On the shear banding flow of elongated micellar solutions

Bautista, F.; Soltero, J. F. A.; Pérez-López, J.H.; Puig, J. E.; Manero, Ο.

doi:10.1016/s0377-0257(00)00128-2

Cited by 87 publications

(106 citation statements)

References 49 publications

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“…Among micelle-inspired approaches, Manero and co-workers [4,113,114] developed a simple model coupling the evolution of the stress to that of the underlying fluid structure. For simplicity, they represented the structure by a single "fluidity" parameter ϕ ≡ 1/η, assumed to be the reciprocal of the fluid viscosity.…”

Section: Other Related Modelsmentioning

confidence: 99%

Rheology of giant micelles

Cates

Fielding

2006

Advances in Physics

318

341

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Giant micelles are elongated, polymer-like objects created by the self-assembly of amphiphilic molecules (such as detergents) in solution. Giant micelles are typically flexible, and can become highly entangled even at modest concentrations. The resulting viscoelastic solutions show fascinating flow behaviour (rheology) which we address theoretically in this article at two levels. First, we summarise advances in understanding linear viscoelastic spectra and steady-state nonlinear flows, based on microscopic constitutive models that combine the physics of polymer entanglement with the reversible kinetics of self-assembly. Such models were first introduced two decades ago, and since then have been shown to explain robustly several distinctive features of the rheology in the strongly entangled regime, including extreme shear-thinning. We then turn to more complex rheological phenomena, particularly involving spatial heterogeneity, spontaneous oscillation, instability, and chaos. Recent understanding of these complex flows is based largely on grossly simplified models which capture in outline just a few pertinent microscopic features, such as coupling between stresses and other order parameters such as concentration. The role of 'structural memory' (the dependence of structural parameters such as the micellar length distribution on the flow history) in explaining these highly nonlinear phenomena is addressed. Structural memory also plays an intriguing role in the little-understood shear-thickening regime, which occurs in a concentration regime close to but below the onset of strong entanglement, and which is marked by a shear-induced transformation from an inviscid to a gelatinous state.

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Section: Other Related Modelsmentioning

confidence: 99%

Rheology of giant micelles

Cates

Fielding

2006

Advances in Physics

318

341

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“…Constitutive modeling of complex fluids that undergo shear banding deformations can be subdivided into two categories: (i) phenomenological models that describe global features such as the plateau in the flow curve but provide no information on local kinematic features such as shear bands (see for example [21]) and (ii) more complex models that result in a non-monotonic flow curve under the assumptions of viscometric deformation [22]. For further details and discussion of these approaches, see for example the recent reviews of [3,4].…”

Section: Introductionmentioning

confidence: 99%

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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“…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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On the shear banding flow of elongated micellar solutions

Cited by 87 publications

References 49 publications

Rheology of giant micelles

Rheology of giant micelles

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

Oscillations of a solid sphere falling through a wormlike micellar fluid

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