We study the dynamics of shear startup of the Johnson-Segalman and non-stretching Rolie-Poly models using nonlinear simulations. We consider cases where the startup is from zero shear rate to shear rates in both the monotonic and nonmonotonic regions of the constitutive curve. For the Johnson-Segalman model, which exhibits a shear stress overshoot during startup, our nonlinear simulations show that transient shear banding is absent regardless of whether the start-up shear rate is in the monotonic or nonmonotonic regions of the constitutive curve. In the latter case, while there is clearly an inhomogeneity en route to the banded state, the extent of shear banding is not substantially large compared to that of the eventual banded state. Marked inhomogeneity in the velocity profile is predicted for the non-stretching Rolie-Poly model only if the solvent to solution viscosity ratio is smaller than O(10^(-3), but its occurrence does not appear to have any correlation with the stress overshoot during startup. These inhomogeneities are also very sensitive to initial amplitude of perturbations and the magnitude of Reynolds number. Our nonlinear simulations show that the transient evolution during shear startup is quite sensitive to the Reynolds number when the solvent viscosity parameter is much smaller than unity for non-stretching Rolie-Poly model. However, the results of the Johnson-Segalman model are very robust for solvent to solution viscosity greater than O(10^(-3) and do not reveal any transient shear banding during shear startup.
We study numerically the formation of long-lived transient shear bands during shear startup within two models of soft glasses (a simple fluidity model and an adapted `soft glassy rheology' model). The degree and duration of banding depends strongly on the applied shear rate, and on sample age before shearing. In both models the ultimate steady flow state is homogeneous at all shear rates, consistent with the underlying constitutive curve being monotonic. However, particularly in the SGR case, the transient bands can be extremely long lived. The banding instability is neither `purely viscous' n…
We investigate theoretically shear banding in large amplitude oscillatory shear (LAOS) of polymers and wormlike micelles. In LAOStrain we find banding at low frequencies and sufficiently high strain rate amplitudes in fluids for which the underlying constitutive curve of shear stress as a function of shear rate is non-monotonic. This is the direct analogue of quasi steady state banding seen in slow strain rate sweeps along the flow curve. At higher frequencies and sufficiently high strain amplitudes we report a different but related phenomenon, which we call `elastic' shear banding. This is as…
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 $\dotγ(t)=\dotγ_0\cos(ωt)$, even in materials that do not permit banding as their steady state response to a steady imposed shear flow $\dotγ=\dotγ_0=$const. Highly counterintuitively, banding persists in LAOS even in the limit of zero frequency $ω\to 0$, where…
We assess the possibility of shear banding of semidilute rod-like colloidal suspensions under steady shear ow very close to the isotropic-nematic spinodal, using a combination of rheology, small angle neutron scattering, and laser Doppler velocimetry. Model systems are employed which allow for a length and stiffness variation of the particles. The rheological signature reveals that these systems are strongly shear thinning at moderate shear rates. It is shown that the longest and most flexible rods undergo the strongest shear thinning and have the greatest potential to form shear bands. Althou…
Using a micro particle imaging velocity technique, we resolve for the first time the three dimensionnal structure of wormlike shear banding flows in straight microchannels. The study revealed two effects, which should be generic for shear banding flows: the first is a strong amplification of the confinement induced by the edge of the channel, the second is an instability of the interface between the shear bands. A detailed quantitative comparison of our experimental measurements with a theoretical study of the diffusive Johnson Segalman model leads to excellent agreement. Our study clarifies t…
This precis is aimed as a practical field-guide to situations in which shear banding might be expected in complex fluids subject to an applied shear flow. Separately for several of the most common flow protocols, it summarises the characteristic signatures in the measured bulk rheological signals that suggest the presence of banding in the underlying flow field. It does so both for a steady applied shear flow, and for the time-dependent protocols of shear startup, step stress, finite strain ramp, and large amplitude oscillatory shear. An important message is that banding might arise rather wid…
Based on numerical modeling with the diffusive Giesekus constitutive equation, a recent Letter [Phys. Rev. Lett. 120, 138002 (2018), arXiv:1801.08798] claimed that the experimental reports of shear banding in entangled polymeric fluids were due to the disturbances from the sample edge. The conclusion that true bulk shear banding is precluded in the presence of edge effects is at odds with many past experimental, theoretical, numerical, and computer simulation studies. We briefly discuss some problems of this work.
Homogeneous polymer solutions are well-known to exhibit viscoelastic flow instabilities: purely elastic when inertia is negligible, inertio-elastic otherwise. Recently, shear-banding wormlike micelles solutions were also discovered to follow a similar phenomenology. In the shear-banding regime, inertia is usually negligible so only purely elastic flows have been reported. Here, we investigate a non-shear-banding solution where inertia becomes significant, leading to flow patterns akin to the inertio-elastic regime of dilute polymer solutions. We show that the instability follows a supercritica…
We study theoretically shear banding in soft glassy materials subject to large amplitude time-periodic shear flows, considering separately the protocols of large amplitude oscillatory shear strain, large amplitude square or triangular or sawtooth strain rate, and large amplitude oscillatory shear stress. In each case, we find shear banding to be an important part of the material's flow response for a broad range of values of the frequency $ω$ and amplitude of the imposed oscillation. Crucially, and highly counterintuitively, in the glass phase this persists even to the lowest frequencies acces…
Edge instabilities are believed to be one of the possible causes of shear banding in entangled polymeric fluids. Here, we investigate the effect of edge disturbance on the shear-induced dynamics of well-entangled DNA solutions. Using a custom high-aspect-ratio planar-Couette cell, we systematically measure the velocity profiles of sheared DNA samples at different distances away from the edge of the shear cell. Under a weak oscillatory shear with the corresponding Weissenberg number (Wi) smaller than 1, where DNA solutions exhibit linear velocity profiles with strong wall slip, the penetration …
We review and compare the phenomenological aspects and physical origin of shear-localization and shear-banding in various material types, namely emulsions, suspensions, colloids, granular materials and micellar systems. It appears that shear-banding, which must be distinguished from the simple effect of coexisting static-flowing regions in yield stress fluids, occurs in the form of a progressive evolution of the local viscosity towards two significantly different values in two adjoining regions of the fluids in which the stress takes slightly different values. This suggests that from a global …
We observe a novel type of shear banding in the rheology of thixotropic yield-stress fluids that is due to the coupling of both non-locality and thixotropy. The latter is known to lead to shear banding even in homogeneous stress fields, but the bands observed in the presence of non-local effects appear different as the shear rate varies continuously over the shear band. Here, we introduce a simple non-local model for the shear banding (NL-SB), and we implement it for the analysis of micron-scale rheo-MRI velocimetry measurements of a milk microgel suspension in a cone-and-plate geometry. The p…
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 sub-critical 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 acco…
Within a highly generalised theoretical framework for the flow properties of complex fluids, we study the onset of shear banding in the three most common time-dependent experimental protocols: step stress, step strain and shear startup. By means of a linear stability analysis we derive a fluid-universal criterion for the onset of banding, separately for each protocol, that depends only on the shape of the experimentally measured time-dependent rheological response function, independent of the constitutive law and internal state variables of the particular fluid in question. Our predictions thu…
Using high-resolution confocal rheometry, we study the shear profiles of well-entangled DNA solutions under large amplitude oscillatory shear (LAOS) in a rectilinear planar shear cell. With increasing Weissenberg number (Wi), we observe successive transitions from normal Newtonian linear shear profiles to wall-slip dominant shear profiles and finally to shear-banding profiles at high Wi. To investigate the microscopic origin of the observed shear banding, we study the dynamics of micron-sized tracers embedded in DNA solutions. Surprisingly, tracer particles in the shear frame exhibit transient…
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 characteri…
We study the dynamics of shear-band formation and evolution using a simple rheological model. The description couples the local structure and viscosity to the applied shear stress. We consider in detail the Couette geometry, where the model is solved iteratively with the Navier-Stokes equation to obtain the time-evolution of the local velocity and viscosity fields. It is found that the underlying reason for dynamic effects is the non-homogeneous shear distribution, which is amplified due to a positive feedback between the flow field and the viscosity response of the shear thinning fluid. This …
Soft Glassy Materials, Non Linear Rheology, Lattice Kinetic models, frustrated phase separation} We present numerical simulations based on a Boltzmann kinetic model with competing interactions, aimed at characterizating the rheological properties of soft-glassy materials. The lattice kinetic model is shown to reproduce typical signatures of driven soft-glassy flows in confined geometries, such as Herschel-Bulkley rheology, shear-banding and histeresys. This lends further credit to the present lattice kinetic model as a valuable tool for the theoretical/computational investigation of the rheolo…
We study the emergence of a yield stress in dense suspensions of non-Brownian particles, by combining local velocity and concentration measurements using Magnetic Resonance Imaging with macroscopic rheometric experiments. We show that the competition between gravity and viscous stresses is at the origin of the development of a yield stress in these systems at relatively low volume fractions. Moreover, it is accompanied by a shear banding phenomenon that is the signature of this competition. However, if the system is carefully density matched, no yield stress is encountered until a volume fract…
We demonstrate that application of an increasing shear field on a glass leads to an intriguing dynamic first order transition in analogy to equilibrium transitions. By following the particle dynamics as a function of the driving field in a colloidal glass, we identify a critical shear rate upon which the diffusion time scale of the glass exhibits a sudden discontinuity. Using a new dynamic order parameter, we show that this discontinuity is analogous to a first order transition, in which the applied stress acts as the conjugate field on the system's dynamic evolution. These results offer new p…
We report a large set of experimental data which demonstrates that a simple yield stress fluid, i.e. which does not present aging or thixotropy, exhibits transient shear banding before reaching a steady state characterized by a homogeneous, linear velocity profile. The duration of the transient regime decreases as a power law with the applied shear rate $\dotγ$. This power law behavior, observed here in carbopol dispersions, does not depend on the gap width and on the boundary conditions for a given sample preparation. For $\dotγ\lesssim 0.1$ s$^{-1}$, heterogeneous flows could be observed for…
We study the steady flow properties of different three-dimensional aqueous foams in a wide gap Couette geometry. From local velocity measurements through Magnetic Resonance Imaging techniques and from viscosity bifurcation experiments, we find that these foams do not exhibit any observable signature of shear banding. This contrasts with two previous results (Rodts et al., Europhys. Lett., 69 (2005) 636 and Da Cruz et al., Phys. Rev. E, 66 (2002) 051305); we discuss possible reasons for this dicrepancy. Moreover, the foams we studied undergo steady flow for shear rates well below the critical s…
Bacterial suspensions--a premier example of active fluids--show an unusual response to shear stresses. Instead of increasing the viscosity of the suspending fluid, the emergent collective motions of swimming bacteria can turn a suspension into a "superfluid" with zero apparent viscosity. Although the existence of active "superfluids" has been demonstrated in bulk rheological measurements, the microscopic origin and dynamics of such an exotic phase have not been experimentally probed. Here, using high-speed confocal rheometry, we study the dynamics of concentrated bacterial suspensions under si…
Jammed systems all have a yield stress. Among these materials some have been shown to shear-band but it is as yet unclear why some materials develop shear-band and some others do not. In order to rationalize existing data concerning the flow characteristics of jammed systems and in particular understand the physical origin of such a difference we propose a simple approach for describing the steady flow behaviour of yield stress fluids, which retains only basic physical ingredients. Within this frame we show that in the liquid regime the behaviour of jammed systems turns from that of a simple y…
Motivated by the need for a theoretical study in a planar geometry that can easily be implemented experimentally, we study the pressure driven Poiseuille flow of a shear banding fluid. After discussing the "basic states" predicted by a one dimensional calculation that assumes a flat interface between the bands, we proceed to demonstrate such an interface to be unstable with respect to the growth of undulations along it. We give results for the growth rate and wavevector of the most unstable mode that grows initially, as well as for the ultimate flow patterns to which the instability leads. We …
We have designed 3D numerical simulations of a soft spheres model, with size polidispersity and in athermal conditions, to study the transient shear banding that occurs during yielding of jammed soft solids. We analyze the effects of different types of drag coefficients used in the simulations and compare the results obtained using Lees-Edwards periodic boundary conditions with the case in which the same model solid is confined between two walls. The specific damping mechanism and the different boundary conditions indeed modify the load curves and the velocity profiles in the transient regime.…
Amorphous solids are critical in the design and production of nanoscale devices, but under strong confinement these materials exhibit changes in their mechanical properties which are not well understood. Phenomenological models explain these properties by postulating an underlying defect structure in these materials but do not detail the microscopic properties of these defects. Using machine learning methods, we identify mesoscale defects that lead to shear banding in polymer nanopillars well below the glass transition temperature as a function of pillar diameter. Our results show that the pri…
In this work, we use flow visualization and rheometry techniques to study the dynamics and evolution of secondary flows in a model wormlike micellar solution sheared between concentric cylinders, i.e., in a Taylor-Couette (TC) cell. The wormlike micellar solution studied in this work contains cetyltrimethylammonium bromide (CTAB) and sodium salicylate (NaSal). This system can be shear banding and highly elastic, non-shear banding and moderately elastic, or nearly Newtonian as the temperature is varied over a narrow range. The effect of elasticity on transitions and instabilities is probed by c…
One prototypical instability in granular flows is the shear-banding instability, in which a uniform granular shear flow breaks into alternating bands of dense and dilute clusters of particles having low and high shear (shear stress or shear rate), respectively. In this work, the shear-banding instability in an arbitrarily inelastic granular shear flow is analyzed through the linear stability analysis of granular hydrodynamic equations closed with Navier--Stokes-level constitutive relations. It is shown that the choice of appropriate constitutive relations plays an important role in predicting …
The interplay between shear band (SB) formation and boundary conditions (BC) is investigated in wormlike micellar systems (CPyCl--NaSal) using ultrasonic velocimetry coupled to standard rheology in Couette geometry. Time-resolved velocity profiles are recorded during transient strain-controlled experiments in smooth and sand-blasted geometries. For stick BC standard SB is observed, although depending on the degree of micellar entanglement temporal fluctuations are reported in the highly sheared band. For slip BC wall slip occurs only for shear rates larger than the start of the stress plateau.…
Many soft materials, including foams, dense emulsions, micro gel bead suspensions, star polymers, dense packing of surfactant onion micelles, 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 r…
Cooperativity effects have been proposed to explain the non-local rheology in the dynamics of soft jammed systems. Based on the analysis of the free-energy model proposed by L. Bocquet, A. Colin \& A. Ajdari ({\em Phys. Rev. Lett.} {\bf 103}, 036001 (2009)), we show that cooperativity effects resulting from the non-local nature of the fluidity (inverse viscosity), are intimately related to the emergence of shear-banding configurations. This connection materializes through the onset of inhomogeneous compact solutions (compactons), wherein the fluidity is confined to finite-support subregions of…
We study theoretically the formation of shear bands in time-dependent flows of polymeric and wormlike micellar surfactant fluids, focussing on the protocols of step shear stress, step shear strain (or in practice a rapid strain ramp), and shear startup, which are commonly studied experimentally. For each protocol we perform a linear stability analysis to provide a fluid-universal criterion for the onset of shear banding, following our recent Letter [Phys. Rev. Lett. 110 (2013) 086001]. In each case this criterion depends only on the shape of the experimentally measured rheological response fun…
The occurence of shear bands in a complex fluid is generally understood as resulting from a structural evolution of the material under shear, which leads (from a theoretical perspective) to a non-monotonic stationnary flow curve related to the coexistence of different states of the material under shear. In this paper we present a scenario for shear-banding in a particular class of complex fluids, namely foams and concentrated emulsions, which differs from other scenarii in two important ways. First, the appearance of shear bands is shown to be possible both without any intrinsic physical evolu…
Wang [Phys. Rev. Lett. 103, 219801 (2009)] makes the following points about our Letter [Phys. Rev. Lett. 102, 067801 (2009), arXiv:0805.0679]: (1) He infers that, "contrary to its title, shear banding emerged from monotonic curves only if there was a stress gradient", and he points out that nonquiescent relaxation was found (experimentally) after step strain in geometries without a stress gradient. (2) He disagrees with the values of the parameters we used. (3) In some recent experiments the flow was homogeneous after cessation of step strain, and only subsequently developed nonquiescent macro…
Edge fracture occurs frequently in non-Newtonian fluids. A similar instability has often been reported at the free surface of fluids undergoing shear banding, and leads to expulsion of the sample. In this paper the distortion of the free surface of such a shear banding fluid is calculated by balancing the surface tension against the second normal stresses induced in the two shear bands, and simultaneously requiring a continuous and smooth meniscus. We show that wormlike micelles typically retain meniscus integrity when shear banding, but in some cases can lose integrity for a range of average …
