Roles of plastic spin in shear banding

In this paper, the effects of plastic spin on shear banding and simple shear are examined systematically. Three types of plastic constitutive model with plastic spin are considered: (i) a non-coaxial model in which the direction of the plastic strain rate depends on that of the stress rate; (ii) a strain-softening model based on the J₂ flow theory; and (iii) the pressure-sensitive porous plasticity model. All the constitutive models are formulated in viscoplastic forms and in conjunction with non-local concepts that have been recently focused and discussed. First, behavior in simple shear is examined by numerical analysee with the aforementioned constitutive models. Moreover, some experimental evidences for stress response to simple shear are shown; that is, several large torsion tests of metal tubes and bars are carried out. Next, finite element simulations of shear banding in plane strain tension are performed. A critical effect of plastic spin on shear banding is observed for the noncoaxial model, while an almost negligible effect is observed for the porous model. The identical effects of plastic spin are observed, whether nonlocality exists or not. Finally, we discuss the relationship between the behavior in simple shear and the shear band formation. It is emphasized that this is a critical issue in predicting shear banding in macroscopic grounds.     

Rheo NMR and shear banding

The phenomenon of shear banding in complex fluids has been investigated using NMR velocimetry and NMR spectroscopy, mostly in wormlike micelle systems, but more recently in colloidal systems and multilayer vesicles. A particular advantage of NMR is the ability to simultaneously investigate structural ordering and to compare such ordering with local strain rates. In this paper, we describe the basics of Rheo-NMR and summarise its recent application to the study of shear banding.     

Rheology of wormlike micelles from non-equilibrium molecular dynamics

In this work, the rheology of complex fluids, i.e., surfactants of varying concentration in a Lennard–Jones fluid, is analyzed with non-equilibrium molecular dynamics simulations. The molecular model considers that the surfactant molecule is composed of a hydrophilic head, affine to solvent, and a hydrophobic tail made of four monomers. The solvent is modeled by a Lennard–Jones fluid, which shows mostly a Newtonian behavior, but at relatively high shear rates, a slight shear-thinning followed by a slight shear thickening are exhibited. The intermolecular potential produces an equilibrium configuration, in which the surfactant molecules self-assemble in a wormlike micelle. With the aim to analyze the system behavior with various stress fields, two flows are simulated under non-equilibrium conditions: (1) simple shear and (2) Poiseuille's flow. In simple shear, by keeping the velocity of the upper plate of the flow cell constant, a monotonic flow curve is predicted within a range of shear rates. At low shear rates, a concentration-dependent Newtonian region of viscosity η₀ corresponds to an isotropic condition in which the wormlike micelle preserves its equilibrium conformation. At intermediate shear rates, the solution exhibits a slight shear thinning, generating bands placed normal to the gradient direction (gradient banding). At high shear rates the solution exhibits shear-thickening, with bands now generated normal to the vorticity direction. These predictions by molecular models explain, to our knowledge for the first time, experiments in shear-thickening wormlike micellar solutions, where shear-thickening appears simultaneously with bands generated perpendicular to the vorticity axis. In Poiseuille's flow, we also find agreement between predictions of the model with theoretical developments and experiments performed by other authors.     

Prediction of normal stresses under large amplitude oscillatory shear flow

The dynamic response of viscoelastic fluids under large amplitude oscillatory shear (LAOS) has been a subject of long history. In the LAOS flow, the analysis has been mostly focused on shear stress, possibly due to the lack of accurate measurement of normal stress. However, the normal stress may become larger than shear stress at high-strain amplitudes, and thus it is important that we have a good understanding of the normal stress behavior. Furthermore, with the advancement in the instrumentation, it has become possible to get more reliable data. The purpose of this paper is to develop a research platform to analyze and to understand the normal stress behavior of complex fluids under LAOS flow. In this study, we utilized the Giesekus model as a representative constitutive model, and investigated its diverse responses. We defined the dynamic properties corresponding to normal stress, in a similar way to define dynamic moduli from shear stress, and examine their behavior with various analyzing tools. Experimental data were also compared with model predictions. Despite the fact that it is not yet possible to compare all of the predictions because of instrumental limitation, the prediction has been found to fit well with the experimental data. This study is expected to provide a useful framework for further understanding the nonlinear behavior of complex fluids at large deformation.     

A rheological model for materials which support coexistent shear rates

In this work we study a version of the three constant differential-type Oldroyd constitutive relation which allows distinct objective time derivatives for the extra stress and the stretching. We integrate the constitutive equation and determine an equivalent history integral representation for this model for the general class of viscometric motions. For certain choices of the material parameters and initial conditions, we find that this model allows for the development of shear rate discontinuities in the flow domain as a steady viscometric flow is achieved. Correspondingly, we also give evidence that intense shear rate oscillations may occur during the transient period as an impulsively started viscometric flow in a channel tends to a steady state under a constant critical shear stress. This critical shear stress lies in an interval of values for which the material experiences the phenomenon of “flow yielding”. A qualitative comparison with experimental data is made for certain creams and greases. The material instabilities inherent in this constitutive theory for viscometric motions are suggestive of the instabilities that occur in many viscoelastic fluids such as sharkskin patterns, wavy fracture, and spurt flow.     

Shear-banding structure orientated in the vorticity direction observed for equimolar micellar solution

 The non-monotonic shear flow of a viscoelastic equimolar aqueous surfactant solution (cetylpyridinium chloride-sodium salicylate) is investigated rheologically and optically in a transparent strain-controlled Taylor Couette flow cell. As reported before, this particular wormlike micellar solution exhibits first a shear thinning and then a pronounced shear-thickening behavior. Once this shear-thickening regime is reached, a transient phase separation/shear banding of the solution into turbid and clear ring-like patterns orientated perpendicular to the vorticity axis, i.e., stacked like pancakes, is observed (Wheeler et al. 1998; Fischer 2000). The solution exhibit several unique features as no induction period of the shear induced phase, no structural build-up at the inner rotating cylinder, jumping pancake structure of clear and turbid ringlike phases, and oscillating shear stresses appear once the pancake structure is present. According to our analysis this flow phenomenon is not purely a mechanical or rheological driven hydrodynamic instability but one has to take into account structural changes of the oriented micellar aggregates (flow induced non-equilibrium phase transition) as proposed by several authors. Although this particular flow behavior and the underlying mixture of shear induced phases and mechanical instabilities is not fully understood yet, some classification characteristics based on a recent theoretical approach by Schmitt et al. (1995) and Porte et al. (1997) where a strong coupling between the flow instability (non-homogeneous flow profile due to the bands) and the structural changes causes the observed transient phenomena can be derived. In reference to the presented model the observed orientation of the rings is typical for complex fluids that undergo a spinodal phase separation coupled with a thermodynamic flow instability. In contrast to other shear banding phenomena, this one is observed in parallel plate, cone-plate, and Couette flow cell as well as under controlled stress and controlled rate conditions. Therefore, it adds an additional aspect to the present discussion on shear banding phenomena, i.e., the coupling of hydrodynamics and phase transition of rheological complex fluids. Received: 8 January 2001 Accepted: 15 May 2001     

Shear banding in reaction-diffusion models

Shear banding occurs in the flow of complex fluids: various types of shear thinning and shear thickening micelle solutions and liquid crystals. In order to cope with the strongly inhomogeneous interface between the bands, constitutive models used in standard rheology must be supplemented by non-local terms. This leads rather generally to non-linear partial differential equations of the reaction-diffusion type. We use this formalism in order to explain some observed experimental features and as a guide for future research in this field. Received: 17 May 1999/Accepted: 3 August 1999     

High shear rate viscometry

We investigate the use of two distinct and complementary approaches in measuring the viscometric properties of low viscosity complex fluids at high shear rates up to 80,000 s^?1. Firstly, we adapt commercial controlled-stress and controlled-rate rheometers to access elevated shear rates by using parallel-plate fixtures with very small gap settings (down to 30 μm). The resulting apparent viscosities are gap dependent and systematically in error, but the data can be corrected—at least for Newtonian fluids—via a simple linear gap correction originally presented by Connelly and Greener, J. Rheol, 29(2):209–226, 1985). Secondly, we use a microfabricated rheometer-on-a-chip to measure the steady flow curve in rectangular microchannels. The Weissenberg–Rabinowitsch–Mooney analysis is used to convert measurements of the pressure-drop/flow-rate relationship into the true wall-shear rate and the corresponding rate-dependent viscosity. Microchannel measurements are presented for a range of Newtonian calibration oils, a weakly shear-thinning dilute solution of poly(ethylene oxide), a strongly shear-thinning concentrated solution of xanthan gum, and a wormlike micelle solution that exhibits shear banding at a critical stress. Excellent agreement between the two approaches is obtained for the Newtonian calibration oils, and the relative benefits of each technique are compared and contrasted by considering the physical processes and instrumental limitations that bound the operating spaces for each device.     

高速切削过程中诱发绝热剪切带形成的热塑性剪切波

提出了高速切削过程中诱发绝热剪切带形成的热塑性剪切波的传播机理,针对锯齿形切屑中热望性区域内的塑性梯度变形特征、动量和能量耗散情况,建立了与切削条件相关的热塑性剪切波的传播模型及剪切带宽度模型.在此基础上,通过淬硬45钢的切削实验并结合改进的Johnson-Cook本构模型分析了热塑性剪切波的传播规律,并将剪切带宽度模型与已提出的DB模型、WR模型和DM模型做了对比,结果表明,由热塑性剪切波传播理论推导的剪切带宽度模型与实验结果较其他模型吻合较好.     

The interface migration in shear-banded micellar solutions

In this work, we study the diffusion of the interface between bands in wormlike micellar solutions that exhibit shear banding flow regimes, namely, systems undergoing coexistence of states of different shear rates along a constant stress plateau. The migration of the interface between bands possessing different birefringence levels is predicted by the BMP (Bautista-Manero-Puig) model in which a structural parameter (the fluidity) presents two states with differing order separated by an interface. The mechanical potential derived from the constitutive equations and a diffusion term for the structure evolution equation predict various time scales of interface migration at the inception of shear flow and under shear-rate changes along the plateau stress. It is shown that the extremes of the plateau (binodals) correspond to the minima in the mechanical potential as a function of fluidity or shear rate. We also predict the dependence of the diffusive length scale on the applied shear rate.     

Pressure-driven flow of wormlike micellar solutions in rectilinear microchannels

In this paper the inhomogeneous response of the (two species) VCM model (Vasquez et al., A network scission model for wormlike micellar solutions. I. Model formulation and homogeneous flow predictions, J. Non-Newtonian Fluid Mech. 144 (2007) 122–139) is examined in steady rectilinear pressure-driven flow through a planar channel. This microstructural network model incorporates elastically active network connections that break and reform mimicking the behavior of concentrated wormlike micellar solutions. The constitutive model, which includes non-local effects arising from Brownian motion and from the coupling between the stress and the microstructure (finite length worms), consists of a set of coupled nonlinear partial differential equations describing the two micellar species (a long species ‘A’ and a shorter species ‘B’) which relax due to reptative and Rouse-like mechanisms as well as rupture of the long micellar chains. In pressure-driven flow, the velocity profile predicted by the VCM model deviates from the regular parabolic profile expected for a Newtonian fluid and exhibits a complex spatial structure. An apparent slip layer develops near the wall as a consequence of the microstructural boundary conditions and the shear-induced diffusion and rupture of the micellar species. Above a critical pressure drop, the flow exhibits shear banding with a high shear rate band located near the channel walls. This pressure-driven shear banding transition or ‘spurt’ has been observed experimentally in macroscopic and microscopic channel flow experiments. The detailed structure of the shear banding profiles and the resulting flow curves predicted by the model depend on the magnitude of the dimensionless diffusion parameter. For small channel dimensions, the solutions exhibit ‘non-local’ effects that are consistent with very recent experiments in microfluidic geometries (Masselon et al., Influence of boundary conditions and confinement on non local effects in flows of wormlike micellar systems, Phys. Rev. E 81 (2010) 021502).     

Gradient and vorticity banding

“Banded structures” of macroscopic dimensions can be induced by simple shear flow in many different types of soft matter systems. Depending on whether these bands extend along the gradient or vorticity direction, the banding transition is referred to as “gradient banding” or “vorticity banding,” respectively. The main features of gradient banding can be understood on the basis of a relatively simple constitutive equation. This minimal model for gradient banding will be discussed in some detail, and its predictions are shown to explain many of the experimentally observed features. The minimal model assumes a decrease of the shear stress of the homogeneously sheared system with increasing shear rate within a certain shear-rate interval. The possible microscopic origin of the severe shear-thinning behaviour that is necessary for the resulting nonmonotonic flow curves is discussed for a few particular systems. Deviations between experimental observations and predictions by the minimal model are due to obvious simplifications within the scope of the minimal model. The most serious simplifications are the neglect of concentration dependence of the shear stress (or on other degrees of freedom) and of the elastic contributions to the stress, normal stresses, and the possibility of shear-induced phase transitions. The consequences of coupling of stress and concentration will be analyzed in some detail. In contrast to predictions of the minimal model, when coupling to concentration is important, a flow instability can occur that does not require strong shear thinning. Gradient banding is sometimes also observed in glassy- and gel-like systems, as well as in shear-thickening systems. Possible mechanisms that could be at the origin of gradient-band formation in such systems are discussed. Gradient banding can also occur in strongly entangled polymeric systems. Banding in these systems is discussed on the basis of computer simulations. Vorticity banding is less well understood and less extensively investigated experimentally as compared to gradient banding. Possible scenarios that are at the origin of vorticity banding will be discussed. Among other systems, the observed vorticity-banding transition in rod-like colloids is discussed in some detail. It is argued, on the basis of experimental observations for these colloidal systems, that the vorticity-banding instability for such colloidal suspensions is probably related to an elastic instability, reminiscent of the Weissenberg effect in polymeric systems. This mechanism might explain vorticity banding in discontinuously shear-thickening systems and could be at work in other vorticity-banding systems as well. This overview does not include time-dependent phenomena like oscillations and chaotic behaviour.     

Probing shear-banding transitions of the VCM model for entangled wormlike micellar solutions using large amplitude oscillatory shear (LAOS) deformations

We explore the use of large amplitude oscillatory shear (LAOS) deformation to probe the dynamics of shear-banding in soft entangled materials, primarily wormlike micellar solutions which are prone to breakage and disentanglement under strong deformations. The state of stress in these complex fluids is described by a class of viscoelastic constitutive models which capture the key linear and nonlinear rheological features of wormlike micellar solutions, including the breakage and reforming of an entangled network. At a frequency-dependent critical strain, the imposed deformation field localizes to form a shear band, with a phase response that depends on the frequency and amplitude of the forcing. The different material responses are compactly represented in the form of Lissajous (phase plane) orbits and a corresponding strain-rate and frequency-dependent Pipkin diagram. Comparisons between the full network model predictions and those of a simpler, limiting case are presented.     

A new constitutive model for shear banding instability in metallic glass

Inelastic deformation of metallic glass is through shear banding, characterized by significantly localized deformation and emerged expeditiously under certain stress state. This study establishes a new constitutive model addressing the physical origin of the shear banding. In the modeling, the atomic structural change and the free volume generation are embodied by the plastic shear strain and the associated dilatation. The rugged free energy landscape is adopted to naturally reflect the rate-independent flow stress and flow serrations. Based on this, the conditions for the onset of shear banding instability are established, which enables the explicit calculation of the shear band inclination angle and its extension speed. The study concludes that shear band angle is significantly influenced by the diltancy factor and pressure sensitivity, that a shear band does not increase its thickness once emanated from a deformation unit, that the spreading speed of a shear band is intersonic, and that more shear bands, which lead to higher ductility, can be induced by high strain rates or by the introduction of a second material phase. The analysis also demonstrates that the ductility of metallic glass depends on the sample geometry and/or the stress state.     

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.     

A molecular dynamics study of the stress–optical behavior of a linear short-chain polyethylene melt under shear

In this study, we present details of the stress–optical behavior of a linear polyethylene melt under shear using a realistic potential model. We demonstrate the existence of the critical shear stress, above which the stress–optical rule (SOR) begins to be invalid. The critical shear stress of the SOR of this melt turns out to be 5.5 MPa, which is fairly higher than 3.2 MPa at which shear thinning starts, indicating that the SOR is valid up to a point well beyond the incipient point of shear thinning. Furthermore, contrary to conventional wisdom, the breakdown of the SOR turns out not to be correlated with the saturation of chain extension and orientation: It occurs at shear rates well before maximum chain extension is obtained. In addition to the stress and birefringence tensors, we also compare two important coarse-grained second-rank tensors, the conformation and orientation tensors. The birefringence, conformation, and orientation tensors display nonlinear relationships to each other at high values of the shear stress, and the deviation from linearity begins at approximately the critical shear stress for breakdown of the SOR.     

Extensional rheology of concentrated poly(ethylene oxide) solutions

The shear and extensional rheology of three concentrated poly(ethylene oxide) solutions is examined. Shear theology including steady shear viscosity, normal stress difference and linear viscoelastic material functions all collapse onto master curves independent of concentration and temperature. Extensional flow experiments are performed in fiber spinning and opposed nozzles geometries. The concentration dependence of extensional behavior measured using both techniques is presented. The zero-shear viscosity and apparent extensional viscosities measured with both extensional rheometers exhibit a power law dependence with polymer concentration. Strain hardening in the fiber spinning device is found to be of similar magnitude for all test fluids, irrespective of strain rate. The opposed nozzle device measures an apparent extensional viscosity which is one order of magnitude smaller than the value determined with the fiber spinline device. This could be attributed to errors caused by shear, dynamic pressure, and the relatively small strains developed in the opposed nozzle device. This instrument cannot measure local kinematics or stresses, but averages these values over the non-homogenous flow field. These results show that it is not possible to measure the extensional viscosity of non-Newtonian and shear thinning fluids with this device. Fiber spin-line experiments are coupled with a momentum balance and constitutive model to predict stress growth and diameter profiles. A one-mode Giesekus model accurately captures the plateau values of steady and dynamic shear properties, but fails to capture the gradual shear thinning of viscosity. Giesekus model parameters determined from shear rheology are not capable of quantitatively predicting fiber spinline kinematics. However, model parameters fit to a single spinline experiment accurately predict stress growth behavior for different applied spinline tensions.     

Steady shear banding in complex fluids

Shear banding (SB) is manifested by the abrupt “demixing” of the flow into regions of high and low shear rate. In this paper, we first relate analytically the rheological parameters of the fluid with the range of shear rates and stresses of SB occurrence. For this, we accept that the origin of shear banding is constitutive, and adopt a non-linear viscoelastic expression able to accommodate the double-valuedness of the stress with flow intensity, under certain conditions. We then implement the model for the case of pressure driven flow through a cylindrical pipe; we derive approximate expressions for the velocity profile in the two-banded regions (core and outer annular), the overall throughput in the presence or absence of “spurt”, and the radial location limits of the shear rate discontinuity.     

Effect of viscoelasticity on the rotation of a sphere in shear flow

When particles are dispersed in viscoelastic rather than Newtonian media, the hydrodynamics will be changed entailing differences in suspension rheology. The disturbance velocity profiles and stress distributions around the particle will depend on the viscoelastic material functions. Even in inertialess flows, changes in particle rotation and migration will occur. The problem of the rotation of a single spherical particle in simple shear flow in viscoelastic fluids was recently studied to understand the effects of changes in the rheological properties with both numerical simulations [D’Avino et al., J. Rheol. 52 (2008) 1331–1346] and experiments [Snijkers et al., J. Rheol. 53 (2009) 459–480]. In the simulations, different constitutive models were used to demonstrate the effects of different rheological behavior. In the experiments, fluids with different constitutive properties were chosen. In both studies a slowing down of the rotation speed of the particles was found, when compared to the Newtonian case, as elasticity increases. Surprisingly, the extent of the slowing down of the rotation rate did not depend strongly on the details of the fluid rheology, but primarily on the Weissenberg number defined as the ratio between the first normal stress difference and the shear stress.In the present work, a quantitative comparison between the experimental measurements and novel simulation results is made by considering more realistic constitutive equations as compared to the model fluids used in previous numerical simulations [D’Avino et al., J. Rheol. 52 (2008) 1331–1346]. A multimode Giesekus model with Newtonian solvent as constitutive equation is fitted to the experimentally obtained linear and nonlinear fluid properties and used to simulate the rotation of a torque-free sphere in a range of Weissenberg numbers similar to those in the experiments. A good agreement between the experimental and numerical results is obtained. The local torque and pressure distributions on the particle surface calculated by simulations are shown.