Thibaut Divoux

Yield stress materials in soft condensed matter

A comprehensive review is presented of the physical behavior of yield stress materials in soft condensed matter, which encompasses 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. Both the physical origin and rheological consequences associated with this nonlinear behavior are discussed and an overview is given of experimental techniques available to measure the yield stress. Recent progress is discussed 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 nonlocal effects in confined geometries.

From stress-induced fluidization processes to Herschel-Bulkley behaviour in simple yield stress fluids

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 solid-like to liquid-like 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 τf of this fluidization process scales as τf ∝ 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.

Shear Banding of Complex Fluids

Even in simple geometries, many complex fluids display nontrivial flow fields, with regions where shear is concentrated. The possibility for such shear banding has been known for several decades, but in recent years, we have seen an upsurge in studies offering an ever-more precise understanding of the phenomenon. The development of new techniques to probe the flow on multiple scales with increasing spatial and temporal resolution has opened the possibility for a synthesis of the many phenomena that could only have been thought of separately before. In this review, we bring together recent research on shear banding in polymeric and soft glassy materials and highlight their similarities and disparities.

Rheological Hysteresis in Soft Glassy Materials

The nonlinear rheology of a soft glassy material is captured by its constitutive relation, shear stress versus shear rate, which is most generally obtained by sweeping up or down the shear rate over a finite temporal window. For a huge amount of complex fluids, the up and down sweeps do not superimpose and define a rheological hysteresis loop. By means of extensive rheometry coupled to time-resolved velocimetry, we unravel the local scenario involved in rheological hysteresis for various types of well-studied soft materials. We introduce two observables that quantify the hysteresis in macroscopic rheology and local velocimetry, respectively, as a function of the sweep rate δt(-1). Strikingly, both observables present a robust maximum with δt, which defines a single material-dependent time scale that grows continuously from vanishingly small values in simple yield stress fluids to large values for strongly time-dependent materials. In line with recent theoretical arguments, these experimental results hint at a universal time scale-based framework for soft glassy materials, where inhomogeneous flows characterized by shear bands and/or pluglike flow play a central role.

Stress overshoot in a simple yield stress fluid: An extensive study combining rheology and velocimetry

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 rate . (i) At small strains (γ w. Finally, by changing the boundary conditions from rough to smooth, we show that there exists a critical shear rate s 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 of s is observed to coincide with the shear rate below which the flow curve displays a kink attributed to wall slip.

Shear-banding in surfactant wormlike micelles: elastic instabilities and wall slip

We report on the flow dynamics of a wormlike micellar system (CPCl/NaSal/brine) undergoing a shear-banding transition using a combination of global rheology, 1D ultrasonic velocimetry and 2D optical visualisation. The different measurements being performed in a single Taylor–Couette geometry, we find a strong correlation between the induced turbid band observed optically and the high shear rate band. This correspondence reveals that fluctuations observed in the 1D velocity profiles are related to elastic instabilities triggered in the high shear rate band: 3D coherent (laminar) flow and 3D turbulent flow successively develop as the applied shear rate is increased. The specific characteristics of the resulting complex dynamics are found to depend on subtle changes in the sample, due to temporary light exposure. The CPCl molecules exhibit a photochemistry mainly influenced by the photo-induced cleavage of the pyridine ring that yields an unstable aldehyde enamine, which further decays by thermally activated processes. The products of the reaction possibly build up a lubrication layer responsible for pathological flow dynamics. Overall, our results bridge the gap between previous independent optical and local velocity measurements and explain most of the observed fluctuations in terms of a sequence of elastic instabilities which turns out to be widespread among semidilute wormlike micellar systems.

Yielding dynamics of a Herschel–Bulkley fluid: a critical-like fluidization behaviour

The shear-induced fluidization of a carbopol microgel is investigated during long start-up experiments using combined rheology and velocimetry in Couette cells of varying gap widths and boundary conditions. As already described in [Divoux et al., Phys. Rev. Lett., 2010, 104, 208301], we show that the fluidization process of this simple yield stress fluid involves a transient shear-banding regime whose duration tau_f decreases as a power law of the applied shear rate gp. We complete our previous findings by an investigation of the influence of the shearing geometry through the gap width e and the boundary conditions. While slip conditions at the walls seem to have a negligible influence on the fluidization time tau_f, different fluidization processes are observed depending on gp and e: the shear band remains almost stationary for several hours at low shear rates or small gap widths before strong fluctuations lead to a homogeneous flow whereas at larger values of gp or e, the transient shear band is seen to invade the whole gap in a much smoother way. Finally, by comparing local and global rheological measurements, we emphasize that the steady state reached by our samples is fully compatible with that expected for a simple yield stress fluid described by a Herschel-Bulkley behaviour.The shear-induced fluidization of a carbopol microgel is investigated during long start-up experiments using combined rheology and velocimetry in Couette cells of varying gap widths and boundary conditions. As already described in [Divoux et al., Phys. Rev. Lett., 2010, 104, 208301], we show that the fluidization process of this simple yield stress fluid involves a transient shear-banding regime whose duration τf decreases as a power law of the applied shear rate . Here we go one step further by an exhaustive investigation of the influence of the shearing geometry through the gap width e and the boundary conditions. While slip conditions at the walls seem to have a negligible influence on the fluidization time τf, different fluidization processes are observed depending on and e: the shear band remains almost stationary for several hours at low shear rates or small gap widths before strong fluctuations lead to a homogeneous flow, whereas at larger values of or e, the transient shear band is seen to invade the whole gap in a much smoother way. Still, the power-law behaviour appears to be very robust and hints to critical-like dynamics. To further discuss these results, we propose (i) a qualitative scenario to explain the induction-like period that precedes full fluidization and (ii) an analogy with critical phenomena that naturally leads to the observed power laws if one assumes that the yield point is the critical point of an underlying out-of-equilibrium phase transition.

Interplay between elastic instabilities and shear-banding: three categories of Taylor–Couette flows and beyond

In the past twenty years, shear-banding flows have been probed by various techniques, such as rheometry, velocimetry and flow birefringence. In micellar solutions, many of the data collected exhibit unexplained spatiotemporal fluctuations. Recently, it has been suggested that those fluctuations originate from a purely elastic instability of the shear-banding flow. In cylindrical Couette geometry, the instability is reminiscent of the Taylor-like instability observed in viscoelastic polymer solutions. The criterion for purely elastic Taylor–Couette instability adapted to shear-banding flows suggested three categories of shear-banding depending on their stability. In the present study, we report on a large set of experimental data which demonstrates the existence of the three categories of shear-banding flows in various surfactant solutions. Consistent with theoretical predictions, increases in the surfactant concentration or in the curvature of the geometry destabilize the flow, whereas an increase in temperature stabilizes the flow. However, experiments also exhibit some interesting behaviors going beyond the purely elastic instability criterion.

Creep and fracture of a protein gel under stress.

Biomaterials such as protein or polysaccharide gels are known to behave qualitatively as soft solids and to rupture under an external load. Combining optical and ultrasonic imaging to shear rheology we show that the failure scenario of a protein gel is reminiscent of brittle solids: after a primary creep regime characterized by a power-law behavior whose exponent is fully accounted for by linear viscoelasticity, fractures nucleate and grow logarithmically perpendicularly to shear, up to the sudden rupture of the gel. A single equation accounting for those two successive processes nicely captures the full rheological response. The failure time follows a decreasing power law with the applied shear stress, similar to the Basquin law of fatigue for solids. These results are in excellent agreement with recent fiber-bundle models that include damage accumulation on elastic fibers and exemplify protein gels as model, brittlelike soft solids.

Creep Motion of a Granular Pile Induced by Thermal Cycling

We report a time-resolved study of the dynamics associated with the slow compaction of a granular column submitted to thermal cycles. The column height displays a complex behavior: for a large amplitude of the temperature cycles, the granular column settles continuously, experiencing a small settling at each cycle. By contrast, for a small-enough amplitude, the column exhibits a discontinuous and intermittent activity: successive collapses are separated by quiescent periods whose duration is exponentially distributed. We then discuss potential mechanisms which would account for both the compaction and the transition at finite amplitude.