Shear Banding Flow Research Articles

Elastic Turbulence in Shear Banding Wormlike Micelles

We study the dynamics of the Taylor-Couette flow of shear banding wormlike micelles. We focus on the high shear rate branch of the flow curve and show that for sufficiently high Weissenberg numbers, this branch becomes unstable. This instability is strongly subcritical and is associated with a shear stress jump. We find that this increase of the flow resistance is related to the nucleation of turbulence. The flow pattern shows similarities with the elastic turbulence, so far only observed for polymer solutions. The unstable character of this branch led us to propose a scenario that could account for the recent observations of Taylor-like vortices during the shear banding flow of wormlike micelles.

Critical Phenomenon Analysis of Shear-Banding Flow in Polymer-like Micellar Solutions. 1. Theoretical Approach

The shear-banding flow in polymer-like micellar solutions is examined here with the generalized Bautista-Manero-Puig model. The coupling between flow and diffusion naturally arises in this model, which is derived from the extended irreversible thermodynamic formalism. The limit of an abrupt interface is treated here. The model predicts a dynamic master steady-flow diagram, in which all data collapse at low shear rates. Moreover, the model predicts that a nonequilibrium critical line is reached upon decreasing the shear-banding intensity parameter of the model, which corresponds to increasing temperature, increasing surfactant concentration, or varying salt-to-surfactant concentration ratio. By employing nonequilibrium critical theory and the concept of dissipated energy (or extended Gibbs free energy), a set of symmetrical reduced stress versus reduced shear-rate curves are obtained similar to gas-liquid transitions around the critical point. In addition, the nonequilibrium critical exponents are derived, which follow the extended Widom's rule and the extended Rushbroke relationship, but they are nonclassical.

Flow of wormlike micelle solutions through a periodic array of cylinders

Solutions of self-assembled wormlike micelles are used with ever increasing frequency in a multitude of consumer products ranging from cosmetic to industrial applications. Owing to the wide range of applications, flows of interest are often complex in nature; exhibiting both extensional and shear regions that can make modeling and prediction both challenging and valuable. Adding to the complexity, the micellar dynamics are continually changing, resulting in a number of interesting phenomena, such as shear banding and extensional flow instabilities. In this paper, we present the results of our investigation into the flow fields generated by a controllable and idealized porous media: a periodic array of cylinders. Our test channel geometry consists of six equally spaced cylinders, arranged perpendicular to the flow. By systematically varying the Deborah number, the flow kinematics, stability and pressure drop were measured. A combination of particle image velocimetry in conjunction with flush mount pressure transducers were used to characterize the flow, while flow induced birefringence measurements were used to determine micelle deformation and alignment. The pressure drop was found to decrease initially due to the shear thinning of the test fluid, and then exhibit a dramatic upturn as other elastic effects begin to dominate. We present evidence of the onset of an elastic instability in one of the test fluids above a critical Deborah number manifest in fluctuating transient pressure drop measurements and asymmetric streamlines. We argue that this disparity in the two test fluids can be attributed to the measurable differences in their extensional rheology.

Taylor-like Vortices in Shear-Banding Flow of Giant Micelles

Using flow visualizations in Couette geometry, we demonstrate the existence of Taylor-like vortices in the shear-banding flow of a giant micelles system. We show that vortices stacked along the vorticity direction develop concomitantly with interfacial undulations. These cellular structures are mainly localized in the induced band and their dynamics is fully correlated with that of the interface. As the control parameter increases, we observe a transition from a steady vortex flow to a state where pairs of vortices are continuously created and destroyed. Normal stress effects are discussed as potential mechanisms driving the three-dimensional flow.

Intermittent dynamics in transient polymer networks under shear: Signs of self-organized criticality

In this paper we demonstrate an unusual behavior in the shear-banded flow of a viscoelastic fluid. We report large and patterned fluctuations in the shear stress in an apparently fluid material undergoing steady shear, which we interpret as an intermittent and microscopic fracture and self-healing process. The statistical pattern of the fluctuations is indicative of self-organized criticality, and their magnitude can be directly related to the constitutive instability that underlies the shear banding.

Visualization of shear banding and entry Poiseuille flow oscillations in a micellar aqueous solution

A study of the plane Poiseuille flow of a micellar aqueous solution of cetylpyridinium chloride 100 mM and sodium salicylate 60 mM was performed in this work. The experiments were run at 27.5 °C under controlled pressure using a transparent flow cell, where simultaneous measurements of transmitted light intensity, pressure drop and flow rate were performed in order to asses the flow stability. Particle image velocimetry (PIV) was also used to analyze the flow kinematics upstream of the contraction. Different regimes were observed in the flow curve, including shear banding and spurt. In the high shear rate branch the flow became unstable and was composed by asymmetric shear bands of structured and isotropic fluid, which oscillated with respect to the zero-shear stress plane. Symmetric lip vortices were observed to grow upstream of the contraction, and then to oscillate and decrease their average length under unstable flow. The shear bands downstream of the contraction oscillated in the same way as upstream vortices, with a frequency that increased along with the flow rate. Finally, the oscillating flow upstream of the contraction produced jets or spurts of highly oriented material followed by recoiling, akin to those reported in the melt fracture regime of polymers.

Shearing Active Gels Close to the Isotropic-Nematic Transition

We study numerically the rheological properties of a slab of active gel close to the isotropic-nematic transition. The flow behavior shows a strong dependence on the sample size, boundary conditions, and on the bulk constitutive curve, which, on entering the nematic phase, acquires an activity-induced discontinuity at the origin. The precursor of this within the metastable isotropic phase for contractile systems (e.g., actomyosin gels) gives a viscosity divergence; its counterpart for extensile suspensions admits instead a shear-banded flow with zero apparent viscosity.

Recent experimental probes of shear banding

Recent experimental techniques used to investigate shear banding are reviewed. After recalling the rheological signature of shear-banded flows, we summarize the various tools for measuring locally the microstructure and the velocity field under shear. Local velocity measurements using dynamic light scattering and ultrasound are emphasized. A few results are extracted from current works to illustrate open questions and directions for future research.

The interplay between boundary conditions and flow geometries in shear banding: Hysteresis, band configurations, and surface transitions

We study shear banding flows in models of wormlike micelles or polymer solutions, and explore the effects of different boundary conditions for the viscoelastic stress. These are needed because the equations of motion are inherently non-local and include “diffusive” or square-gradient terms. Using the diffusive Johnson–Segalman model and a variant of the Rolie-Poly model for entangled micelles or polymer solutions, we study the interplay between different boundary conditions and the intrinsic stress gradient imposed by the flow geometry. We consider prescribed gradient (Neumann) or value (Dirichlet) of the viscoelastic stress tensor at the boundary, as well as mixed boundary conditions in which an anchoring strength competes with the gradient contribution to the stress dynamics. We find that hysteresis during shear rate sweeps is suppressed if the boundary conditions favor the state that is induced by the sweep. For example, if the boundaries favor the high shear rate phase then hysteresis is suppressed at the low shear rate edges of the stress plateau. If the boundaries favor the low shear rate state, then the high shear rate band can lie in the center of the flow cell, leading to a three-band configuration. Sufficiently strong stress gradients due to curved flow geometries, such as that of cylindrical Couette flow, can convert this to a two-band state by forcing the high shear rate phase against the wall of higher stress, and can suppress the hysteresis loop observed during a shear rate sweep.

Constitutive Modeling and Simulation of Perforation of Targets by Projectiles

DOI: 10.2514/1.26011 The effective use of existing finite element codes in the direct simulation of hypervelocity impacts by projectiles is limited by the dependence of the size of localized failure regions on the mesh size and alignment. This gives rise to a nonphysical description of the penetration and perforation processes. A micromechanical constitutive model that couples the anisotropic thermoviscodamage mechanism with the thermohypoelastoviscoplastic deformation is presented here as a remedy to this situation. Explicit and implicit microstructural length-scale measures, which preserve the well-posed nature of the differential equations, are introduced through the use of the viscosity and gradient localization limiters. Simple and robust numerical algorithms for the integration of the constitutive equations are also presented. The proposed unified integration algorithms are extensions of the classical rateindependent return-mapping algorithms to the rate-dependent problems. A simple and direct computational algorithmisalsousedforimplementingthegradient-dependentequations.Thisalgorithmcanbeimplementedinthe existing finite element codes without numerous modifications, compared with the current numerical approaches for integratinggradient-dependent models.Modelcapabilitiesarepreliminarilyillustrated forthedynamiclocalization of inelastic flow in adiabatic shear bands and the perforation of a 12-mm-thick Weldox 460E steel plate by a deformable blunt projectile at various impact speeds.

Nonlocal Effects in Flows of Wormlike Micellar Solutions

The flow curve of wormlike micelles usually exhibits a stress plateau sigma* separating high and low viscosity branches, leading to shear-banded flows. We study the flow of semidilute wormlike micellar systems in a confined geometry: a straight microchannel. We characterize their local rheology thanks to particle image velocimetry. We show that flow curves cannot be described by a simple constitutive equation linking the local shear stress to the local shear rate. We demonstrate the existence of nonlocal effects in the flow of wormlike micellar systems and make use of a theoretical framework allowing the measurement of correlation lengths.

Interface dynamics in shear-banding flow of giant micelles

We report on the non trivial dynamics of the interface between shear-bands following the initiation of flow in a semi-dilute wormlike micellar system investigated using a combination of mechanical and optical measurements under strain-controlled conditions. During build up of the banding structure, we observed the stages of formation and migration of the interface between bands and finally the destabilization of this interface along the vorticity axis. The mechanical signature of these processes has been identified in the time series of the shear stress. Interface instability occurs all along the stress plateau, the asymptotic wavelength of the patterns increasing with the control parameter, typically from a fraction of the gap width to about four times the gap width. Three main dynamics regimes are highlighted: a spatially stable oscillating mode approximately in the middle of the coexistence zone flanked by two regions where the dynamics appears more exotic with propagative and chaotic events respectively at low and high shear rates. The distribution of small particles seeded in the solution strongly suggests that the flow is three-dimensional. Finally, we demonstrate that the shear-banding scenario described in this paper is not specific to our system.

Applications of extreme deformation

Examples of extreme deformation (ED) are presented for friction stir welding of dissimilar metal and alloy systems, explosive welding of a steel/Zr/Al complex, impact and penetration of [001] W rods into rolled homogeneous armour (RHA) steel targets, and machining of 304 stainless steel. These examples illustrate ED to be facilitated by solid state flow in adiabatic shear bands (ASBs) composed of dynamic recrystallised (DRX) grains.

Phase and rheological behavior of the polymerizable surfactant CTAVB and water

The phase and rheological behaviors of the polymerizable surfactant, cetyltrimethylammonium benzoate (CTAVB), and water as a function of surfactant concentration and temperature are investigated here. The critical micelle concentration (cmc) and the (cmc 2), as well as the Krafft temperature ( T K ), are reported. A large highly viscous micellar solution region and hexagonal- and lamellar-phase regions were identified. The micellar solutions exhibit shear thickening in the dilute regime, below the overlapping or entanglement concentration. At higher concentrations, wormlike micelles form and the solutions show strong viscoelasticity and Maxwell behavior in the linear regime and shear banding flow in the nonlinear regime. The linear viscoelastic regime is analyzed with the Granek–Cates model, showing that the relaxation is controlled by the kinetics of reformation and scission of the micelles. The steady and unsteady responses in the nonlinear regime are compared with the predictions of the Bautista–Manero–Puig (BMP) model. Model predictions follow the experimental data closely.

Stability analysis of shear banding flow with the BMP model

The Bautista–Manero–Puig (BMP) model, consisting of the upper-convected Maxwell constitutive equation coupled to a kinetic equation that takes into account structural changes induced by flow, predicts the basic features of shear banding flow in polymer-like micellar solutions. In this work, the Lyapunov stability analysis applied to this model is used to determine the regions of stability and instability under conditions of shear banding flow. Results indicate that the steady state is reached very slowly within the meta-stable regions and quite rapidly in the homogeneous flow regions as well as in the unstable region where the slope of the constitutive flow curve is negative. Moreover, the Lyapunov stability criterion suggests the locus of the spinodal curve and the existence of a critical point for specific values of temperature and surfactant concentration. In addition, a criterion to set the stress plateau is derived from Extended Irreversible Thermodynamic (EIT) that consists in the equality of the minima in extended Gibbs free energy of the stable flow branches. This approach relates the EIT criterion for the stress plateau to the stability analysis for shear banding flow.

A thermodynamic approach to rheology of complex fluids: The generalized BMP model

In this paper, a set of constitutive relationships arising from the coupling of stress with concentration, are derived using the extended irreversible thermodynamics formalism. In complex fluids that present flow-induced changes in their internal structure, the stress constitutive equation is coupled to an evolution equation of a scalar representing the flow-induced modifications in the internal structure of the fluid, and to the constitutive equation for the mass flux. In particular, the generalization of a simple model, the Bautista–Manero–Puig (BMP) model, which has been used to reproduce the nonlinear viscoelastic behavior of polymer-like micellar solutions and other complex fluids, is derived. This model predicts rather well steady and unsteady nonlinear features of semi-dilute solutions that exhibit shear-banding flow and the shear-thickening transition observed in dilute surfactant solutions.

Effect of a hydrotrope on the viscoelastic properties of polymer-like micellar solutions

Low-viscosity micellar aqueous solutions of cetyltrimethylammonium bromide (CTAB) undergo a major change in the presence of the hydrotrope, potassium 1-phenylmethylsulfate (KPhMS), producing a highly viscoelastic entanglement network of polymer-like micelles. The system studied here shows typical shear banding flow behavior, which tends to disappear with increasing the hydrotrope-to-surfactant concentration ratio (C H / C S). The linear rheological response was analyzed with the model of Granek–Cates, whereas the nonlinear behavior was reproduced with the Bautista–Manero–Puig (BMP) model. Both models introduce a kinetic equation to account for the breaking and reformation of the micelles, and they predict the linear and nonlinear rheological data very well.

Strain gradient crystal plasticity effects on flow localization

In metal grains one of the most important failure mechanisms involves shear band localization. As the band width is small, the deformations are affected by material length scales. To study localization in single grains a rate-dependent crystal plasticity formulation for finite strains is presented for metals described by the reformulated Fleck–Hutchinson strain gradient plasticity theory. The theory is implemented numerically within a finite element framework using slip rate increments and displacement increments as state variables. The formulation reduces to the classical crystal plasticity theory in the absence of strain gradients. The model is used to study the effect of an internal material length scale on the localization of plastic flow in shear bands in a single crystal under plane strain tension. It is shown that the mesh sensitivity is removed when using the nonlocal material model considered. Furthermore, it is illustrated how different hardening functions affect the formation of shear bands.

A Finite Strain Plastic-damage Model for High Velocity Impacts using Combined Viscosity and Gradient Localization Limiters: Part II - Numerical Aspects and Simulations

In this companion article, we present within the finite element context the numerical algorithms for the integration of the thermodynamically consistent formulation of geometrically nonlinear gradient-enhanced viscoinelasticity derived in the first part of the article. The proposed unified integration algorithms are extensions of the classical rate-independent return mapping algorithms to the rate-dependent problems. An operator split structure is used consisting of a trial state followed by the return map by imposing the generalized viscoplastic and visco-damage consistency conditions simultaneously. Furthermore, a trivially incrementally objective integration scheme is established for the rate constitutive relations. The proposed finite deformation scheme is based on hypoelastic stress-strain representations and the proposed elastic predictor and coupled viscoplastic-viscodamage corrector algorithm allows for the total uncoupling of geometrical and material nonlinearities. A simple and direct computational algorithm is also used for calculation of the higher-order gradients. This algorithm can be implemented in the existing finite element codes without numerous modifications as compared to the current numerical approaches for integrating gradient-dependent models. The nonlinear algebraic system of equations is solved by consistent linearization and the Newton-Raphson iteration. The proposed model is implemented in the explicit finite element code ABAQUS via the user subroutine VUMAT. Model capabilities are preliminarily illustrated for the dynamic localization of inelastic flow in adiabatic shear bands and the perforation of a 12 mm thick Weldox 460E steel plates by deformable blunt projectiles at various impact speeds. The simulated shear band results well illustrated the potential of the proposed model in dealing with the well-known mesh sensitivity problem. Consequently, the introduced implicit and explicit length-scale measures are able to predict size effects in localization failures. Moreover, good agreement is obtained between the numerical simulations and experimental results of the perforation problem.

A numerical examination of shear banding and simple shear non-coaxial flow rules

Strain localisation and shear band formation is frequently observed during the handling and flow of dense phase particulate materials. However, a complete understanding of how shear bands form and what happens inside shear bands is still lacking. In order to address this problem, discrete particle simulations have been carried out to examine the detailed processes that occur at the grain scale associated with the initiation and development of shear bands. To reliably identify the continuum model applicable within a shear band is difficult due to the small number of particles/contacts involved. However, it is normally accepted that the mode of deformation within a shear band is one of simple shear. Consequently, simple shear simulations have been performed in order to determine the evolution of the stress tensor, dilation rate, and the principal directions of stress and strain-rate. It is demonstrated that the corresponding non-coaxial flow rule is equivalent to that suggested by Tatsuoka et al. (Géotechnique 38 148 (1988)). Furthermore, at fully developed flow when there is no further change in volume, the stress and strain-rate directions are coaxial and the flow rule is that proposed by Hill (The Mathematical Theory of Plasticity (Oxford University Press, 1950) p. 294).