Spurt and instability in a two-layer Johnson-Segalman liquid

Renardy, Yuriko

doi:10.1007/bf00418144

Cited by 45 publications

(43 citation statements)

References 31 publications

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“…As the flow rate through the pipe was increased, a transition from a Newtonian-like velocity profile to a profile with thin regions of high shear rate near the walls and plug-like flow in the core of the fluid was commonly observed. For the flow rates coinciding with the high shear rate bands, a marginal change in wall shear stress led to very large changes in the volumetric flow rate, this phenomenon known in the literature as spurt [McLeish & Ball (1986); Renardy (1995)]. …”

Section: A Macroscale Shear Flows and Shear-bandingmentioning

confidence: 99%

Spatially resolved quantitative rheo-optics of complex fluids in a microfluidic device

Ober¹,

Soulages²,

McKinley³

2011

Journal of Rheology

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In this study, we use micro-particle image velocimetry (µ-PIV) and adapt a commercial birefringence microscopy system for making full-field, quantitative measurements of flow-induced birefringence (FIB) for the purpose of microfluidic, opticalrheometry of two worm-like micellar solutions. In combination with conventional rheometric techniques, we use our microfluidic rheometer to study the properties of a shear-banding solution of cetylpyridinium chloride (CPyCl) with sodium salicylate (NaSal) and a nominally shear thinning system of cetyltrimethylammonium bromide (CTAB) with NaSal across many orders of magnitude of deformation rates (10 −2 ≤γ ≤ 10 4 s −1 ). We use µ-PIV to quantify the local kinematics and use the birefringence microscopy system in order to obtain high-resolution measurements of the changes in molecular orientation in the worm-like fluids under strong deformations in a microchannel. The FIB measurements reveal that the CPyCl system exhibits regions of localized, high optical anisotropy indicative of shear bands near the channel walls, whereas the birefringence in the shear-thinning CTAB system varies more smoothly across the width of the channel as the volumetric flow rate is increased. We compare the experimental results to the predictions of a simple constitutive model, and we document the break-down in the stress optical rule as the characteristic rate of deformation is increased.

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Section: A Macroscale Shear Flows and Shear-bandingmentioning

confidence: 99%

Spatially resolved quantitative rheo-optics of complex fluids in a microfluidic device

Ober¹,

Soulages²,

McKinley³

2011

Journal of Rheology

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“…We are now dealing with the original JohnsonSegalman fluid [19] and considering a stability problem which was studied by Renardy [37] in 1995, although we have some analytical results for long waves where her work was purely numerical. However, as discussed above, for planar Couette flow of a Johnson-Segalman fluid in the non-monotonic region of the flow curve, there is no mechanism for selection of the shear stress.…”

Section: Wall Boundary Conditionsmentioning

confidence: 99%

“…s ii , ω = kω, then the governing equations within each fluid, from (37)(38)(39)(40)(41)(42)(43), become, for the force balance:…”

Section: Wall Boundary Conditionsmentioning

confidence: 99%

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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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“…It is well known that steady-shear flow in the decreasing region of a nonmonotonic flow curve is unstable (it is ill-posed in the Hadamard sense [35]). Such an instability has been attributed to cause different physical effects such as shearbanding in micellar solutions [36], and the shark-skin [35] and spurt [37] instabilities in polymer melts. Heuristically, the onset of oscillations of a falling sphere could be due to the same instability.…”

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confidence: 99%

Oscillations of a solid sphere falling through a wormlike micellar fluid

Jayaraman

Belmonte

2003

Phys. Rev. E

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We present an experimental study of the motion of a solid sphere falling through a wormlike micellar fluid. While smaller or lighter spheres quickly reach a terminal velocity, larger or heavier spheres are found to oscillate in the direction of their falling motion. The onset of this instability correlates with a critical value of the velocity gradient scale Γc ∼ 1 s −1 . We relate this condition to the known complex rheology of wormlike micellar fluids, and suggest that the unsteady motion of the sphere is caused by the formation and breaking of flow-induced structures.PACS numbers: 47.50.+d, 83.50.Jf, 83.60.Wc A sphere falling through a viscous Newtonian fluid is a classic problem in fluid dynamics, first solved mathematically by Stokes in 1851 [1]. Stokes provided a formula for the drag force F experienced by a sphere of radius R when moving at constant speed V 0 though a fluid with viscosity µ: F = 6πµRV 0 . The simplicity of the falling sphere experiment has meant that the viscosity can be measured directly from the terminal velocity V 0 , using a modified Stokes drag which takes into account wall effects [2]. The falling sphere experiment has also been used to study the viscoelastic properties of many polymeric (nonNewtonian) fluids [3,4,5]. In general, a falling sphere in a non-Newtonian fluid always approaches a terminal velocity, though sometimes with an oscillating transient [6,7,8]. In this paper we present evidence that a sphere falling in a wormlike micellar solution does not seem to approach a steady terminal velocity; instead it undergoes continual oscillations as it falls, as shown in Fig. 1.A wormlike micellar fluid is an aqueous solution in which amphiphilic (surfactant) molecules self-assemble in the presence of NaSal into long tubelike structures, or worms [9]; these micelles can sometimes be as long as 1µm [10]. Most wormlike micellar solutions are viscoelastic, and at low shear rates their rheological behavior is very similar to that of polymer solutions. However, unlike polymers, which are held together by strong covalent bonds, the micelles are held together by relatively weak entropic and screened electrostatic forces, and hence can break under shear. In fact, under equilibrium conditions these micelles are constantly breaking and reforming, providing a new mechanism for stress relaxation [11].The nonlinear rheology of these micellar fluids can be very different from standard polymer solutions [11,12,13]. Several observations of new phenomena have been reported, including shear thickening [14,15], a stress plateau in steady shear rheology [16,17], and flow instabilities such as shear-banding [18]. Bandyopadhyay et al. have observed chaotic fluctuations in the stress when a wormlike micellar solution is subjected to a step shear rate above a certain critical value (in the plateau region of stress-shear rate curve) [19]. A shear-induced transition from an isotropic to a nematic micellar ordering has also been observed [20]. There is increasing experimental evidence relating the onset of...

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Spurt and instability in a two-layer Johnson-Segalman liquid

Cited by 45 publications

References 31 publications

Spatially resolved quantitative rheo-optics of complex fluids in a microfluidic device

Spatially resolved quantitative rheo-optics of complex fluids in a microfluidic device

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

Oscillations of a solid sphere falling through a wormlike micellar fluid

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