Constitutive equations for extensional flow of wormlike micelles: stability analysis of the Bautista–Manero model

Boek, Edo S.; Padding, JT Johan; Anderson, Valerie J.; Tardy, Philippe Michel Jacques; Crawshaw, John; Pearson, J. R. A.

doi:10.1016/j.jnnfm.2005.01.001

Cited by 50 publications

(53 citation statements)

References 14 publications

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“…From equation (4), the shear rate is given byγ = |∂û/∂ŷ|. The momentum balance in theŷ-direction yieldsp =p(t) only so pressure need not be considered, while in thex-direction combining equation (5) with the constitutive equation (3) yields…”

Section: Xmentioning

confidence: 99%

“…A model for such fluids was developed by Bautista et al [3]: this has since been employed both in its full form [4,5] and in a simplified form [6], while other models have more recently been introduced [7,8]. As our interest in the present study is in purely viscous structured fluids, such as muds, for which viscoelastic effects are insignificant, we will not discuss viscoelastic models further.…”

Section: Introductionmentioning

confidence: 99%

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The Stokes boundary layer for a thixotropic or antithixotropic fluid

McArdle

Pritchard

Wilson

2012

Journal of Non-Newtonian Fluid Mechanics

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We present a mathematical investigation of the oscillatory boundary layer ('Stokes layer') in a semi-infinite fluid bounded by an oscillating wall (the socalled 'Stokes problem'), when the fluid has a thixotropic or antithixotropic rheology. We obtain asymptotic solutions in the limit of small-amplitude oscillations, and we use numerical integration to validate the asymptotic solutions and to explore the behaviour of the system for larger-amplitude oscillations. The solutions that we obtain differ significantly from the classical solution for a Newtonian fluid. In particular, for antithixotropic fluids the velocity reaches zero at a finite distance from the wall, in contrast to the exponential decay for a thixotropic or a Newtonian fluid.For small amplitudes of oscillation, three regimes of behaviour are possible: the structure parameter may take values defined instantaneously by the shear rate, or by a long-term average; or it may behave hysteretically. The regime boundaries depend on the precise specification of structure build-up * Corresponding author. E-mail: david.pritchard@strath.ac.uk. Tel.: (+44)(0)141 548 3819. Fax: (+44)(0)141 548 3345.Preprint submitted to Journal of Non-Newtonian Fluid Mechanics June 12, 2012 and breakdown rates in the rheological model, illustrating the subtleties of complex fluid models in non-rheometric settings. For larger amplitudes of oscillation the dominant behaviour is hysteretic. We discuss in particular the relationship between the shear stress and the shear rate at the oscillating wall.

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Section: Xmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Stokes boundary layer for a thixotropic or antithixotropic fluid

McArdle

Pritchard

Wilson

2012

Journal of Non-Newtonian Fluid Mechanics

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“…We employed the modified Bautista-Manero model 23) as a constitutive equation. This model is described by the following equations: ( .…”

Section: Constitutive Equationmentioning

confidence: 99%

“…In the present study, we used a modified 23) was used as a constitutive equation for micellar solutions also in our previous studies 26,27) to numerically simulate the flow in a capillary channel. In addition, the numerical results were compared with experimental results of flow visualization and velocity measurements with particle tracking velocimetry.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Startup Flows of Wormlike Micellar Solutions in an Axisymmetric Capillary Channel using a Modified Bautista-Manero Model

Yamashita

Yamamoto

Hashimoto

2009

J. Soc. Rheol., Jpn

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Startup flows of wormlike micellar solutions in an axisymmetric capillary channel were numerically studied using a modified Bautista-Manero (MBM) model as a constitutive equation. The values of model parameter of the MBM model decided for a CTAB/NaSal solution were employed. The velocity profile at steady state predicted by the numerical simulation agreed with corresponding experimental data. The present study treated startup flows at a constant pressure gradient, which corresponds to a stress-controlled-type flow. The flow rate increased with time until the flow reached a steady state. The velocity profile had an inflection point around which the velocity gradient rapidly changed. The position of inflection point slightly changed with time. Temporal changes in both fluidity and the micellar contribution to shear stress occurred within a wall side region of the inflection point, where a white turbidity phenomenon was observed in our previous experiments. These temporal responses are characteristic of the startup flow at constant pressure gradients.

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“…In numerical studies, flow analyses for wormlike micelle solutions using continuum constitutive equations, such as the diffusive Johnson-Segalman model [13][14][15][16][17] , the Giesekus model [18][19][20] , and Bautista-Manero models [21][22][23][24][25] were performed. In continuum constitutive equations, the behavior of microscopic or mesoscopic network structures of micelles are not explicitly described.…”

Section: Introductionmentioning

confidence: 99%

Numerical Analysis of Shear Banding Flow of Wormlike Micelle Solutions between Parallel Channels using a Network Scission Model

Yamamoto

Sawa

2011

J. Soc. Rheol., Jpn

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Shear banding emerges in shear flows of wormlike micelle solutions and is observed as band velocity profiles in velocity measurement experiments. In our previous experiments, multi-band velocity profiles were captured in shear flows of a CTAB/NaSal solution between parallel plates. The relationship between the band velocity profile and the micellar network structure is an interesting issue. In the present study, the orientation behavior of the micelle network was numerically analyzed using a network scission model. Brownian dynamics simulations were carried out for a twospecies model of micelle networks derived in the Vasquez-Cook-McKinley model. The numerical results indicate that the effect of the orientation of short micelles on the behavior of the entire system is small, whereas long micelles tend to align well in the flow direction, their degree of orientation is relatively high, and their orientation behavior strongly affects the orientation of the entire system. Numerical analysis using the BD simulation provides useful information on the flow-induced structures of the micelle network, and hence the present approach is effective for the analysis of the mechanism of shear banding.

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Constitutive equations for extensional flow of wormlike micelles: stability analysis of the Bautista–Manero model

Cited by 50 publications

References 14 publications

The Stokes boundary layer for a thixotropic or antithixotropic fluid

The Stokes boundary layer for a thixotropic or antithixotropic fluid

Numerical Simulation of Startup Flows of Wormlike Micellar Solutions in an Axisymmetric Capillary Channel using a Modified Bautista-Manero Model

Numerical Analysis of Shear Banding Flow of Wormlike Micelle Solutions between Parallel Channels using a Network Scission Model

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