Minimal model for chaotic shear banding in shear thickening fluids

Aradian, Ashod; Cates, Michael E.

doi:10.1103/physreve.73.041508

Cited by 34 publications

(70 citation statements)

References 54 publications

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“…Our data [26] also indicate that the band velocity decreases as τ S is increased. Somewhat similar band motion was reported in Ref.…”

Section: −1 Ssupporting

confidence: 64%

“…(Occasionally a band survives longer and shoots across the cell.) Other types of chaotic space-time patterns were also found [26]: 'wiggling' travelling bands and 'defect dominated' regimes (the latter close to those found for shear thinning micelles Ref. [16]).…”

Section: −1 Smentioning

confidence: 83%

“…To test this, we studied the case N = 3; with σ 0 and m 0 fixed by σ , our dynamical variables comprise σ 1 (t), σ 2 (t), m 1 (t) and m 2 (t). Our numerics show [26] that, although shrunk, the chaotic regions persist. Sharply resolved band interfaces are thus not essential to rheochaos.…”

Section: −1 Smentioning

confidence: 87%

“…2: for our parameters, this happens roughly when τ S becomes equal to the typical diffusion time across the Couette, τ diff = 1/κq 2 (with q = π/H). We do find the crossover to move towards longer timescales as κ is reduced [26].…”

Section: −1 Smentioning

confidence: 96%

“…Rarely, bands can nucleate periodically from a nonboundary point [26], giving two outgoing bands in a one-dimensional analogue of the 'target patterns' seen in chemical oscillators [28]. Details here depend strongly on the initial noise.…”

Section: −1 Smentioning

confidence: 99%

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Instability and spatiotemporal rheochaos in a shear-thickening fluid model

Aradian¹,

Cates²

2005

Europhys. Lett.

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We model a shear-thickening fluid that combines a tendency to form inhomogeneous, shear-banded flows with a slow relaxational dynamics for fluid microstructure. The interplay between these factors gives rich dynamics, with periodic regimes (oscillating bands, travelling bands, and more complex oscillations) and spatiotemporal rheochaos. These phenomena, arising from constitutive nonlinearity not inertia, can occur even when the steady-state flow curve is monotonic. Our model also shows rheochaos in a low-dimensional truncation where sharply defined shear bands cannot form.Complex fluids exhibit much interesting behavior under shear, due to strong couplings between mesoscopic structure and flow. Experiments show cases where, under steady external driving, an unstable flow arises, giving a time-dependent strain rate at constant imposed shear stress, or vice versa. Sustained temporal oscillations are seen in surfactant mesophases and solutions [1,2,3,4,5,6] and polymer solutions [7], while erratic temporal responses have been found both in these and in related materials, e.g., wormlike micelles [8,9,10], lamellar phases [4,5,11] and colloids [12,13]. There are strong indications [4,8,9] that these erratic signals result from a deterministic chaotic dynamics. Chaotic behavior of bulk flows at virtually zero Reynolds number (negligible inertia) must stem from nonlinearity within the rheological constitutive equation, and has been dubbed 'rheochaos ' [14, 15, 16].Such flow instabilities affect both shear-thinning [8] and shear-thickening micellar materials [9]. Shear-thickening is, in itself, a widely observed but poorly understood phenomenon which affects not only micelles but, e.g., dense colloids, where there is again evidence of bulk rheological instability [12,13]. Below we study a simple model for a shear-thickening fluid at steady controlled stress, which generalises to spatially inhomogeneous flows a model first proposed in Ref. [14]. The latter was shown to give simple oscillations but not chaos (unless an unconvincing 'double memory' term was used). We find that the interplay of a very simple structural memory with constitutive nonlinearity can, as hoped by the authors of [14], give complex dynamics and rheochaos -but only if spatial heterogeneity is allowed for. Our work is related to, but different from, that of Fielding and Olmsted [16] which addresses shear-thinning fluids [17]. Also related is Ref.[15] which concerns nematic liquid crystals (which can be chaotic even without spatial heterogeneity). We show below that there are robust generic features in the rheochaos produced in these various models, which generally involve a failed attempt to create a steady shearbanded flow. (In the shear thinning case the bands have a common stress but unequal strain rates; for us, the reverse is true.) One distinctive finding of our work is rheochaos in a model where the steady state flow curve is strictly monotonic. Here (in contrast with [16]) no steady banded solution, stable or otherwise, exists. Yet an innate t...

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“…Our data [26] also indicate that the band velocity decreases as τ S is increased. Somewhat similar band motion was reported in Ref.…”

Section: −1 Ssupporting

confidence: 64%

Section: −1 Smentioning

confidence: 83%

Section: −1 Smentioning

confidence: 87%

Section: −1 Smentioning

confidence: 96%

Section: −1 Smentioning

confidence: 99%

See 3 more Smart Citations

Instability and spatiotemporal rheochaos in a shear-thickening fluid model

Aradian¹,

Cates²

2005

Europhys. Lett.

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Shear-Induced Transitions and Instabilities in Surfactant Wormlike Micelles

Lerouge

Berret

2009

Polymer Characterization

147

153

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In this review, we report recent developments on the shear-induced transitions and instabilities found in surfactant wormlike micelles. The survey focuses on the nonlinear shear rheology and covers a broad range of surfactant concentrations, from the dilute to the liquid-crystalline states and including the semidilute and concentrated regimes. Based on a systematic analysis of many surfactant systems, the present approach aims to identify the essential features of the transitions. It is suggested that these features define classes of behaviors. The review describes three types of transitions and/or instabilities: the shear-thickening found in the dilute regime, the shear-banding which is linked in some systems to the isotropic-tonematic transition, and the flow-aligning and tumbling instabilities characteristic of nematic structures. In these three classes of behaviors, the shear-induced transitions are the result of a coupling between the internal structure of the fluid and the flow, resulting in a new mesoscopic organization under shear. This survey finally highlights the potential use of wormlike micelles as model systems for complex fluids and for applications.

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Is vorticity-banding due to an elastic instability?

2008

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The electrorheological (ER) effect is commonly known as a reversible increase in the viscosity of a suspension of solid particles dispersed in an insulating liquid after application of an external electric field. In this study, ER properties of poly(Lithium-2-hydroxyethyl methacrylate)-co-poly(4-vinyl pyridine), poly(Li-HEMA)-co-poly(4-VP), ionomeric salt (ionomer) was investigated. The ionomer particle sizes were characterized by dynamic light scattering, (DLS) method. Suspensions of ionomers were prepared in insulating silicone oil, at a series of concentrations (c = 5-30 %, m/m). Effects of particle size, temperature and concentration on the sedimentation stabilities of these suspensions were determined. Flow times of the suspensions were measured under no electric field (E = 0 kV/mm), and under an applied electric field (E 0 kV/mm) strength and a strong ER activity was observed for all the suspensions studied. Further, the effects of particle size, concentration, shear rate, electric field strength, frequency, promoter and temperature onto ER activities of ionomer suspensions were investigated.

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Minimal model for chaotic shear banding in shear thickening fluids

Cited by 34 publications

References 54 publications

Instability and spatiotemporal rheochaos in a shear-thickening fluid model

Instability and spatiotemporal rheochaos in a shear-thickening fluid model

Shear-Induced Transitions and Instabilities in Surfactant Wormlike Micelles

Is vorticity-banding due to an elastic instability?

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