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

Divoux, Thibaut; Tamarii, David; Barentin, Catherine; Teitel, S.; Manneville, Sébastien

doi:10.1039/c2sm06918k

Cited by 80 publications

(79 citation statements)

References 67 publications

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“…This is since even the smallest stress gradient is enough to trigger the transient shear bands due to the shear dependent response of the fluid. Experimental observations of stress signatures associated with transient shear banding found in a cone-and-plate geometry, where the stress gradient is extremely small, also support this finding [36]. Furthermore, in Eq.…”

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confidence: 73%

Transient shear banding in time-dependent fluids

et al. 2013

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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 nonhomogeneous shear distribution, which is amplified due to a positive feedback between the flow field and the viscosity response of the shear thinning fluid. This offers a simple explanation for the recent observations of transient shear banding in time-dependent fluids. Extensions to more complicated rheological systems are considered. The property that characterizes complex fluids is their nontrivial rheology, shear rate-stress relation. They are generally further categorized into shear thinning or shear thickening fluids. Both cases are additionally complicated by time dependence. Due to the stress-shear interaction, already small perturbations in the local stress can result in a positive feedback with the flow promoting shear instabilities in each case [1,2]. The understanding of complex fluids is of enormous importance for many practical applications [3] and the theory touches on many branches of physics. Recent advances make it possible to follow the suspension local velocity during a standard rheological experiment [4,5]. Quantifying the local flow field simultaneously with rheological measurements gives the possibility to measure both the intrinsic and apparent rheology. This has led to the discovery that a heterogeneous shear distribution in samples during such tests is ubiquitous. Shear banding [6] has been observed in many systems composed of substantially different building blocks, such as colloidal glasses, wormlike micelles, foams, and granular matter [7]. The current viewpoint, both phenomenologically and theoretically, is that a nonmonotonic intrinsic flow curve is what is common to most of these materials [6,8], but also other mechanisms have been suggested [9].A branch of complex fluids are the simple yield stress fluids [10]. These materials do not show aging phenomena (thixotropy). Therefore, they are expected to have a monotonic intrinsic flow curve and a steady state without shear bands [11]. However, recent experiments [12] display shear banding during startup flows in a rotational rheometer indicating timedependent behavior. These so called transient shear bands can be very long lasting, but eventually vanish with a homogeneous steady state. The transient shear banding phenomenon tests our fundamental understanding of non-Newtonian fluids, and is also important for industrial processes and simply for understanding usual rheological measurements. A particular feature of the transient shear banding is that it appears to exhibit scaling familiar from critical phenomena: The time it takes for the transient to disappear (fluidization time τ f ) is a power-law functi...

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confidence: 73%

Transient shear banding in time-dependent fluids

et al. 2013

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“…Finally, our work paves the way for a more realistic modeling of flows of dense suspensions in the presence of slip. Spatially resolved model such as SGR and fluidity models [42] should focus on the scaling of v s with σ before turning to transient regimes for which wall slip goes hand in hand with long-lived heterogeneous dynamics [43,44].…”

Section: Discussionmentioning

confidence: 99%

Wall slip across the jamming transition of soft thermoresponsive particles

et al. 2015

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Flows of suspensions are often affected by wall slip, that is the fluid velocity v f in the vicinity of a boundary differs from the wall velocity vw due to the presence of a lubrication layer. While the slip velocity vs = |v f − vw| robustly scales linearly with the stress σ at the wall in dilute suspensions, there is no consensus regarding denser suspensions that are sheared in the bulk, for which slip velocities have been reported to scale as a vs ∝ σ p with exponents p inconsistently ranging between 0 and 2. Here we focus on a suspension of soft thermoresponsive particles and show that vs actually scales as a power law of the viscous stress σ − σc, where σc denotes the yield stress of the bulk material. By tuning the temperature across the jamming transition, we further demonstrate that this scaling holds true over a large range of packing fractions φ on both sides of the jamming point and that the exponent p increases continuously with φ, from p = 1 in the case of dilute suspensions to p = 2 for jammed assemblies. These results allow us to successfully revisit inconsistent data from the literature and paves the way for a continuous description of wall slip above and below jamming.

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“…These materials should thus behave as yield stress fluids, but the features of this behavior have not been studied in detail in the literature. The local flow properties at flow start-up of a carbon black suspension have been studied by Gibaud et al 27 ; they have shown that flow starts inhomogeneously, following a complex scenario observed in other yield stress fluids 28,29 . However, the behavior at flow start-up of yield stress fluids is known to be much more complex than that at flow stoppage…”

Section: Methodsmentioning

confidence: 99%

Rheopexy and tunable yield stress of carbon black suspensions

et al. 2013

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Abstract:We show that besides simple or thixotropic yield stress fluids there exists a third class of yield stress fluids. This is illustrated through the rheological behavior of a carbon black suspension, which is shown to exhibit a viscosity bifurcation effect around a critical stress along with rheopectic trends, i.e., after a preshear at a given stress the fluid tends to accelerate when it is submitted to a lower stress. Viscosity bifurcation displays here original features: the yield stress and the critical shear rate depend on the previous flow history. The most spectacular property due to these specificities is that the material structure can be adjusted at will through an appropriate flow history. In particular it is possible to tune the material yield stress to arbitrary low values. A simple model assuming that the stress is the sum of one component due to structure deformation and one component due to hydrodynamic interactions predicts all rheological trends observed and appears to well represent quantitatively the data.

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

Cited by 80 publications

References 67 publications

Transient shear banding in time-dependent fluids

Transient shear banding in time-dependent fluids

Wall slip across the jamming transition of soft thermoresponsive particles

Rheopexy and tunable yield stress of carbon black suspensions

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