Universal rescaling of flow curves for yield-stress fluids close to jamming

Strain-dependent evolution of avalanche dynamics in bulk metallic glass

Avalanche phenomena characterized by power-law scaling are observed in amorphous solids and many other nonequilibrium systems during their deformation. Avalanches in these systems often exhibit scale invariance, a feature reminiscent of critical phenomena and universality classes, although their fundamental nature remains unclear. In this paper, we use in situ acoustic emission techniques to experimentally investigate the characteristics and evolution of avalanches during the deformation process of bulk metallic glass (BMG), a representative amorphous solid. We observed abundant avalanche events from the microplastic deformation region to the failure of the sample. We find that avalanches are power-law distributed with an exponent decreasing from 1.61 to 1.49 with increasing deformation throughout the tensile experiment. By quantitatively analyzing the strong strain dependence of various avalanche characteristics, we highlight the importance of additional coefficients that complete the widely studied finite size scaling description of avalanche dynamics and revealed a strain-mediated avalanche scaling mechanism. Through surface morphology analysis and spectral analysis of avalanche signals in BMG samples, we conclude that the underlying process of these avalanches are not macroscopic, such as cracks and large shear band propagation, but is instead related to nanoscale microstructural adjustments. Our results encourage further exploration into the microscopic origins of avalanches and suggest that theoretical frameworks beyond finite-size scaling merit more in-depth investigations.

Droplet Size Distribution in Emulsions

The droplet size in emulsions is known to affect the rheological properties and plays a crucial role in many applications of emulsions. Despite its importance, the underlying mechanisms governing droplet size in emulsification remain poorly understood. We investigate the average drop size and size distribution upon emulsification with a high-shear mixer for model oil-in-water emulsions stabilized by a surfactant. The size distribution is found to be a log-normal distribution resulting from the repetitive random breakup of drops. High-shear emulsification, the usual way of making emulsions, is therefore found to be very different from turbulent emulsification given by the Kolmogorov-Hinze theory, for which power-law distributions of the drop size are expected. In agreement with this, the mean droplet size does not follow a scaling with the Reynolds number of the emulsification flow but rather a capillary number scaling based on the viscosity of the continuous phase.

Soft glassy materials with tunable extensibility

Extensibility is beyond the paradigm of classical soft glassy materials, and more broadly, yield-stress fluids. Recently, model yield-stress fluids with significant extensibility have been designed by adding polymeric phases to classically viscoplastic dispersions [Nelson et al., J. Rheol., 2018, 62, 357; Nelson et al., Curr. Opin. Solid State Mater. Sci., 2019, 23, 100758; Dekker et al., J. Non-Newtonian Fluid Mech., 2022, 310, 104938]. However, fundamental questions remain about the design of and coupling between the shear and extensional rheology of such systems. In this work, we propose a model material, a mixture of soft glassy microgels and solutions of high molecular weight linear polymers. We establish systematic criteria for the design and thorough rheological characterization of such systems, in both shear and extension. Using our material, we show that it is possible to dramatically change the behavior in extension with minimal change in the shear yield stress and elastic modulus, thus enabling applications that exploit orthogonal modulation of shear and extensional material properties.

Glassy and compressed nanoemulsions stabilized with sodium dodecyl sulfate in the presence of poly(ethylene glycol)-diacrylate

The rheology of concentrated nanoemulsions is critical for their formulation in various applications, such as pharmaceuticals, foods, cosmetics, and templating advanced materials. The rheological properties of nanoemulsions depend on interdroplet interactions, Laplace pressure, dispersed phase volume fraction, and continuous phase properties. The interdroplet forces can be tuned by background electrolytes (i.e., charge screening), surfactant type, the excess surfactant micelle concentration, and depletant molecules such as polymer chains. In the current research, we study the effect of varying the content of poly(ethylene glycol)-diacrylate (PEGDA) on the interfacial tension of the water-oil phase and rheological properties of concentrated nanoemulsions with 50% and 60% volume fractions. Sodium dodecyl sulfate (SDS) is used as the ionic surfactant. The final concentrated nanoemulsions are repulsive according to overall interaction potentials and are in the glass and compressed states based on the effective volume fraction estimation. They contain nearly same SDS concentration on the droplet surface and also in the bulk, but a different amount of PEGDA. The scaled rheological properties of the glassy nanoemulsions show a higher dependency on the PEGDA content and the possible effect of polymer-surfactant complexations compared to those of the compressed ones. This dependency is more pronounced in small strain amplitudes but not in large strains in the non-linear regime. These results provide insights into formulating concentrated nanoemulsions with controlled rheology for expanded application areas.

Critical yielding rheology: from externally deformed glasses to active systems

We use extensive computer simulations to study the yielding transition under two different loading schemes: standard simple shear dynamics and self-propelled dense active systems. In the active systems, a yielding transition toward an out-of-equilibrium flowing state known as the liquid phase is observed when self-propulsion is increased. The range of self-propulsions in which this pure liquid regime exists appears to vanish upon approaching the so-called 'jamming point' at which the solidity of soft-sphere packings is lost. Such an 'active yielding' transition shares similarities with the generic yielding transition for shear flows. A Herschel-Bulkley law is observed along the liquid regime in both loading scenarios, with a clear difference in the critical scaling exponents between the two, suggesting the existence of different universality classes for the yielding transition under different driving conditions. In addition, we present the direct measurements of growing length and time scales for both driving scenarios. A comparison with theoretical predictions from the recent literature reveals poor agreement with our numerical results.

Continuum modeling of shear startup in soft glassy materials

Yield stress fluids (YSFs) display a dual nature highlighted by the existence of a critical stress σ_{y} such that YSFs are solid for stresses σ imposed below σ_{y}, whereas they flow like liquids for σ>σ_{y}. Under an applied shear rate γ[over ̇], the solid-to-liquid transition is associated with a complex spatiotemporal scenario that depends on the microscopic details of the system, on the boundary conditions, and on the system size. Still, the general phenomenology reported in the literature boils down to a simple sequence that can be divided into a short-time response characterized by the so-called "stress overshoot," followed by stress relaxation towards a steady state. Such relaxation can be either (1) long-lasting, which usually involves the growth of a shear band that can be only transient or that may persist at steady state or (2) abrupt, in which case the solid-to-liquid transition resembles the failure of a brittle material, involving avalanches. In the present paper, we use a continuum model based on a spatially resolved fluidity approach to rationalize the complete scenario associated with the shear-induced yielding of YSFs. A key feature of our model is to provide a scaling for the coordinates of the stress overshoot, i.e., stress σ_{M} and strain γ_{M} as a function of γ[over ̇], which shows good agreement with experimental and numerical data extracted from the literature. Moreover, our approach shows that the power-law scaling σ_{M}(γ[over ̇]) is intimately linked to the growth dynamics of a fluidized boundary layer in the vicinity of the moving boundary. Yet such scaling is independent of the fate of that layer, and of the long-term behavior of the YSF, i.e., whether the steady-state flow profile is homogeneous or shear-banded. Finally, when including the presence of "long-range" correlations, we show that our model displays a ductile to brittle transition, i.e., the stress overshoot reduces into a sharp stress drop associated with avalanches, which impacts the scaling σ_{M}(γ[over ̇]). This generalized model nicely captures subtle avalanche-like features of the transient shear banding dynamics reported in experiments. Our work offers a unified picture of shear-induced yielding in YSFs, whose complex spatiotemporal dynamics are deeply connected to nonlocal effects.

Instantaneous Normal Modes Reveal Structural Signatures for the Herschel-Bulkley Rheology in Sheared Glasses

The Herschel-Bulkley law, a universal constitutive relation, has been empirically known to be applicable to a vast range of soft materials, including sheared glasses. Although the Herschel-Bulkley law has attracted public attention, its structural origin has remained an open question. In this Letter, by means of atomistic simulation of binary Lennard-Jones glasses, we report that the instantaneous normal modes with negative eigenvalues, or so-called imaginary modes, serve as the structural signatures for the Herschel-Bulkley rheology in sheared glasses.

Carbomer microgels as model yield-stress fluids

The review presents current research results for Carbopol-based microgels as yield-stress materials, covering three aspects: chemical, physical and rheological. Such a joint three-aspect study has no analog in the literature. The chemical aspects of Carbopol polymers are presented in terms of a cross-linking polymerization of acrylic acid, their molecular structure, microgel formulation, polyacid dissociation and neutralization, osmotic pressure and associated immense microgel swelling. The physical characterization is focused on models of the shear-induced solid-to-liquid transition of microgels, which are formed of mesoscopic particles typical for soft matter materials. Models that describe interparticle effects are presented to explain the energy states of microgel particles at the mesoscale of scrutiny. Typical representatives of the models utilize attributes of jamming dispersions, micromechanical and polyelectrolyte reactions. Selected relationships that result from the models, such as scaling rules and nondimensional flow characteristics are also presented. The rheological part presents the discussion of problems of yield stress in 2D and 3D deformations, appearance and magnitude of the wall slip. The theory and characteristics of Carbopol microgel deformation in rotational rheometers are presented with graphs for the steady-state measurements, stress-controlled oscillation and two types of transient shear deformation. The review is concluded with suggestions for future research.

Glass and Jamming Rheology in Soft Particles Made of PNIPAM and Polyacrylic Acid

The phase behaviour of soft colloids has attracted great attention due to the large variety of new phenomenologies emerging from their ability to pack at very high volume fractions. Here we report rheological measurements on interpenetrated polymer network microgels composed of poly(N-isopropylacrylamide) (PNIPAM) and polyacrylic acid (PAAc) at fixed PAAc content as a function of weight concentration. We found three different rheological regimes characteristic of three different states: a Newtonian shear-thinning fluid, an attractive glass characterized by a yield stress, and a jamming state. We discuss the possible molecular mechanisms driving the formation of these states.

Critical scaling of compression-driven jamming of athermal frictionless spheres in suspension

We study numerically a system of athermal, overdamped, frictionless spheres, as in a non-Brownian suspension, in two and three dimensions. Compressing the system isotropically at a fixed rate ε[over ̇], we investigate the critical behavior at the jamming transition. The finite compression rate introduces a control timescale, which allows one to probe the critical timescale associated with jamming. As was found previously for steady-state shear-driven jamming, we find for compression-driven jamming that pressure obeys a critical scaling relation as a function of packing fraction ϕ and compression rate ε[over ̇], and that the bulk viscosity p/ε[over ̇] diverges upon jamming. A scaling analysis determines the critical exponents associated with the compression-driven jamming transition. Our results suggest that stress-isotropic, compression-driven jamming may be in the same universality class as stress-anisotropic, shear-driven jamming.

Rheology finds distinct glass and jamming transitions in emulsions

We study the rheology of monodisperse and bidisperse emulsions with various droplet sizes (1-2 μm diameter). Above a critical volume fraction φc, these systems exhibit solid-like behavior and a yield stress can be detected. Previous experiments suggest that for small thermal particles, rheology will see a glass transition at φc = φg ≈ 0.58; for large athermal systems, rheology will see a jamming transition at φc = φJ ≈ 0.64. However, simulations point out that at the crossover of thermal and athermal regimes, the glass and jamming transitions may both be observed in the same sample. Here we conduct an experiment by shearing four oil-in-water emulsions with a rheometer. We observe both a glass and a jamming transition for our smaller diameter droplets, and only a jamming transition for our larger diameter droplets. The bidisperse sample behaves similarly to the small droplet sample, with two transitions observed. Our rheology data are well-fit by both the Herschel-Bulkley model and the three component model. Based on the fitting parameters, our raw rheological data would not collapse onto a master curve. Our results show that liquid-solid transitions in dispersions are not universal, but depend on particle size.

Rheological similarities between dense self-propelled and sheared particulate systems

Different from previous modeling of self-propelled particles, we develop a method to propel particles with a constant average velocity instead of a constant force. This constant propulsion velocity (CPV) approach is validated by its agreement with the conventional constant propulsion force (CPF) approach in the flowing regime. However, the CPV approach shows its advantage of accessing quasistatic flows of yield stress fluids with a vanishing propulsion velocity, while the CPF approach is usually unable to because of finite system size. Taking this advantage, we realize cyclic self-propulsion and study the evolution of the propulsion force with the propelled particle displacement, both in the quasistatic flow regime. By mapping the shear stress and shear rate to the propulsion force and propulsion velocity, we find similar rheological behaviors of self-propelled systems to sheared systems, including the yield force gap between the CPF and CPV approaches, propulsion force overshoot, reversible-irreversible transition under cyclic propulsion, and propulsion bands in plastic flows. These similarities suggest underlying connections between self-propulsion and shear, although they act on systems in different ways.

Crossover between Athermal Jamming and the Thermal Glass Transition of Suspensions

The non-Newtonian flow behavior of thermal and athermal disordered systems of dispersed uniform particles at high densities have strikingly similar features. By investigating the flow curves of yield-stress fluids and colloidal glasses having different volume fractions, particle sizes, and interactions, we show that both thermal and athermal systems exhibit power-law scaling with respect to the glass and jamming point, respectively, with the same exponents. All yield-stress flow curves can be scaled onto a single universal curve using the Laplace pressure as the stress scale for athermal systems and the osmotic pressure for the thermal systems. Strikingly, the details of interparticle interactions do not matter for the rescaling, showing that they are akin to usual phase transitions of the same universality class. The rescaling allows us to predict the flow properties of these systems from the volume fraction and known material properties.

On the universality of the flow properties of soft-particle glasses

We identify the minimal interparticle interactions necessary for a particle dynamics simulation to predict the structure and flow behaviour of soft particle glasses (SPGs). Generally, two kinds of forces between the particles must be accounted for in simulations of SPGs: viscous or frictional drag forces and elastic contact forces. Far field drag forces are required to dissipate energy in the simulations and capture the effect of the rheology of the suspending fluid. Elastic forces are found to be dominant compared to near-field drag or other forms of friction forces and are the most important component to compute the rheology. The shear stress, the first and second normal stress differences for different interparticle force laws collapse onto universal master curves of the Herschel-Bulkley form by non-dimensionalizing the stress with the yield stress and the shear rate with the viscosity of the suspending fluid divided by the low-frequency shear modulus. The Herschel-Bulkley exponents are close to 0.5 with a slight dependence on the repulsive pairwise elastic forces.

Design of yield-stress fluids: a rheology-to-structure inverse problem

We present a paradigm for the design of yield-stress fluids, using six archetypal materials for demonstration. By applying concepts of engineering design, we outline a materials design paradigm that includes (i) morphological organization based on jammed versus networked microstructures, (ii) collected scaling laws for predictive design, (iii) low-dimensional descriptions of function-valued flow data, (iv) consideration of secondary properties including viscous behavior, and (v) a strategy for material concept synthesis based on the juxtaposition of microstructures. By explicitly specifying these design strategies, we seek to create an ontology and database for the engineering of yield-stress fluids. Our proposed design strategy increases the likelihood of finding an optimal material and prevents design fixation by considering multiple material classes to achieve a desired rheological performance. This flips the typical structure-to-rheology analysis to become the inverse: rheology-to-structure with multiple possible materials as solutions.

Non-trivial rheological exponents in sheared yield stress fluids

In this work we discuss possible physical origins of non-trivial exponents in the athermal rheology of soft materials at low but finite driving rates. A key ingredient in our scenario is the presence of a self-consistent mechanical noise that stems from the spatial superposition of long-range elastic responses to localized plastically deforming regions. We study analytically a mean-field model, in which this mechanical noise is accounted for by a stress diffusion term coupled to the plastic activity. Within this description we show how a dependence of the shear modulus and/or the local relaxation time on the shear rate introduces corrections to the usual mean-field prediction, concerning the Herschel-Bulkley-type rheological response of exponent 1/2. This feature of the mean-field picture is then shown to be robust with respect to structural disorder and partial relaxation of the local stress. We test this prediction numerically on a mesoscopic lattice model that implements explicitly the long-range elastic response to localized shear transformations, and we conclude on how our scenario might be tested in rheological experiments.

Characterizing rare fluctuations in soft particulate flows

Soft particulate media include a wide range of systems involving athermal dissipative particles both in non-living and biological materials. Characterization of flows of particulate media is of great practical and theoretical importance. A fascinating feature of these systems is the existence of a critical rigidity transition in the dense regime dominated by highly intermittent fluctuations that severely affects the flow properties. Here, we unveil the underlying mechanisms of rare fluctuations in soft particulate flows. We find that rare fluctuations have different origins above and below the critical jamming density and become suppressed near the jamming transition. We then conjecture a time-independent local fluctuation relation, which we verify numerically, and that gives rise to an effective temperature. We discuss similarities and differences between our proposed effective temperature with the conventional kinetic temperature in the system by means of a universal scaling collapse.

Soft particulate flows such as granular media are prone to fluctuations like jamming and avalanches. Here Rahbari et al. consider the statistics of rare fluctuations to identify an effective temperature which, unlike previous ones, is valid for packing fractions both near and far from the jamming point.

Merging fluid and solid granular behavior

Simple homogeneous shear flows of frictionless, deformable particles are studied by particle simulations at large shear rates and for differently soft, deformable particles. Particle stiffness sets a time-scale that can be used to scale the physical quantities; thus the dimensionless shear rate, i.e. the inertial number I (inversely proportional to pressure), can alternatively be expressed as inversely proportional to the square root of particle stiffness. Asymptotic scaling relations for the field variables pressure, shear stress and granular temperature are inferred from simulations in both fluid and solid regimes, corresponding to unjammed and jammed conditions. Then the limit cases are merged to unique constitutive relations that cover also the transition zone in the proximity of jamming. By exploiting the diverging behavior of the scaling laws at the jamming density, we arrive at continuous and differentiable phenomenological constitutive relations for stresses and granular temperature as functions of the volume fraction, shear rate, particle stiffness and distance from jamming. In contrast to steady shear flows of hard particles the (shear) stress ratio μ does not collapse as a function of the inertial number, indicating the need for an additional control parameter. In the range of particle stiffnesses investigated, in the solid regime, only pressure is rate independent, whereas shear stress exhibits a slight shear rate- and stiffness-dependency.