slightly different constitutive equations and Poiseuille flow, for which the parameters for instability appear to be much more restricted.We identify two driving terms that can cause instability: one, a jump in N 1 , as reported previously by Hinch et al. [2]; and the second, a discontinuity in shear rate. The mechanism for instability from the second of these is not thoroughly understood. Preprint submitted to Elsevier Science 3 May 2006We discuss the relevance of this work to recent experimental observations of complex dynamics seen in shear-banded flows.

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“…The steady state flow curve then has the form ABFG. Several constitutive models augmented with interfacial gradient terms have captured this behaviour [5,6,7,8].…”

Section: Introductionmentioning

confidence: 99%

Flow phase diagrams for concentration-coupled shear banding

2003

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After surveying the experimental evidence for concentration coupling in the shear banding of wormlike micellar surfactant systems, we present flow phase diagrams spanned by shear stress (or strain-rate) and concentration, calculated within the two-fluid, non-local Johnson-Segalman (d-JS-φ) model. We also give results for the macroscopic flow curves Σ(γ,φ) for a range of (average) concentrationsφ. For any concentration that is high enough to give shear banding, the flow curve shows the usual non-analytic kink at the onset of banding, followed by a coexistence "plateau" that slopes upwards, dΣ/dγ > 0. As the concentration is reduced, the width of the coexistence regime diminishes and eventually terminates at a non-equilibrium critical point [Σc,φc,γc]. We outline the way in which the flow phase diagram can be reconstructed from a family of such flow curves, Σ(γ,φ), measured for several different values ofφ. This reconstruction could be used to check new measurements of concentration differences between the coexisting bands. Our d-JS-φ model contains two different spatial gradient terms that describe the interface between the shear bands. The first is in the viscoelastic constitutive equation, with a characteristic (mesh) length l. The second is in the (generalised) Cahn-Hilliard equation, with the characteristic length ξ for equilibrium concentrationfluctuations. We show that the phase diagrams (and so also the flow curves) depend on the ratio r ≡ l/ξ, with loss of unique state selection at r = 0. We also give results for the full shear-banded profiles, and study the divergence of the interfacial width (relative to l and ξ) at the critical point.

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Nonmonotonic Constitutive Laws and the Formation of Shear-Banded Flows

Cited by 133 publications

References 0 publications

Modeling the inhomogeneous response and formation of shear bands in steady and transient flows of entangled liquids

Modeling the inhomogeneous response and formation of shear bands in steady and transient flows of entangled liquids

Linear instability of planar shear banded flow of both diffusive and non-diffusive Johnson–Segalman fluids

Flow phase diagrams for concentration-coupled shear banding

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