We present a comprehensive review of the physical behavior of yield stress materials in soft condensed matter, which encompass a broad range of materials from colloidal assemblies and gels to emulsions and non-Brownian suspensions. All these disordered materials display a nonlinear flow behavior in response to external mechanical forces, due to the existence of a finite force threshold for flow to occur: the yield stress. We discuss both the physical origin and rheological consequences associated with this nonlinear behavior, and give an overview of experimental techniques available to measure the yield stress. We discuss recent progress concerning a microscopic theoretical description of the flow dynamics of yield stress materials, emphasizing in particular the role played by relaxation time scales, the interplay between shear flow and aging behavior, the existence of inhomogeneous shear flows and shear bands, wall slip, and non-local effects in confined geometries.

The decomposition of the time reversal operator ͑DORT͒ method is a selective detection and focusing technique using an array of transmit-receive transducers. It relies on the theory of iterative time reversal mirrors which was presented by Prada et al. ͓C. Prada, J. L. Thomas, and M. Fink, J. Acoust. Soc. Am. 97, 62-71 ͑1995͔͒. The time reversal operator was defined as K*()K(), where is the frequency, * means complex conjugate, and K͑͒ is the transfer matrix of the array of L transducers insonifying a time invariant scattering medium. It was shown that this time reversal operator can be diagonalized and that for ideally resolved scatterers of different reflectivities, each of its eigenvectors of nonzero eigenvalue provides the phase law to be applied to the transducers in order to focus on one of the scatterers. The DORT method consists in determining these eigenvectors and using them for the selective focusing. This paper presents a complete analysis of this method in the case of two scatterers. The mathematical expressions of the eigenvectors are given and several experimental results are described. In particular, the effectiveness of the method to focus selectively through an inhomogeneous medium is established.

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 γ. 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 γ≲0.1  s(-1), heterogeneous flows could be observed for as long as 10(5)  s. These local dynamics account for the ultraslow stress relaxation observed at low shear rates.

Stress-induced fluidization of a simple yield stress fluid, namely a carbopol microgel, is addressed through extensive rheological measurements coupled to simultaneous temporally and spatially resolved velocimetry. These combined measurements allow us to rule out any bulk fracture-like scenario during the fluidization process such as that suggested in [Caton et al., Rheol Acta, 2008, 47, 601-607]. On the contrary, we observe that the transient regime from solidlike to liquidlike behaviour under a constant shear stress σ successively involves creep deformation, total wall slip, and shear banding before a homogeneous steady state is reached. Interestingly, the total duration τ f of this fluidization process scales as τ f ∝ 1/(σ − σc) β , where σc stands for the yield stress of the microgel, and β is an exponent which only depends on the microgel properties and not on the gap width or on the boundary conditions. Together with recent experiments under imposed shear rate [Divoux et al., Phys. Rev. Lett., 2010, 104, 208301], this scaling law suggests a route to rationalize the phenomenological Herschel-Bulkley (HB) power-law classically used to describe the steady-state rheology of simple yield stress fluids. In particular, we show that the steady-state HB exponent appears as the ratio of the two fluidization exponents extracted separately from the transient fluidization processes respectively under controlled shear rate and under controlled shear stress.

The nonlinear rheological response of soft glassy materials is addressed experimentally by focusing on concentrated emulsions where interdroplet attraction is tuned through varying the surfactant content. Velocity profiles are recorded using ultrasonic velocimetry simultaneously to global rheological data in the Couette geometry. Our data show that non-adhesive and adhesive emulsions have radically different flow behaviors in the vicinity of yielding: while the flow remains homogeneous in the non-adhesive emulsion and the Herschel-Bulkley model for a yield stress fluid describes the data very accurately, the adhesive system displays shear localization and does not follow a simple constitutive equation, suggesting that the mechanisms involved in yielding transitions are not universal.PACS numbers: 83.60. La, 83.80.Iz, 83.50.Rp, 83.60.Rs The term "jamming" describes different ways by which a system of particles loses its ability to flow: increasing the volume fraction, lowering the temperature, or releasing some external stress [1,2]. It occurs in a wide variety of materials known as "soft glassy materials," ranging from polymers and colloids to granular assemblies [3,4] (for a recent review see Ref.[5]). The response of such systems to an external shear stress is characterized by two regimes: for stresses below the yield stress σ 0 they remain jammed and respond elastically, whereas for stresses above σ 0 they flow as liquids [6].A first way to investigate this stress-induced solid-fluid transition (hereafter referred to as the yielding transition) is to perform oscillatory shear experiments and to measure the viscoelastic moduli of the system during frequency or stress/strain sweeps. Very useful information on the yielding behavior can be gained from such measurements e.g. estimations of σ 0 [4,7], and when coupled to dynamic light scattering, the number of local rearrangements within the material [8,9].Another way to study the yielding transition is to probe the sample response to steady shear and to focus on the flow behavior deep into the nonlinear regime. Such experiments, which are the subject of the present contribution, have already attracted a lot of attention during the last decade. In particular magnetic resonance imaging (MRI) has shown that various colloidal suspensions and emulsions cannot flow at a uniform shear rate smaller than some critical valueγ c in the vicinity of the yield stress: under applied shear rate a "liquid" zone sheared at a rate larger thanγ c coexists with a jammed, solid-like region which disappears as the shear rate is increased [10]. Similar shear localization (or shear banding) had already been observed in thixotropic suspensions [11] and was confirmed very recently using MRI in a concentrated hard-sphere colloidal system [12]. This picture also emerges from molecular dynamics simulations of model glasses [13] and athermal systems [14].However at this stage it is not clear whether all systems that are jammed at rest display shear localization as they go through the yieldin...

Using Dynamic Light Scattering in heterodyne mode, we measure velocity profiles in a much studied system of wormlike micelles (CPCl/NaSal) known to exhibit both shear-banding and stress plateau behavior. Our data provide evidence for the simplest shear-banding scenario, according to which the effective viscosity drop in the system is due to the nucleation and growth of a highly sheared band in the gap, whose thickness linearly increases with the imposed shear rate. We discuss various details of the velocity profiles in all the regions of the flow curve and emphasize on the complex, non-Newtonian nature of the flow in the highly sheared band.PACS numbers: 83.80.Qr, 47.50.+d, 83.85.Ei Understanding the correlation between mechanical and structural response in non-Newtonian fluids submitted to high deformation rates is crucial on both fondamental and technological grounds [1]. Among the variety of complex fluids investigated in recent years, a wide class exhibits flow-structure coupling that leads to a strong shear-thinning behavior: along the steady-state flow curve (shear stress σ vs. shear rateγ), a drop of up to three orders of magnitude in the effective viscosity η = σ/γ is observed in a very narrow stress range leading to a stress plateau (for a review, see for instance Refs. [1,2]). In correlation with this stress plateau, bands of different micro-structures and normal to the velocity gradient appear. Such bands correspond to a new shearinduced structure (SIS), whose low viscosity is in general supposed to be responsible for the shear-thinning. This so-called shear-banding behavior has been observed in both ordered mesophases (lamellar, hexagonal, cubic) [3] and transient gels [4].A particularly well-documented example is the group of wormlike micellar systems of self-assembled surfactant molecules [5,6]. They consist of very long cylindrical aggregates whose configurations mimic polymer solutions. However their dynamics is strongly modified by the equilibrium character of the chains, which enables them to break and recombine [7]. Generically, one starts from an isotropic viscoelastic solution of these micelles above the semidilute regime, which behaves like a Maxwell fluid at low shear rates. Upon increasingγ and entering the nonlinear regime, the onset of the stress plateau for a critical shear rateγ 1 is associated with the nucleation and growth of highly birefringent bands, suggesting strong alignment of the micelles along the velocity direction [5,6]. As the shear rate is further increased aboveγ 1 , the new organization progressively fills the gap at almost constant stress, up to a second critical shear rateγ 2 . Aboveγ 2 , the system enters a second regime of apparently homogeneous structure, with a second branch of increasing stress. The flow curve of Fig. 1 is typical of micellar systems like that investigated in the present work. Such a stress plateau has been reported for concentrations close to the equilibrium isotropic-nematic (I-N) transition, where coupling between the order parameter an...

Attractive colloidal gels display a solid-to-fluid transition as shear stresses above the yield stress are applied. This shear-induced transition is involved in virtually any application of colloidal gels. It is also crucial for controlling material properties. Still, in spite of its ubiquity, the yielding transition is far from understood, mainly because rheological measurements are spatially averaged over the whole sample. Here, the instrumentation of creep and oscillatory shear experiments with high-frequency ultrasound opens new routes to observing the local dynamics of opaque attractive colloidal gels. The transition proceeds from the cell walls and heterogeneously fluidizes the whole sample with a characteristic time whose variations with applied stress suggest the existence of an energy barrier linked to the gelation process. The present results provide new test grounds for computer simulations and theoretical calculations in the attempt to better understand the yielding transition. The versatility of the technique should also allow extensive mesoscopic studies of rupture mechanisms in soft solids ranging from crystals to glassy materials.

We report a large amount of experimental data on the stress overshoot phenomenon which takes place during start-up shear flows in a simple yield stress fluid, namely a carbopol microgel. A combination of classical rheological measurements and ultrasonic velocimetry makes it possible to get physical insights on the transient dynamics of both the stress σ(t) and the velocity field across the gap of a rough cylindrical Couette cell during the start-up of shear under an applied shear ratė γ. (i) At small strains (γ < 1), σ(t) increases linearly and the microgel undergoes homogeneous deformation. (ii) At a time tm, the stress reaches a maximum value σm which corresponds to the failure of the microgel and to the nucleation of a thin lubrication layer at the moving wall. (iii) The microgel then experiences a strong elastic recoil and enters a regime of total wall slip while the stress slowly decreases. (iv) Total wall slip gives way to a transient shear-banding phenomenon, which occurs on timescales much longer than that of the stress overshoot and has been described elsewhere [Divoux et al., Phys. Rev. Lett., 2010, 104, 208301]. This whole sequence is very robust to concentration changes in the explored range (0.5 ≤ C ≤ 3% w/w). We further demonstrate that the maximum stress σm and the corresponding strain γm =γtm both depend on the applied shear rateγ and on the waiting time tw between preshear and shear start-up: they remain roughly constant as long asγ is smaller than some critical shear rateγw ∼ 1/tw and they increase as weak power laws ofγ forγ >γw. Finally, by changing the boundary conditions from rough to smooth, we show that there exists a critical shear rateγs fixed by the wall surface roughness below which slip at both walls allows for faster stress relaxation and for stress fluctuations strongly reminiscent of stick-slip. Interestingly, the value ofγs is observed to coincide with the shear rate below which the flow curve displays a kink attributed to wall slip. PACS numbers:The transient response of complex materials to the application of an external shear deformation is of huge importance not only for the practical use of such materials but also during the processing stage. The archetypal experiment used for transient rheological characterization is a "start-up experiment" where a constant shear rateγ is applied from rest and the subsequent stress response is monitored until steady-state is reached. A host of widely different systems from soft and hard condensed matter have been reported to present a non-monotonic stress response during start-up experiments. Roughly, the stress σ versus time t first increases linearly, reaches a maximum value denoted σ m at a time t m and then decreases towards it steady-state value. This temporal sequence is usually referred to as a stress overshoot. It has been reported experimentally for both amorphous materials, such as amorphous polymers [1][2][3] and metallic glasses [4,5], and for soft glassy materials, namely emulsions [6][7][8][9], foams [10,11], microgels [12,13]...