Effects of nonlocal stress on the determination of shear banding flow

Slow Fatigue and Highly Delayed Yielding via Shear Banding in Oscillatory Shear

We study theoretically the dynamical process of yielding in cyclically sheared amorphous materials, within a thermal elastoplastic model and the soft glassy rheology model. Within both models we find an initially slow accumulation, over many cycles after the inception of shear, of low levels of damage in the form strain heterogeneity across the sample. This slow fatigue then suddenly gives way to catastrophic yielding and material failure. Strong strain localization in the form of shear banding is key to the failure mechanism. We characterize in detail the dependence of the number of cycles N^{*} before failure on the amplitude of imposed strain, the working temperature, and the degree to which the sample is annealed prior to shear. We discuss our finding with reference to existing experiments and particle simulations, and suggest new ones to test our predictions.

Viscoelasticity enhances collective motion of bacteria

Bacteria form human and animal microbiota. They are the leading causes of many infections and constitute an important class of active matter. Concentrated bacterial suspensions exhibit large-scale turbulent-like locomotion and swarming. While the collective behavior of bacteria in Newtonian fluids is relatively well understood, many fundamental questions remain open for complex fluids. Here, we report on the collective bacterial motion in a representative biological non-Newtonian viscoelastic environment exemplified by mucus. Experiments are performed with synthetic porcine gastric mucus, natural cow cervical mucus, and a Newtonian-like polymer solution. We have found that an increase in mucin concentration and, correspondingly, an increase in the suspension's elasticity monotonously increases the length scale of collective bacterial locomotion. On the contrary, this length remains practically unchanged in Newtonian polymer solution in a wide range of concentrations. The experimental observations are supported by computational modeling. Our results provide insight into how viscoelasticity affects the spatiotemporal organization of bacterial active matter. They also expand our understanding of bacterial colonization of mucosal surfaces and the onset of antibiotic resistance due to swarming.

Numerical Simulation of Rheological Models for Complex Fluids Using Hierarchical Grids

In this work, we implement models that are able to describe complex rheological behaviour (such as shear-banding and elastoviscoplasticity) in the HiGTree/HiGFlow system, which is a recently developed Computational Fluid Dynamics (CFD) software that can simulate Newtonian, Generalised-Newtonian and viscoelastic flows using finite differences in hierarchical grids. The system uses a moving least squares (MLS) meshless interpolation technique, allowing for more complex mesh configurations while still keeping the overall order of accuracy. The selected models are the Vasquez-Cook-McKinley (VCM) model for shear-banding micellar solutions and the Saramito model for viscoelastic fluids with yield stress. Development of solvers and numerical simulations of inertial flows of these models in 2D channels and planar-contraction 4:1 are carried out in the HiGTree/HiGFlow system. Our results are compared with those predicted by two other methodologies: the OpenFOAM-based software RheoTool that uses the Finite-Volume-Method and an in-house code that uses the Vorticity-Velocity-Formulation (VVF). We found an excellent agreement between the numerical results obtained by these three different methods. A mesh convergence analysis using uniform and refined meshes is also carried out, where we show that great convergence results in tree-based grids are obtained thanks to the finite difference method and the meshless interpolation scheme used by the HiGFlow software. More importantly, we show that our methodology implemented in the HiGTreee/HiGFlow system can successfully reproduce rheological behaviour of high interest by the rheology community, such as non-monotonic flow curves of micellar solutions and plug-flow velocity profiles of yield-stress viscoelastic fluids.

Interplay between hysteresis and nonlocality during onset and arrest of flow in granular materials

The jamming transition in granular materials is well-known for exhibiting hysteresis, wherein the level of shear stress required to trigger flow is larger than that below which flow stops. Although such behavior is typically modeled as a simple non-monotonic flow rule, the rheology of granular materials is also nonlocal due to cooperativity at the grain scale, leading for instance to increased strengthening of the flow threshold as system size is reduced. We investigate how these two effects - hysteresis and nonlocality - couple with each other by incorporating non-monotonicity of the flow rule into the nonlocal granular fluidity (NGF) model, a nonlocal constitutive model for granular flows. By artificially tuning the strength of nonlocal diffusion, we demonstrate that both ingredients are key to explaining certain features of the hysteretic transition between flow and arrest. Finally, we assess the ability of the NGF model to quantitatively predict material behavior both around the transition and in the flowing regime, through stress-driven discrete element method (DEM) simulations of flow onset and arrest in various geometries. Along the way, we develop a new methodology to compare deterministic model predictions with the stochastic behavior exhibited by the DEM simulations around the jamming transition.

Structure-property relationship of a soft colloidal glass in simple and mixed flows

HYPOTHESIS

Under specific conditions, rod-like cellulose nanocrystals (CNC) can assemble into structurally ordered soft glasses (SGs) with anisotropy that can be controlled by applying shear. However, to achieve full structural control of SGs in real industrial processes, their response to mixed shear and extensional kinematics needs to be determined. We hypothesise that by knowing the shear rheology of the CNC-based soft glass and adopting a suitable constitutive model, it is possible to predict the structure-property relationship of the SG under mixed flows.

EXPERIMENTS

We use an aqueous suspension with 2 wt% CNC at 25 mM NaCl to form a structurally ordered SG composed of a CNC network containing nematic domains. We combine rheometry and microfluidic experiments with numerical simulations to study the flow properties of the SG in shear, extension, and mixed flow conditions. Extensional flow is investigated in the Optimised Shape Cross-slot Extensional Rheometer (OSCER), where the SG is exposed to shear-free planar elongation. Mixed flow kinematics are investigated in a benchmark microfluidic cylinder device (MCD) where the SG flows past a confined cylinder in a microchannel.

FINDINGS

The SG in the MCD displays a velocity overshoot (negative wake) and a pronounced CNC alignment downstream of the cylinder. Simulations using the thixotropic elasto-visco-plastic (TEVP) model yield near quantitative agreement of the velocity profiles in simple and mixed flows and capture the structural fingerprint of the material. Our results provide a comprehensive link between the structural behaviour of a CNC-based SG and its mechanistic properties, laying foundations for the development of functional, built-to-order soft materials.

Effect of chain scission on flow characteristics of wormlike micellar solutions past a confined microfluidic cylinder: a numerical analysis

Flow past a microfluidic cylinder confined in a channel is considered as one of the benchmark problems for the analysis of transport phenomena of complex fluids. Earlier experiments show the existence of an elastic instability for the flow of a wormlike micellar solution in this model system after a critical value of the Weissenberg number in the creeping flow regime (G. R. Moss and J. P. Rothstein, J. Non-Newtonian Fluid Mech., 2010, 165, 1505-1515; Y. A. Zhao et al., Soft Matter, 2016, 12, 8666-8681; S. J. Haward et al., Soft Matter, 2019, 15, 1927-1941). This study presents a detailed numerical investigation of this elastic instability in this model system using the two-species VCM (Vasquez-Cook-McKinley) constitutive model for the wormlike micellar solution. Inline with the experimental trends, we also observe the existence of a similar elastic instability in this flow once the Weissenberg number exceeds a critical value. However, we additionally find that the elastic instability in this model geometry is greatly influenced by the breakage and reformation dynamics of the wormlike micelles. In particular, the onset of such an elastic instability is delayed or even may be completely suppressed as the micelles become progressively easier to break. Furthermore, this elastic instability is seen to be associated with the elastic wave phenomena which has been recently observed experimentally for polymer solutions. The present study reveals that the speed of such an elastic wave increases non-linearly with the Weissenberg number similar to that seen in polymer solutions.

Unified Theoretical and Experimental View on Transient Shear Banding

Dense emulsions, colloidal gels, microgels, and foams all display a solidlike behavior at rest characterized by a yield stress, above which the material flows like a liquid. Such a fluidization transition often consists of long-lasting transient flows that involve shear-banded velocity profiles. The characteristic time for full fluidization τ_{f} has been reported to decay as a power law of the shear rate γ[over ˙] and of the shear stress σ with respective exponents α and β. Strikingly, the ratio of these exponents was empirically observed to coincide with the exponent of the Herschel-Bulkley law that describes the steady-state flow behavior of these complex fluids. Here we introduce a continuum model, based on the minimization of a "free energy," that captures quantitatively all the salient features associated with such transient shear banding. More generally, our results provide a unified theoretical framework for describing the yielding transition and the steady-state flow properties of yield stress fluids.

Time-dependent shear rate inhomogeneities and shear bands in a thixotropic yield-stress fluid under transient shear

We study the rheological responses and shear-rate inhomogeneities and shear banding behaviors of a thixotropic fumed silica suspension in shear startup tests and flow reversal tests. We find that this suspension under transient shear exhibits not only viscoelasticity, yielding, kinematic hardening, and thixotropy, but also time-dependent shear inhomogeneities including bands when the apparent shear rate is below a critical value between 0.1 and 0.25 s-1. Through multiple shear startup tests and flow reversal tests, we find that thixotropy promotes flow heterogeneity while kinematic hardening suppresses it. We propose a simple thixo-plastic constitutive equation that can qualitatively predict the important features of the rheological response and banding dynamics in shear startup tests and flow reversal tests.

Non-local stresses in highly non-uniformly flowing suspensions: The shear-curvature viscosity

For highly non-uniformly flowing fluids, there are contributions to the stress related to spatial variations of the shear rate, which are commonly referred to as non-local stresses. The standard expression for the shear stress, which states that the shear stress is proportional to the shear rate, is based on a formal expansion of the stress tensor with respect to spatial gradients in the flow velocity up to leading order. Such a leading order expansion is not able to describe fluids with very rapid spatial variations of the shear rate, like in micro-fluidics devices and in shear-banding suspensions. Spatial derivatives of the shear rate then significantly contribute to the stress. Such non-local stresses have so far been introduced on a phenomenological level. In particular, a formal gradient expansion of the stress tensor beyond the above mentioned leading order contribution leads to a phenomenological formulation of non-local stresses in terms of the so-called "shear-curvature viscosity". We derive an expression for the shear-curvature viscosity for dilute suspensions of spherical colloids and propose an effective-medium approach to extend this result to concentrated suspensions. The validity of the effective-medium prediction is confirmed by Brownian dynamics simulations on highly non-uniformly flowing fluids.

Transient shear banding in the nematic dumbbell model of liquid crystalline polymers

In the shear flow of liquid crystalline polymers (LCPs) the nematic director orientation can align with the flow direction for some materials but continuously tumble in others. The nematic dumbbell (ND) model was originally developed to describe the rheology of flow-aligning semiflexible LCPs, and flow-aligning LCPs are the focus in this paper. In the shear flow of monodomain LCPs, it is usually assumed that the spatial distribution of the velocity is uniform. This is in contrast to polymer solutions, where highly nonuniform spatial velocity profiles have been observed in experiments. We analyze the ND model, with an additional gradient term in the constitutive model, using a linear stability analysis. We investigate the separate cases of constant applied shear stress and constant applied shear rate. We find that the ND model has a transient flow instability to the formation of a spatially inhomogeneous flow velocity for certain starting orientations of the director. We calculate the spatially resolved flow profile in both constant applied stress and constant applied shear rate in start up from rest, using a model with one spatial dimension to illustrate the flow behavior of the fluid. For low shear rates flow reversal can be seen as the director realigns with the flow direction, whereas for high shear rates the director reorientation occurs simultaneously across the gap. Experimentally, this inhomogeneous flow is predicted to be observed in flow reversal experiments in LCPs.

Edge-Induced Shear Banding in Entangled Polymeric Fluids

Despite decades of research, the question of whether solutions and melts of highly entangled polymers exhibit shear banding as their steady state response to a steadily imposed shear flow remains controversial. From a theoretical viewpoint, an important unanswered question is whether the underlying constitutive curve of shear stress σ as a function of shear rate γ[over ˙] (for states of homogeneous shear) is monotonic, or has a region of negative slope, dσ/dγ[over ˙]<0, which would trigger banding. Attempts to settle the question experimentally via velocimetry of the flow field inside the fluid are often confounded by an instability of the free surface where the sample meets the outside air, known as "edge fracture." Here we show by numerical simulation that in fact even only very modest edge disturbances-which are the precursor of full edge fracture but might well, in themselves, go unnoticed experimentally-can cause strong secondary flows in the form of shear bands that invade deep into the fluid bulk. Crucially, this is true even when the underlying constitutive curve is monotonically increasing, precluding true bulk shear banding in the absence of edge effects.

Understanding rheological hysteresis in soft glassy materials

Motivated by recent experimental studies of rheological hysteresis in soft glassy materials, we study numerically strain rate sweeps in simple yield stress fluids and viscosity bifurcating yield stress fluids. Our simulations of downward followed by upward strain rate sweeps, performed within fluidity models and the soft glassy rheology model, successfully capture the experimentally observed monotonic decrease of the area of the rheological hysteresis loop with sweep time in simple yield stress fluids, and the bell shaped dependence of hysteresis loop area on sweep time in viscosity bifurcating fluids. We provide arguments explaining these two different functional forms in terms of differing tendencies of simple and viscosity bifurcating fluids to form shear bands during the sweeps, and show that the banding behaviour captured by our simulations indeed agrees with that reported experimentally. We also discuss the difference in hysteresis behaviour between inelastic and viscoelastic fluids. Our simulations qualitatively agree with the experimental data discussed here for four different soft glassy materials.

Shear-induced structural and thermodynamic phase transitions in micellar systems

In this contribution a methodology to compute and classify shear-induced structural and phase transitions in surfactant/water mixtures from rheological measurements is presented. Non-linear rheological experiments, considering variations in surfactant concentration and temperature, are analyzed. In particular, the parameters of the BMP (Bautista-Manero-Puig) model, obtained from the fitting of the shear stress versus shear rate data, which are functions of surfactant concentration and temperature, allow classifying structural and phase transition boundaries. To test this methodology, we consider the analysis of the shear-induced structural and phase transitions of two micellar systems, cetyltrimethylammonium tosylate (CTAT)/water as a function of CTAT concentrations and Pluronics P103/water as a function of temperature. We found that the CTAT/water system presents a first-order phase transition at 30 ^° C, and around 31 to 32 wt.% from isotropic to nematic phases, whereas a 20 wt.% Pluronics P103 aqueous micellar solution has two second-order (structural) phase transitions, one from spherical to cylindrical micelles at 33.1 ^° C, and another one from cylindrical micelles to a nematic phase at 35.8 ^° C and one first-order phase transition around 37.9 ^° C at high shear rates near to the cloud point previously reported. The proposed methodology is also able to identify the instability regions where the wormlike micelles are broken, producing the typical shear banding behavior.

Shear Banding of Soft Glassy Materials in Large Amplitude Oscillatory Shear

We study shear banding in soft glassy materials subject to a large amplitude oscillatory shear flow (LAOS). By numerical simulations of the widely used soft glassy rheology model, supplemented by more general physical arguments, we demonstrate strong banding over an extensive range of amplitudes and frequencies of the imposed shear rate γ[over ˙](t)=γ[over ˙]_{0}cos(ωt), even in materials that do not permit banding as their steady state response to a steadily imposed shear flow γ[over ˙]=γ[over ˙]_{0}=const. Highly counterintuitively, banding persists in LAOS even in the limit of zero frequency ω→0, where one might a priori have expected a homogeneous flow response in a material that does not display banding under conditions of steadily imposed shear. We explain this finding in terms of an alternating competition within each cycle between glassy aging and flow rejuvenation. Our predictions have far-reaching implications for the flow behavior of aging yield stress fluids, suggesting a generic expectation of shear banding in flows of even arbitrarily slow time variation.

Shear banding in nematogenic fluids with oscillating orientational dynamics

We investigate the occurrence of shear banding in nematogenic fluids under planar Couette flow, based on mesoscopic dynamical equations for the orientational order parameter and the shear stress. We focus on parameter values where the sheared homogeneous system exhibits regular oscillatory orientational dynamics, whereas the equilibrium system is either isotropic (albeit close to the isotropic-nematic transition) or deep in its nematic phase. The numerical calculations are restricted to spatial variations in shear gradient direction. We find several new types of shear-banded states characterized by regions with regular oscillatory orientational dynamics. In all cases shear banding is accompanied by a non-monotonicity of the flow curve of the homogeneous system; however, only in the case of the initially isotropic system this curve has the typical S-like shape. We also analyze the influence of different orientational boundary conditions and of the spatial correlation length.

Pressure and phase equilibria in interacting active brownian spheres

We derive a microscopic expression for the mechanical pressure P in a system of spherical active Brownian particles at density ρ. Our exact result relates P, defined as the force per unit area on a bounding wall, to bulk correlation functions evaluated far away from the wall. It shows that (i) P(ρ) is a state function, independent of the particle-wall interaction; (ii) interactions contribute two terms to P, one encoding the slow-down that drives motility-induced phase separation, and the other a direct contribution well known for passive systems; and (iii) P is equal in coexisting phases. We discuss the consequences of these results for the motility-induced phase separation of active Brownian particles and show that the densities at coexistence do not satisfy a Maxwell construction on P.

Magnetic microwire probes for the magnetic rod interfacial stress rheometer

The magnetic needle interfacial shear rheometer is a valuable tool for the study of the mechanical properties of thin fluid films or monolayers. However, it is difficult to differentiate the interfacial and subphase contributions to the drag on the needle. In principle, the problem can be addressed by decreasing the needle diameter, which decreases the bulk contribution while the interfacial contribution remains essentially the same. Here we show the results obtained when using a new type of needle, that of magnetic microwires with diameter approximately 10 times thinner than for commercial needles. We show that the lower inertia of the microwires calls for a new calibration procedure. We propose such a new calibration procedure based on the flow field solution around the needle introduced in refs 1 and 2. By measuring thin silicone oil films with well-controlled interfacial viscosities as well as eicosanol (C20) and pentadecanoic acid (PDA, C15) Langmuir monolayers, we show that the new calibration method works well for standard needles as well as for the microwire probes. Moreover, we show that the analysis of the force terms contributing to the force on the needle helps to ascertain whether the measurements obtained are reliable for given surface shear viscosity values. We also show that the microwire probes have at least a 10-fold-lower resolution limit, allowing one to measure interfacial viscosities as low as 10(-7) N·m/s.

Manipulating shear-induced non-equilibrium transitions in colloidal films by feedback control

Using Brownian Dynamics (BD) simulations we investigate non-equilibrium transitions of sheared colloidal films under controlled shear stress σxz. In our approach the shear rate [small gamma, Greek, dot above] is a dynamical variable, which relaxes on a time scale τc such that the instantaneous, configuration-dependent stress σxz(t) approaches a pre-imposed value. Investigating the dynamics under this "feedback-control" scheme we find unique behavior in regions where the flow curve σxz([small gamma, Greek, dot above]) of the uncontrolled system is monotonic. However, in non-monotonic regions our method allows to select between dynamical states characterized by different in-plane structure and viscosities. Indeed, the final state strongly depends on τc relative to an intrinsic relaxation time of the uncontrolled system. The critical values of τc are estimated on the basis of a simple model.

Shear banding in soft glassy materials

Many soft materials, including microgels, dense colloidal emulsions, star polymers, dense packings of multilamellar vesicles, and textured morphologies of liquid crystals, share the basic 'glassy' features of structural disorder and metastability. These in turn give rise to several notable features in the low frequency shear rheology (deformation and flow properties) of these materials: in particular, the existence of a yield stress below which the material behaves like a solid, and above which it flows like a liquid. In the last decade, intense experimental activity has also revealed that these materials often display a phenomenon known as shear banding, in which the flow profile across the shear cell exhibits macroscopic bands of different viscosity. Two distinct classes of yield stress fluid have been identified: those in which the shear bands apparently persist permanently (for as long as the flow remains applied), and those in which banding arises only transiently during a process in which a steady flowing state is established out of an initial rest state (for example, in a shear startup or step stress experiment). Despite being technically transient, such bands may in practice persist for a very long time and so be mistaken for the true steady state response of the material in experimental practice. After surveying the motivating experimental data, we describe recent progress in addressing it theoretically, using the soft glassy rheology model and a simple fluidity model. We also briefly place these theoretical approaches in the context of others in the literature, including elasto-plastic models, shear transformation zone theories, and molecular dynamics simulations. We discuss finally some challenges that remain open to theory and experiment alike.

Spatially Resolved Concentration and Segmental Flow Alignment in a Shear-Banding Solution of Polymer-Like Micelles

We measure the spatially resolved microstructure and concentration in the plane of flow for a viscoelastic solution of polymer-like micelles comprised of mass fraction 6.0% (volume fraction 6.6%) solution of 2:1 molar ratio cetylpyridinium chloride/sodium salicylate in 0.5 mol/L NaCl/D₂O through the shear banding transition. Spatially resolved flow small-angle neutron scattering measurements in the velocity-velocity gradient (1-2) plane of flow establish the local microstructure, and scanning narrow-aperture flow ultrasmall-angle neutron scattering (SNAFUSANS) measurements indicate no flow-induced concentration gradients within measurement accuracy. These results show shear banding in this solution is not associated with an isotropic-nematic transition and are fundamentally important for validating models of shear-banding complex fluids. Improvements in the SNAFUSANS method are also documented.

Apparent fracture in polymeric fluids under step shear

Recent step strain experiments in well-entangled polymeric liquids demonstrated a bulk fracturelike phenomenon. We study this instability by using a modern version of the Doi-Edwards theory for entangled polymers, and we find close quantitative agreement with the experiments. The phenomenon occurs because the viscoelastic liquid is sheared into a rubbery state that possesses an elastic constitutive instability [G. Marrucci and N. Grizzuti, J. Rheol. 27, 433 (1983)]. The fracture is a transient manifestation of this instability, which relies on the amplification of spatially inhomogeneous fluctuations. This mechanism differs from the fracture in glassy materials and dense suspensions.

Instabilities in wormlike micelle systems. From shear-banding to elastic turbulence

Shear-banding is ubiquitous in complex fluids. It is related to the organization of the flow into macroscopic bands bearing different viscosities and local shear rates and stacked along the velocity gradient direction. This flow-induced transition towards a heterogeneous flow state has been reported in a variety of systems, including wormlike micellar solutions, telechelic polymers, emulsions, clay suspensions, colloidal gels, star polymers, granular materials, or foams. In the past twenty years, shear-banding flows have been probed by various techniques, such as rheometry, velocimetry and flow birefringence. In wormlike micelle solutions, many of the data collected exhibit unexplained spatio-temporal fluctuations. Different candidates have been identified, the main ones being wall slip, interfacial instability between bands or bulk instability of one of the bands. In this review, we present experimental evidence for a purely elastic instability of the high shear rate band as the main origin for fluctuating shear-banding flows.

Self-organization in the flow of complex fluids (colloid and polymer systems). Part 2: Theoretical models

Flow induced transitions in complex fluids are usually accompanied by changes in the internal media structure and the flow symmetry. In this review paper, we discuss the theoretical models and approaches that have been used for the analysis of different types of flow instabilities and flow patterns. The main attention is focused on the basic fluid models which reveal vortex and banding flow structures at high shear rates. The Oldroyd-B fluid is one of such models. The Reynolds and the Weissenberg (or Deborah) numbers are the parameters governing its flow behavior. For this model, the secondary flow patterns arising in viscometric flows of different geometries at the bifurcation point are described. Complex fluids which are able to exist in multiple states can form coexisting bands of different structures with different rheological properties and flowing with different shear rates at the same shear stress. Shear banding is typical for fluids demonstrating non-monotonous flow curves described by such models as the diffusive Johnson-Segalman fluid model, for example. Recent progress in exploring this phenomenon is discussed.

Viscoelastic Taylor-Couette instability of shear banded flow

We study numerically shear banded flow in planar and curved Couette geometries. Our aim is to capture two recent observations in shear banding systems of roll cells stacked in the vorticity direction, associated with an undulation of the interface between the bands. Depending on the degree of cell curvature and on the material's constitutive properties, we find either (i) an instability of the interface between the bands driven by a jump in second normal stress across it or (ii) a bulk viscoelastic Taylor-Couette instability in the high shear band driven by a large first normal stress within it. Both lead to roll cells and interfacial undulations but with a different signature in each case, thereby suggesting that the roll cells in each of the recent experiments are different in origin.

Why does shear banding behave like first-order phase transitions? Derivation of a potential from a mechanical constitutive model

Numerous numerical and experimental evidence suggest that shear banding behavior looks like first-order phase transitions. In this paper, we demonstrate that this correspondence is actually established in the so-called non-local diffusive Johnson-Segalman model (the DJS model), a typical mechanical constitutive model that has been widely used for describing shear banding phenomena. In the neighborhood of the critical point, we apply the reduction procedure based on the center manifold theory to the governing equations of the DJS model. As a result, we obtain a time evolution equation of the flow field that is equivalent to the time-dependent Ginzburg-Landau (TDGL) equations for modeling thermodynamic first-order phase transitions. This result, for the first time, provides a mathematical proof that there is an analogy between the mechanical instability and thermodynamic phase transition at least in the vicinity of the critical point of the shear banding of DJS model. Within this framework, we can clearly distinguish the metastable branch in the stress-strain rate curve around the shear banding region from the globally stable branch. A simple extension of this analysis to a class of more general constitutive models is also discussed. Numerical simulations for the original DJS model and the reduced TDGL equation is performed to confirm the range of validity of our reduction theory.

Influence of boundary conditions and confinement on nonlocal effects in flows of wormlike micellar systems

In this paper we report on the influence of different geometric and boundary constraints on nonlocal (spatially inhomogeneous) effects in wormlike micellar systems. In a previous paper, nonlocal effects were observable by measuring the local rheological flow curves of micelles flowing in a microchannel under different pressure drops, which appeared to differ from the flow curve measured using conventional rheometry. Here we show that both the confinement and the boundary conditions can influence those nonlocal effects. The role of the nature of the surface is analyzed in detail using a simple scalar model that incorporates inhomogeneities, which captures the flow behavior in both wide and confined geometries. This leads to an estimate for the nonlocal "diffusion" coefficient (i.e., the shear curvature viscosity) which corresponds to a characteristic length from 1 to 10 microm.

Transition to mixing and oscillations in a Stokesian viscoelastic flow

In seeking to understand experiments on low-Reynolds-number mixing and flow transitions in viscoelastic fluids, we simulate the dynamics of the Oldroyd-B model, with a simple background force driving the flow. We find that at small Weissenberg number, flows are "slaved" to the extensional geometry imposed by forcing. For large Weissenberg number, such solutions become unstable and transit to a structurally dissimilar state dominated by a single large vortex. This new state can show persistent oscillatory behavior with the production and destruction of smaller-scale vortices that drive mixing.

Two-dimensional perturbations in a scalar model for shear banding

We present an analytical study of a toy model for shear banding, without normal stresses, which uses a piecewise linear approximation to the flow curve (shear stress as a function of shear rate). This model exhibits multiple stationary states, one of which is linearly stable against general two-dimensional perturbations. This is in contrast to analogous results for the Johnson-Segalman model, which includes normal stresses, and which has been reported to be linearly unstable for general two-dimensional perturbations. This strongly suggests that the linear instabilities found in the Johnson-Segalman can be attributed to normal stress effects.

Electrorheological response and orientational bistability of a homogeneously aligned nematic capillary

We consider a homogeneously aligned nematic liquid crystal confined in the region between two rotating coaxial cylinders. We study the nematic's director and velocity profiles induced by the imposed Couette flow and an applied radial electric field. We present calculations for the specific flow-aligning nematic liquid crystal 4(')-n-pentyl-4-cyanobiphenyl and numerically solve a hydrodynamic model assuming hard anchoring and nonslip boundary conditions. We calculate a phase diagram in the parameter space showing a region where there exist multiple equilibrium solutions for the nematic's configuration and a region where there exists only one stationary solution. We also study the rheology of the system by calculating the apparent viscosity and the first normal stress difference. We find that the competition between the Couette flow and the electric field gives rise to an interesting non-Newtonian response which switches its behavior from shear thickening to shear thinning by exceeding a critical field.

Shear-banding phenomena and dynamical behavior in a Laponite suspension

Shear localization in an aqueous clay suspension of Laponite is investigated through dynamic light scattering, which provides access both to the dynamics of the system (homodyne mode) and to the local velocity profile (heterodyne mode). When shear bands form, a relaxation of the dynamics typical of a gel phase is observed in both bands soon after the flow stops. Periodic oscillations of the flow behavior, typical of a stick-slip phenomenon, are also observed when shear localization occurs. Both results are discussed in the light of various theoretical models for soft glassy gels.

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.

Electrorheological effect and directional non-Newtonian behavior in a nematic capillary subjected to a pressure gradient

We consider a capillary consisting of two coaxial cylinders whose core is filled with a nematic liquid crystal (LC) subjected to the simultaneous action of both a pressure gradient applied parallel to the axis of the cylinders and a radial low frequency electric field. We find the configuration of the director of the nematic, initially with an escaped-like configuration, for the flow aligning LC 4'-n-pentyl-4-cyanobiphenyl (5CB) by assuming hard anchoring hybrid boundary conditions. Also, we obtain the velocity profile parametrized by the electric field and the pressure gradient for nonslip boundary conditions. Finally, we calculate exactly the effective viscosity, the first normal stress difference, and the dragging forces on the cylinders. The results show an important electrorheological effect and a directional non-Newtonian response with regions of flow thinning and thickening.

Strain localization in a shear transformation zone model for amorphous solids

We model a sheared disordered solid using the theory of shear transformation zones (STZs). In this mean-field continuum model the density of zones is governed by an effective temperature that approaches a steady state value as energy is dissipated. We compare the STZ model to simulations by Shi [Phys. Rev. Lett. 98, 185505 (2007)], finding that the model generates solutions that fit the data, exhibit strain localization, and capture important features of the localization process. We show that perturbations to the effective temperature grow due to an instability in the transient dynamics, but unstable systems do not always develop shear bands. Nonlinear energy dissipation processes interact with perturbation growth to determine whether a material exhibits strain localization. By estimating the effects of these interactions, we derive a criterion that determines which materials exhibit shear bands based on the initial conditions alone. We also show that the shear band width is not set by an inherent diffusion length scale but instead by a dynamical scale that depends on the imposed strain rate.

Complex dynamics of shear banded flows

Many complex fluids undergo a flow induced transition to a state of coexisting bands of differing viscosities and internal structuring. This effect, which is called "shear banding", is widely observed in wormlike micellar surfactants, onion surfactants, colloidal suspensions and polymer solutions. According to a rapidly accumulating body of experimental evidence, shear bands often exhibit complex dynamics, which can be either oscillatory or chaotic in nature. This can be seen in the unsteady response of the bulk rheological signals, and in the motion of the interface between the bands. After giving a brief overview of this experimental evidence, we review in some detail recent efforts to address it theoretically.

Rheology modification in mixed shape colloidal dispersions. Part I: pure components

The flow behaviour and rheology of colloidal dispersions are of considerable interest in many applications, for example colloidal clay particles find applications in oilfield and construction-drilling fluids. The rheological properties of such fluids can be enhanced significantly by adding colloidal particles of different size and shape. To gain insight into the mechanism of this phenomenon, we have studied model mineral-colloid systems whose shape changes systematically from a plate-like aluminasol (gibbsite), through a lath-like smectite clay (hectorite), to a rod-like aluminasol (boehmite).The paper presents the results of a systematic and comprehensive multi-technique study (oscillatory, transient and steady shear) of the rheology of dispersions of these model systems. This gives a detailed account of the 'yield space' that characterises the complex transition of these soft materials from elastoviscous gels to viscoelastic liquids, and of the effect of particle size and shape on this behaviour. The observed phenomena are underpinned by two competing flow-mediated microstructural rearrangements that have significantly different timescales. A physical model invoking flow-mediated building and disruption of fluid structure is described to rationalise the observed behaviour. The study also forms the baseline to a companion study (part II), which investigates the rheological behaviour of mixed anisometric colloid systems based on these pure components.

Vorticity structuring and velocity rolls triggered by gradient shear bands

We suggest a mechanism by which vorticity structuring and velocity rolls can form in complex fluids, triggered by the linear instability of one-dimensional gradient shear banded flow. We support this with a numerical study of the diffusive Johnson-Segalman model. In the steady vorticity structured state, the thickness of the interface between the bands remains finite in the limit of zero stress diffusivity, presenting a possible challenge to the accepted theory of shear banding.

Wall slip, shear banding, and instability in the flow of a triblock copolymer micellar solution

The shear flow of a triblock copolymer micellar solution (PEO-PPO-PEO Pluronic P84 in brine) is investigated using simultaneous rheological and velocity profile measurements in the concentric cylinder geometry. We focus on two different temperatures below and above the transition temperature T{c} which was previously associated with the apparition of a stress plateau in the flow curve. (i) At T=37.0 degrees C<T{c}, the bulk flow remains homogeneous and Newtonian-like, although significant wall slip is measured at the rotor that can be linked to an inflexion point in the flow curve. (ii) At T=39.4 degrees C>T{c}, the stress plateau is shown to correspond to stationary shear-banded states characterized by two high shear rate bands close to the walls and a very weakly sheared central band, together with large slip velocities at the rotor. In both cases, the high shear branch of the flow curve is characterized by flow instability. Interpretations of wall slip, three-band structure, and instability are proposed in light of recent theoretical models and experiments.

Instabilities and constitutive modelling

The plastics industry today sees huge wastage through product defects caused by unstable flows during the manufacturing process. In addition, many production lines are throughput-limited by a flow speed threshold above which the process becomes unstable. Therefore, it is critically important to understand the mechanisms behind these instabilities. In order to investigate the flow of a molten plastic, the first step is a model of the liquid itself, a relation between its current stress and its flow history called a constitutive relation. These are derived in many ways and tested on several benchmark flows, but rarely is the stability of the model used as a criterion for selection. The relationship between the constitutive model and the stability properties of even simple flows is not yet well understood. We show that in one case a small change to the model, which does not affect the steady flow behaviour, entirely removes a known instability. In another, a change that makes a qualitative difference to the steady flow makes only tiny changes to the stability.The long-term vision of this research is to exactly quantify what are the important properties of a constitutive relation as far as stability is concerned. If we could understand that, not only could very simple stability experiments be used to choose the best constitutive models for a particular material, but our ability to predict and avoid wasteful industrial instabilities would also be vastly improved.

Vorticity banding during the lamellar-to-onion transition in a lyotropic surfactant solution in shear flow

We report on the rheology of a lyotropic lamellar surfactant solution (SDS/dodecane/pentanol/ water), and identify a discontinuous transition between two shear thinning regimes which correspond to the low-stress lamellar phase and the more viscous shear-induced multilamellar vesicle, or "onion" phase. We study in detail the flow curve, stress as a function of shear rate, during the transition region, and present evidence that the region consists of a shear-banded phase where the material has macroscopically separated into bands of lamellae and onions stacked in the vorticity direction. We infer very slow and irregular transformations from lamellae to onions as the stress is increased through the two-phase region, and identify distinct events consistent with the nucleation of small fractions of onions that coexist with sheared lamellae.

Vorticity banding in rodlike virus suspensions

Vorticity banding under steady shear flow is observed in a suspension of semiflexible colloidal rods (fd virus particles) within a part of the paranematic-nematic biphasic region. Banding occurs uniformly throughout the cell gap within a shear-rate interval (.gamma-, .gamma+) , which depends on the fd concentration. For shear rates below the lower-border shear rate .gamma- only shear elongation of inhomogeneities, which are formed due to paranematic-nematic phase separation, is observed. Within a small region just above the upper-border shear rate .gamma+ , banding occurs heterogeneously. An essential difference in the kinetics of vorticity banding is observed, depending on the morphology of inhomogeneities formed during the initial stages of the paranematic-nematic phase separation. Particle tracking and polarization experiments indicate that the vorticity bands are in a weak rolling flow, superimposed on the applied shear flow. We propose a mechanism for the origin of the banding instability and the transient stability of the banded states. This mechanism is related to the normal stresses generated by inhomogeneities formed due to the underlying paranematic-nematic phase transition.

Morphologies and flow patterns in quenching of lamellar systems with shear

We study the behavior of a fluid quenched from the disordered into the lamellar phase under the action of a shear flow. The dynamics of the system is described by Navier-Stokes and convection-diffusion equations with the pressure tensor and the chemical potential derived by the Brazovskii free energy. Our simulations are based on a mixed numerical method with the lattice Boltzmann equation and a finite difference scheme for Navier-Stokes and order parameter equations, respectively. We focus on cases where banded flows are observed with two different slopes for the component of velocity in the direction of the applied flow. Close to the walls the system reaches a lamellar order with very few defects, and the slope of the horizontal velocity is higher than the imposed shear rate. In the middle of the system the local shear rate is lower than the imposed one, and the system looks like a mixture of tilted lamellae, droplets, and small elongated domains. We refer to this as a region with a shear-induced structures (SIS) configuration. The local behavior of the stress shows that the system with the coexisting lamellar and SIS regions is in mechanical equilibrium. This phenomenon occurs, at fixed viscosity, for shear rates under a certain threshold; when the imposed shear rate is sufficiently large, lamellar order develops in the whole system. Effects of different viscosities have been also considered. The SIS region is observed only at low enough viscosity. We compare the above scenario with the usual one of shear banding. In particular, we do not find evidence for a plateau of the stress at varying imposed shear rates in the region with banded flow. We interpret our results as due to a tendency of the lamellar system to oppose the presence of the applied flow.

Banding in entangled polymer fluids under oscillatory shearing

We report a flow phenomenon in entangled polymer solutions that has never been described in the literature. A large-amplitude oscillatory shear was imposed on the polymer sample at a frequency higher than the overall chain relaxation rate. The resulting chain orientation led to a new environment in which the initially well-entangled chains managed to disentangle inhomogeneously in space. A layer lacking chain entanglement developed to take the load of the imposed strain. As a result of this nonlinearity, the rest of the sample avoided significant deformation and its chain entanglement remained intact.