Measurement of Stress Redistribution in Flowing Emulsions

Rearrangements during slow compression of a jammed two-dimensional emulsion

As amorphous materials get jammed, both geometric and dynamic heterogeneity are observed. We investigate the correlation between the local geometric heterogeneity and local rearrangements in a slowly compressed bidisperse quasi-two-dimensional emulsion system. The compression is driven by evaporation of the continuous phase and causes the area packing fraction to increase from 0.88 to 0.99. We quantify the structural heterogeneity of the system using the radical Voronoi tessellation following the method of Rieser et al. [Phys. Rev. Lett. 116, 088001 (2016)]0031-900710.1103/PhysRevLett.116.088001. We define two structural quantities characterizing local structure, the first of which considers nearest neighbors and the second of which includes information from second-nearest neighbors. We find that droplets in heterogeneous local regions are more likely to have local rearrangements. These rearrangements are generally T1 events where two droplets converge toward a void, and two droplets move away from the void to make room for the converging droplets. Thus, the presence of the voids tends to orient the T1 events. The presence of a correlation between the structural quantities and the rearrangement dynamics remains qualitatively unchanged over the entire range of packing fractions observed.

Strain correlation functions in isotropic elastic bodies: large wavelength limit for two-dimensional systems

Strain correlation functions in two-dimensional isotropic elastic bodies are shown both theoretically (using the general structure of isotropic tensor fields) and numerically (using a glass-forming model system) to depend on the coordinates of the field variable (position vector r in real space or wavevector q in reciprocal space) and thus on the direction of the field vector and the orientation of the coordinate system. Since the fluctuations of the longitudinal and transverse components of the strain field in reciprocal space are known in the long-wavelength limit from the equipartition theorem, all components of the correlation function tensor field are imposed and no additional physical assumptions are needed. An observed dependence on the field vector direction thus cannot be used as an indication for anisotropy or for a plastic rearrangement. This dependence is different for the associated strain response field containing also information on the localized stress perturbation.

Correlations of tensor field components in isotropic systems with an application to stress correlations in elastic bodies

Correlation functions of components of second-order tensor fields in isotropic systems can be reduced to an isotropic fourth-order tensor field characterized by a few invariant correlation functions (ICFs). It is emphasized that components of this field depend in general on the coordinates of the field vector variable and thus on the orientation of the coordinate system. These angular dependencies are distinct from those of ordinary anisotropic systems. As a simple example of the procedure to obtain the ICFs we discuss correlations of time-averaged stresses in isotropic glasses where only one ICF in reciprocal space becomes a finite constant e for large sampling times and small wave vectors. It is shown that e is set by the typical size of the frozen-in stress components normal to the wave vectors, i.e., it is caused by the symmetry breaking of the stress for each independent configuration. Using the presented general mathematical formalism for isotropic tensor fields this finding explains in turn the observed long-range stress correlations in real space. Under additional but rather general assumptions e is shown to be given by a thermodynamic quantity, the equilibrium Young modulus E. We thus relate for certain isotropic amorphous bodies the existence of finite Young or shear moduli to the symmetry breaking of a stress component in reciprocal space.

Generic stress rectification in nonlinear elastic media

Stress propagation in nonlinear media is crucial in cell biology, where molecular motors exert anisotropic force dipoles on the fibrous cytoskeleton. While the force dipoles can be either contractile or expansile, a medium made of fibers which buckle under compression rectifies these stresses towards a biologically crucial contraction. A general understanding of this rectification phenomenon as a function of the medium's elasticity is however lacking. Here we use theoretical continuum elasticity to show that rectification is actually a very general effect in nonlinear materials subjected to anisotropic internal stresses. We analytically show that both bucklable and constitutively linear materials subjected to geometrical nonlinearities rectify small forces towards contraction, while granular-like materials rectify towards expansion. Using simulations, we moreover show that these results extend to larger forces. Beyond fiber networks, these results could shed light on the propagation of stresses in brittle or granular materials following a local plastic rearrangement.

The rheology of confined colloidal hard disks

Colloids may be treated as “big atoms” so that they are good models for atomic and molecular systems. Colloidal hard disks are, therefore, good models for 2d materials, and although their phase behavior is well characterized, rheology has received relatively little attention. Here, we exploit a novel, particle-resolved, experimental setup and complementary computer simulations to measure the shear rheology of quasi-hard-disk colloids in extreme confinement. In particular, we confine quasi-2d hard disks in a circular “corral” comprised of 27 particles held in optical traps. Confinement and shear suppress hexagonal ordering that would occur in the bulk and create a layered fluid. We measure the rheology of our system by balancing drag and driving forces on each layer. Given the extreme confinement, it is remarkable that our system exhibits rheological behavior very similar to unconfined 2d and 3d hard particle systems, characterized by a dynamic yield stress and shear-thinning of comparable magnitude. By quantifying particle motion perpendicular to shear, we show that particles become more tightly confined to their layers with no concomitant increase in density upon increasing the shear rate. Shear thinning is, therefore, a consequence of a reduction in dissipation due to weakening in interactions between layers as the shear rate increases. We reproduce our experiments with Brownian dynamics simulations with Hydrodynamic Interactions (HI) included at the level of the Rotne–Prager tensor. That the inclusion of HI is necessary to reproduce our experiments is evidence of their importance in transmission of momentum through the system.

Power fluctuations in sheared amorphous materials: A minimal model

The importance of mesoscale fluctuations in flowing amorphous materials is widely accepted, without a clear understanding of their role. We propose a mean-field elastoplastic model that admits both stress and strain-rate fluctuations, and investigate the character of its power distribution under steady shear flow. The model predicts the suppression of negative power fluctuations near the liquid-solid transition; the existence of a fluctuation relation in limiting regimes but its replacement in general by stretched-exponential power-distribution tails; and a crossover between two distinct mechanisms for negative power fluctuations in the liquid and the yielding solid phases. We connect these predictions with recent results from particle-based, numerical microrheological experiments.

Origin of nonlinear force distributions in a composite system

Composite materials have been actively developed in recent years because they are highly functional such as lightweight, high yield strength, and superior load response. In spite of importance of the composite materials, mechanisms of the mechanical responses of composites have been unrevealed. Here, in order to understand the mechanical responses of composites, we investigated the origin and nature of the force distribution in heterogeneous materials using a soft particle model. We arranged particles with different softness in a lamellar structure and then we applied homogeneous pressure to the top surface of the system. It is found that the density in each region differently changes and then the density difference induces a nonlinear force distribution. In addition, it is found that the attractive interaction suppresses the density difference and then the force distribution is close to the theoretical prediction. Those findings may lead material designs for functional composite materials.

Detailed Balance Broken by Catch Bond Kinetics Enables Mechanical-Adaptation in Active Materials

Unlike nearly all engineered materials which contain bonds that weaken under load, biological materials contain "catch" bonds which are reinforced under load. Consequently, materials, such as the cell cytoskeleton, can adapt their mechanical properties in response to their state of internal, non-equilibrium (active) stress. However, how large-scale material properties vary with the distance from equilibrium is unknown, as are the relative roles of active stress and binding kinetics in establishing this distance. Through course-grained molecular dynamics simulations, the effect of breaking of detailed balance by catch bonds on the accumulation and dissipation of energy within a model of the actomyosin cytoskeleton is explored. It is found that the extent to which detailed balance is broken uniquely determines a large-scale fluid-solid transition with characteristic time-reversal symmetries. The transition depends critically on the strength of the catch bond, suggesting that active stress is necessary but insufficient to mount an adaptive mechanical response.

Evaporation kinetics of continuous water and dispersed oil droplets

Drying of volatile oil droplets immersed in a continuous water phase was observed and analysed. Drying sample solutions were sandwiched between two glass plates and the water and oil phases were observed by confocal microscopy. In the initial stage of drying, evaporation of water was dominant and drying of the oil droplets was negligible. However, the rate of water evaporation decreased when the oil droplets were compressed. Comparison of experimental data with a diffusion model of water vapour showed that the decline in drying rates occurred earlier in the experiment than in the theoretical prediction. This implies that compression and narrowing of water paths caused the decline in the rate of water evaporation. After most water had evaporated, evaporation of the oil droplets occurred. The oil droplets did not shrink isotropically and the air-liquid interface invaded into the drying oil droplets. Cross-sectional observation by z-scanning revealed direct exposure of the oil droplets and they were pinned by the residual water phase. The water network between the oil droplets collapsed after the oil droplets had evaporated. The correlation between changes in structures and drying kinetics in both liquid phases was discussed.

Emergent solidity of amorphous materials as a consequence of mechanical self-organisation

Amorphous solids have peculiar properties distinct from crystals. One of the most fundamental mysteries is the emergence of solidity in such nonequilibrium, disordered state without the protection by long-range translational order. A jammed system at zero temperature, although marginally stable, has solidity stemming from the space-spanning force network, which gives rise to the long-range stress correlation. Here, we show that such nonlocal correlation already appears at the nonequilibrium glass transition upon cooling. This is surprising since we also find that the system suffers from giant anharmonic fluctuations originated from the fractal-like potential energy landscape. We reveal that it is the percolation of the force-bearing network that allows long-range stress transmission even under such circumstance. Thus, the emergent solidity of amorphous materials is a consequence of nontrivial self-organisation of the disordered mechanical architecture. Our findings point to the significance of understanding amorphous solids and nonequilibrium glass transition from a mechanical perspective.

Connecting shear localization with the long-range correlated polarized stress fields in granular materials

One long-lasting puzzle in amorphous solids is shear localization, where local plastic deformation involves cooperative particle rearrangements in small regions of a few inter-particle distances, self-organizing into shear bands and eventually leading to the material failure. Understanding the connection between the structure and dynamics of amorphous solids is essential in physics, material sciences, geotechnical and civil engineering, and geophysics. Here we show a deep connection between shear localization and the intrinsic structures of internal stresses in an isotropically jammed granular material subject to shear. Specifically, we find strong (anti)correlations between the micro shear bands and two polarized stress fields along two directions of maximal shear. By exploring the tensorial characteristics and the rotational symmetry of force network, we reveal that such profound connection is a result of symmetry breaking by shear. Finally, we provide the solid experimental evidence of long-range correlated inherent shear stress in an isotropically jammed granular system.

Rheology of colloidal and metallic glass formers

Colloidal hard-sphere suspensions are convenient experimental models to understand soft matter, and also by analogy the structural-relaxation behavior of atomic or small-molecular fluids. We discuss this analogy for the flow and deformation behavior close to the glass transition. Based on a mapping of temperature to effective hard-sphere packing, the stress–strain curves of typical bulk metallic glass formers can be quantitatively compared with those of hard-sphere suspensions. Experiments on colloids give access to the microscopic structure under deformation on a single-particle level, providing insight into the yielding mechanisms that are likely also relevant for metallic glasses. We discuss the influence of higher-order angular signals in connection with non-affine particle rearrangements close to yielding. The results are qualitatively explained on the basis of the mode-coupling theory. We further illustrate the analogy of pre-strain dependence of the linear-elastic moduli using data on PS-PNiPAM suspensions.

Spontaneous oscillations and negative-conductance transitions in microfluidic networks

The tendency for flows in microfluidic systems to behave linearly poses challenges for designing integrated flow control schemes to carry out complex fluid processing tasks. This hindrance precipitated the use of numerous external control devices to manipulate flows, thereby thwarting the potential scalability and portability of lab-on-a-chip technology. Here, we devise a microfluidic network exhibiting nonlinear flow dynamics that enable new mechanisms for on-chip flow control. This network is shown to exhibit oscillatory output patterns, bistable flow states, hysteresis, signal amplification, and negative-conductance transitions, all without reliance on dedicated external control hardware, movable parts, flexible components, or oscillatory inputs. These dynamics arise from nonlinear fluid inertia effects in laminar flows that we amplify and harness through the design of the network geometry. These results, which are supported by theory and simulations, have the potential to inspire development of new built-in control capabilities, such as on-chip timing and synchronized flow patterns.

Depletion attraction impairs the plasticity of emulsions flowing in a constriction

We study the elasto-plastic behavior of dense attractive emulsions under a mechanical perturbation. The attraction is introduced through non-specific depletion interactions between the droplets and is controlled by changing the concentration of surfactant micelles in the continuous phase. We find that such attractive forces are not sufficient to induce any measurable modification on the scalings between the local packing fraction and the deformation of the droplets. However, when the emulsions are flowed through 2D microfluidic constrictions, we uncover a measurable effect of attraction on their elasto-plastic response. Indeed, we measure higher levels of deformation inside the constriction for attractive droplets. In addition, we show that these measurements correlate with droplet rearrangements that are spatially delayed in the constriction for higher attraction forces.

Order to Disorder Transition in a Coarsening Two-Dimensional Foam

We quantify the spatiotemporal transformation of a monodisperse and well-ordered monolayer of bubbles, as they undergo Ostwald ripening, by tracking the size polydispersity of the bubbles and local ordering of the foam. After nuclei of disorder appear at random locations, the transition takes place through two successive phases: first, the disordered regions grow while the value of polydispersity increases slowly, then the polydispersity grows rapidly once the disordered zones begin to merge together. The transition is captured by a modified logistic model.

Slow Coarsening in Jammed Athermal Soft Particle Suspensions

We simulate a densely jammed, athermal assembly of repulsive soft particles immersed in a solvent. Starting from an initial condition corresponding to a quench from a high temperature, we find nontrivial slow dynamics driven by a gradual release of stored elastic energy, with the root mean squared particle speed decaying as a power law in time with a fractional exponent. This decay is accompanied by the presence within the assembly of spatially localized and temporally intermittent "hot spots" of nonaffine deformation, connected by long-ranged swirls in the velocity field, reminiscent of the local plastic events and long-ranged elastic propagation that have been intensively studied in sheared amorphous materials. The pattern of hot spots progressively coarsens, with the hot-spot size and separation slowly growing over time, and the associated correlation length in particle speed increasing as a sublinear power law. Each individual spot, however, exists only transiently within an overall picture of strongly intermittent dynamics.

Strength of Mechanical Memories is Maximal at the Yield Point of a Soft Glass

We show experimentally that both single and multiple mechanical memories can be encoded in an amorphous bubble raft, a prototypical soft glass, subject to an oscillatory strain. In line with recent numerical results, we find that multiple memories can be formed sans external noise. By systematically investigating memory formation for a range of training strain amplitudes spanning yield, we find clear signatures of memory even beyond yielding. Most strikingly, the extent to which the system recollects memory is largest for training amplitudes near the yield strain and is a direct consequence of the spatial extent over which the system reorganizes during the encoding process. Our study further suggests that the evolution of force networks on training plays a decisive role in memory formation in jammed packings.

Detection and tracking of anisotropic core-shell colloids

Optical microscopy techniques with three dimensional (3D) resolution are powerful tools for the real-space imaging of the structure and dynamics of colloidal systems. While real-space imaging of spherical particles is well established, the observation of shape anisotropic particles has only recently met a lot of interest. Apart from translation, shape anisotropic particles also possess additional rotational degrees of freedom. In this manuscript, we introduce a novel technique to find the position and the orientation of anisotropic particles in 3D. It is based on an algorithm which is applicable to core-shell particles consisting of a spherical core and a shell with arbitrary shape. We demonstrate the performance of this algorithm using PMMA/PMMA (polymethyl methacrylate) core-shell ellipsoids. The algorithm is tested on artificial images and on experimental data. The correct identification of particle positions with subpixel accuracy and of their orientations with high angular precision in dilute and dense systems is shown. In addition, we developed an advanced particle tracking algorithm that takes both translational and rotational movements of the anisotropic particles into account. We show that our 3D detection and tracking technique is suitable for the accurate and reliable detection of large and dense colloidal systems containing several thousands of particles.

Long-range stress correlations in viscoelastic and glass-forming fluids

A simple and rigorous approach to obtain stress correlations in viscoelastic liquids (including supercooled liquid and equilibrium amorphous systems) is proposed. The long-range dynamical correlations of local shear stress are calculated and analyzed in 2-dimensional space. It is established how the long-range character of the stress correlations gradually emerges as the relevant dynamical correlation length l grows in time. The correlation range l is defined by momentum propagation due to acoustic waves and vorticity diffusion which are the basic mechanisms for transmission of shear stress perturbations. We obtain the general expression defining the time- and distance-dependent stress correlation tensor in terms of material functions (generalized relaxation moduli). The effect of liquid compressibility is quantitatively analyzed; it is shown to be important at large distances and/or short times. The revealed long-range stress correlation effect is shown to be dynamical in nature and unconnected with static structural correlations in liquids (correlation length ξ_s). Our approach is based on the assumption that ξ_s is small enough as reflected in weak wave-number dependencies of the generalized relaxation moduli. We provide a simple physical picture connecting the elucidated long-range fluctuation effect with anisotropic correlations of the (transient) inherent stress field, and discuss its implications.

Crackling Dynamics in the Mechanical Response of Knitted Fabrics

Crackling noise, which occurs in a wide range of situations, is characterized by discrete events of various sizes, often correlated in the form of avalanches. We report experimental evidence that the mechanical response of a knitted fabric displays such broadly distributed events both in the force signal and in the deformation field, with statistics analogous to that of earthquakes or soft amorphous materials. A knit consists of a regular network of frictional contacts, linked by the elasticity of the yarn. When deformed, the fabric displays spatially extended avalanchelike yielding events resulting from collective interyarn contact slips. We measure the size distribution of these avalanches, at the stitch level from the analysis of nonelastic displacement fields and externally from force fluctuations. The two measurements yield consistent power law distributions reminiscent of those found in other avalanching systems. Our study shows that a knitted fabric is not only a thread-based metamaterial with highly sought after mechanical properties, but also an original, model system, with topologically protected structural order, where an intermittent, scale-invariant response emerges from minimal ingredients, and thus a significant landmark in the study of out-of-equilibrium universality.

Critical exponents of the yielding transition of amorphous solids

We investigate numerically the yielding transition of a two-dimensional model amorphous solid under external shear. We use a scalar model in terms of values of the total local strain, derived from the full (tensorial) description of the elastic interactions in the system, in which plastic deformations are accounted for by introducing a stochastic "plastic disorder" potential. This scalar model is seen to be equivalent to a collection of Prandtl-Tomlinson particles, which are coupled through an Eshelby quadrupolar kernel. Numerical simulations of this scalar model reveal that the strain rate versus stress curve, close to the critical stress, is of the form γ[over ̇]∼(σ-σ_{c})^{β}. Remarkably, we find that the value of β depends on details of the microscopic plastic potential used, confirming and giving additional support to results previously obtained with the full tensorial model. To rationalize this result, we argue that the Eshelby interaction in the scalar model can be treated to a good approximation in a sort of "dynamical" mean field, which corresponds to a Prandtl-Tomlinson particle that is driven by the applied strain rate in the presence of a stochastic noise generated by all other particles. The dynamics of this Prandtl-Tomlinson particle displays different values of the β exponent depending on the analytical properties of the microscopic potential, thus giving support to the results of the numerical simulations. Moreover, we find that other critical exponents that depend on details of the dynamics show also a dependence with the form of the disorder, while static exponents are independent of the details of the disorder. Finally, we show how our scalar model relates to other elastoplastic models and to the widely used mean-field version known as the Hébraud-Lequeux model.

Orientation of plastic rearrangements in two-dimensional model glasses under shear

The plastic deformation of amorphous solids is mediated by localized shear transformations involving small groups of particles rearranging irreversibly in an elastic background. We introduce and compare three different computational methods to extract the size and orientation of these shear transformations in simulations of a two-dimensional athermal model glass under simple shear. We find that the shear angles are broadly distributed around the macroscopic shear direction, with a more or less Gaussian distribution with a standard deviation of around 20^{∘}. The distributions of sizes and orientations of shear transformations display no substantial sensitivity to the shear rate. These results can notably be used to refine the description of rearrangements in elastoplastic models.

Microscopic Origins of Shear Jamming for 2D Frictional Grains

Shear jamming (SJ) occurs for frictional granular materials with packing fractions ϕ in ϕ_{S}<ϕ<ϕ_{J}^{0}, when the material is subject to shear strain γ starting from a force-free state. Here, ϕ_{J}^{μ} is the isotropic jamming point for particles with a friction coefficient μ. SJ states have mechanically stable anisotropic force networks, e.g., force chains. Here, we investigate the origins of SJ by considering small-scale structures-trimers and branches-whose response to shear leads to SJ. Trimers are any three grains where the two outer grains contact a center one. Branches occur where three or more quasilinear force chain segments intersect. Certain trimers respond to shear by compressing and bending; bending is a nonlinear symmetry-breaking process that can push particles in the dilation direction faster than the affine dilation. We identify these structures in physical experiments on systems of two-dimensional frictional discs, and verify their role in SJ. Trimer bending and branch creation both increase Z above Z_{iso}≃3 needed for jamming 2D frictional grains, and grow the strong force network, leading to SJ.

Wall fluidization in two acts: from stiff to soft roughness

Fluidization of soft glassy materials (SGMs) in microfluidic channels is affected by the wall roughness in the form of microtexturing. When SGMs flow across microgrooves, their constituents are likely trapped within the grooves' gap, and the way they are released locally modifies the fluidization close to the walls. By leveraging a suitable combination of experiments and numerical simulations on concentrated emulsions (a model SGM), we quantitatively report the existence of two physically different scenarios. When the gap is large compared to the droplets in the emulsion, the droplets hit the solid obstacles and easily escape scrambling with their neighbors. Conversely, as the gap spacing is reduced, droplets get trapped inside, creating a "soft roughness" layer, i.e. a complementary series of deformable posts from which overlying droplets are in turn released. In both cases, the induced fluidization scales with the grooves' density, although with a reduced prefactor for narrow gaps, accounting for the softness of the roughness. Both scenarios are also well distinguished via the statistics of the droplets displacement field close to the walls, with large deviations induced by the surface roughness, depending on its stiffness.

Rate Dependence of Elementary Rearrangements and Spatiotemporal Correlations in the 3D Flow of Soft Solids

We use a combination of confocal microscopy, rheology, and molecular dynamics simulations to investigate jammed emulsions under shear, by analyzing the 3D droplets rearrangements in the shear frame. Our quantitative analysis of local dynamics reveals elementary nonaffine rearrangements that underlie the onset of the flow at small strains. We find that the mechanism of unjamming and the upturn in the material flow curve are associated to a qualitative change in spatiotemporal correlations of such rearrangements with the applied shear rate. At high shear rates, droplet clusters follow coordinated, stringlike motion. Conversely, at low shear rates, the elementary nonaffine rearrangements exhibit longer-ranged correlations, with complex spatiotemporal patterns. The 3D microscopic details provide novel insights into the specific features of the material flow curve, common to a large class of technologically relevant soft disordered solids and new fundamental ingredients for constitutive models.

Emergence of Long-Ranged Stress Correlations at the Liquid to Glass Transition

A theory for the nonlocal shear stress correlations in supercooled liquids is derived from first principles. It captures the crossover from viscous to elastic dynamics at an idealized liquid to glass transition and explains the emergence of long-ranged stress correlations in glass, as expected from classical continuum elasticity. The long-ranged stress correlations can be traced to the coupling of shear stress to transverse momentum, which is ignored in the classic Maxwell model. To rescue this widely used model, we suggest a generalization in terms of a single relaxation time τ for the fast degrees of freedom only. This generalized Maxwell model implies a divergent correlation length ξ∝τ as well as dynamic critical scaling and correctly accounts for the far-field stress correlations. It can be rephrased in terms of generalized hydrodynamic equations, which naturally couple stress and momentum and furthermore allow us to connect to fluidity and elastoplastic models.

Modeling shear-induced particle ordering and deformation in a dense soft particle suspension

We apply the lattice Boltzmann method and the bead-spring network model of deformable particles (DPs) to study shear-induced particle ordering and deformation and the corresponding rheological behavior for dense DP suspensions confined in a narrow gap under steady external shear. The particle configuration is characterized with small-angle scattering intensity, the real-space 2D local order parameter, and the particle shape factors including deformation, stretching and tilt angles. We investigate how particle ordering and deformation vary with the particle volume fraction ϕ (=0.45-0.65) and the external shear rate characterized with the capillary number Ca (=0.003-0.191). The degree of particle deformation increases mildly with ϕ but significantly with Ca. Under moderate shear rate (Ca  =  0.105), the inter-particle structure evolves from string-like ordering to layered hexagonal close packing (HCP) as ϕ increases. A long wavelength particle slithering motion emerges for sufficiently large ϕ. For ϕ  =  0.61, the structure maintains layered HCP for Ca  =  0.031-0.143 but gradually becomes disordered for larger and smaller Ca. The correlation in particle zigzag movements depends sensitively on ϕ and particle ordering. Layer-by-layer analysis reveals how the non-slippery hard walls affect particle ordering and deformation. The shear-induced reconfiguration of DPs observed in the simulation agrees qualitatively with experimental results of sheared uniform emulsions. The apparent suspension viscosity increases with ϕ but exhibits much weaker dependence compared to hard-sphere suspensions, indicating that particle deformation and unjamming under shear can significantly reduce the viscous stress. Furthermore, the suspension shear-thins, corresponding to increased inter-DP ordering and particle deformation with Ca. This work provides useful insights into the microstructure-rheology relationship of concentrated deformable particle suspensions.

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.

Stable small bubble clusters in two-dimensional foams

Key features of the mechanical response of amorphous particulate materials, such as foams, emulsions, and granular media, to applied stress are determined by the frequency and size of particle rearrangements that occur as the system transitions from one mechanically stable state to another. This work describes coordinated experimental and computational studies of bubble rafts, which are quasi-two dimensional systems of bubbles confined to the air-water interface. We focus on small mechanically stable clusters of four, five, six, and seven bubbles with two different sizes with diameter ratio σ_L/σ_S ≃ 1.4. Focusing on small bubble clusters, which can be viewed as subsystems of a larger system, allows us to investigate the full ensemble of clusters that form, measure the respective frequencies with which the clusters occur, and determine the form of the bubble-bubble interactions. We emphasize several important results. First, for clusters with N > 5 bubbles, we find using discrete element simulations that short-range attractive interactions between bubbles give rise to a larger ensemble of distinct mechanically stable clusters compared to that generated by long-range attractive interactions. The additional clusters in systems with short-range attractions possess larger gaps between pairs of neighboring bubbles on the periphery of the clusters. The ensemble of bubble clusters observed in experiments is similar to the ensemble of clusters with long-range attractive interactions. We also compare the frequency with which each cluster occurs in simulations and experiments. We find that the cluster frequencies are extremely sensitive to the protocol used to generate them and only weakly correlated to the energy of the clusters.

Slow creep in soft granular packings

Transient creep mechanisms in soft granular packings are studied numerically using a constant pressure and constant stress simulation method. Rapid compression followed by slow dilation is predicted on the basis of a logarithmic creep phenomenon. Characteristic scales of creep strain and time exhibit a power-law dependence on jamming pressure, and they diverge at the jamming point. Microscopic analysis indicates the existence of a correlation between rheology and nonaffine fluctuations. Localized regions of large strain appear during creep and grow in magnitude and size at short times. At long times, the spatial structure of highly correlated local deformation becomes time-invariant. Finally, a microscale connection between local rheology and local fluctuations is demonstrated in the form of a linear scaling between granular fluidity and nonaffine velocity.

Fluidization and wall slip of soft glassy materials by controlled surface roughness

We present a comprehensive study of concentrated emulsions flowing in microfluidic channels, one wall of which is patterned with micron-size equally spaced grooves oriented perpendicularly to the flow direction. We find a scaling law describing the roughness-induced fluidization as a function of the density of the grooves, thus fluidization can be predicted and quantitatively regulated. This suggests common scenarios for droplet trapping and release, potentially applicable for other jammed systems as well. Numerical simulations confirm these views and provide a direct link between fluidization and the spatial distribution of plastic rearrangements.

Strain Pattern in Supercooled Liquids

Investigations of strain correlations at the glass transition reveal unexpected phenomena. The shear strain fluctuations show an Eshelby-strain pattern [∼cos(4θ)/r^{2}], characteristic of elastic response, even in liquids, at long times. We address this using a mode-coupling theory for the strain fluctuations in supercooled liquids and data from both video microscopy of a two-dimensional colloidal glass former and simulations of Brownian hard disks. We show that the long-ranged and long-lived strain signatures follow a scaling law valid close to the glass transition. For large enough viscosities, the Eshelby-strain pattern is visible even on time scales longer than the structural relaxation time τ and after the shear modulus has relaxed to zero.

Eshelby inclusions in granular matter: Theory and simulations

We present a numerical implementation of an active inclusion in a granular material submitted to a biaxial test. We discuss the dependence of the response to this perturbation on two parameters: the intragranular friction coefficient on one hand, and the degree of the loading on the other hand. We compare the numerical results to theoretical predictions taking into account the change of volume of the inclusion as well as the anisotropy of the elastic matrix.

Non-local rheology in dense granular flows: Revisiting the concept of fluidity

The aim of this article is to discuss the concepts of non-local rheology and fluidity, recently introduced to describe dense granular flows. We review and compare various approaches based on different constitutive relations and choices for the fluidity parameter, focusing on the kinetic elasto-plastic model introduced by Bocquet et al. (Phys. Rev. Lett 103, 036001 (2009)) for soft matter, and adapted for granular matter by Kamrin et al. (Phys. Rev. Lett. 108, 178301 (2012)), and the gradient expansion of the local rheology μ(I) that we have proposed (Phys. Rev. Lett. 111, 238301 (2013)). We emphasise that, to discriminate between these approaches, one has to go beyond the predictions derived from linearisation around a uniform stress profile, such as that obtained in a simple shear cell. We argue that future tests can be based on the nature of the chosen fluidity parameter, and the related boundary conditions, as well as the hypothesis made to derive the models and the dynamical mechanisms underlying their dynamics.

Flow of foam through a convergent channel

We study experimentally the flow of a foam confined as a bubble monolayer between two plates through a convergent channel. We quantify the velocity, the distribution and orientation of plastic events, and the elastic stress, using image analysis. We use two different soap solutions: a sodium dodecyl sulfate (SDS) solution, with a negligible wall friction between the bubbles and the confining plates, and a mixture containing a fatty acid, giving a large wall friction. We show that for SDS solutions, the velocity profile obeys a self-similar form which results from the superposition of plastic events, and the elastic deformation is uniform. For the other solution, the velocity field differs and the elastic deformation increases towards the exit of the channel. We discuss and quantify the role of wall friction on the velocity profile, the elastic deformation, and the rate of plastic events.