Anomalous viscous loss in emulsions

Shear layers and plugs in the capillary flow of wormlike micellar gels

Wormlike micellar solutions formed by long-chained zwitterionic surfactants show gel-like rheology at room temperature and have recently been found to exhibit other complex and interesting rheological features. We study the dynamics of these wormlike micellar gels in a pipe-flow scenario using particle imaging and tracking velocimetry and report the existence of plug flows with strong wall slip and non-parabolic velocity profiles for different surfactant concentrations and imposed flow rates. We rationalize these results as features of a developing transient flow of a viscoelastic solution in space and time. We show that evolution of shear layers is governed by intermittent flows, asymmetric velocity profiles and flow induced heterogeneity. Our experiments shed light on the transient fluid dynamics of wormlike micelles in simple geometries and highlight the complexity of flows involving wormlike micellar gels and similar soft matter systems in canonical flows.

Activity-dependent glassy cell mechanics II: Nonthermal fluctuations under metabolic activity

The glassy cytoplasm, crowded with bio-macromolecules, is fluidized in living cells by mechanical energy derived from metabolism. Characterizing the living cytoplasm as a nonequilibrium system is crucial in elucidating the intricate mechanism that relates cell mechanics to metabolic activities. In this study, we conducted active and passive microrheology in eukaryotic cells, and quantified nonthermal fluctuations by examining the violation of the fluctuation-dissipation theorem. The power spectral density of active force generation was estimated following the Langevin theory extended to nonequilibrium systems. However, experiments performed while regulating cellular metabolic activity showed that the nonthermal displacement fluctuation, rather than the active nonthermal force, is linked to metabolism. We discuss that mechano-enzymes in living cells do not act as microscopic objects. Instead, they generate meso-scale collective fluctuations with displacements controlled by enzymatic activity. The activity induces structural relaxations in glassy cytoplasm. Even though the autocorrelation of nonthermal fluctuations is lost at long timescales due to the structural relaxations, the nonthermal displacement fluctuation remains regulated by metabolic reactions. Our results therefore demonstrate that nonthermal fluctuations serve as a valuable indicator of a cell's metabolic activities, regardless of the presence or absence of structural relaxations.

Rheological study of nanoemulsions with repulsive and attractive interdroplet interactions

Nanoemulsions have adjustable transparency, tunable rheology, high stability, and low sensitivity to changes in pH and temperature, which make them interesting for applications such as low-fat and low-calorie foods. In this research, we study model concentrated nanoemulsions which are stabilized by sodium dodecyl sulfate (SDS). To prepare samples in different structural states, semi-dilute nanoemulsions are prepared at 25% droplet volume fraction (φ), after which evaporating the continuous phase at room temperature leads to concentrated nanoemulsions up to 60% volume fraction. Surfactant concentration is also tuned to induce different interdroplet interactions so that concentrated nanoemulsions in repulsive glass, attractive glass, and gel states are achieved. Rheological properties of nanoemulsions with different structural states are comprehensively studied over a volume fraction range. Utilizing the existing predictive models for (nano)emulsion rheology reveals a more satisfactory prediction for repulsive systems than systems with attractive interactions. In addition, a master curve is constructed for storage and loss moduli of nanoemulsions with different interdroplet interactions. The present work offers control over physicochemical properties of nanoemulsions for design of new food products with enhanced quality and functionality.

Effects of polydispersity on the plastic behaviors of dense two-dimensional granular systems under shear

We study particle-scale motion in sheared highly polydisperse amorphous materials, in which the largest particles are as much as ten times the size of the smallest. We find strikingly different behavior from the more commonly studied amorphous systems with low polydispersity. In particular, an analysis of the nonaffine motion of particles reveals qualitative differences between large and small particles: The smaller particles have dramatically more nonaffine motion, which is induced by the presence of the large particles. We characterize how the nonaffine motion changes from the low- to high-polydispersity regimes. We further demonstrate a quantitative way to distinguish between "large" and "small" particles in systems with broad distributions of particle sizes. A macroscopic consequence of the nonaffine motion is a decrease in the energy dissipation rate for highly polydisperse samples, which is due both to a geometric consequence of the changing jamming conditions for higher polydispersity and to the changing character of nonaffine motion.

Non-Maxwellian viscoelastic stress relaxations in soft matter

Viscoelastic stress relaxation is a basic characteristic of soft matter systems such as colloids, gels, and biological networks. Although the Maxwell model of linear viscoelasticity provides a classical description of stress relaxation, it is often not sufficient for capturing the complex relaxation dynamics of soft matter. In this Tutorial, we introduce and discuss the physics of non-Maxwellian linear stress relaxation as observed in soft materials, the ascribed origins of this effect in different systems, and appropriate models that can be used to capture this relaxation behavior. We provide a basic toolkit that can assist the understanding and modeling of the mechanical relaxation of soft materials for diverse applications.

Microrheology near jamming

The jamming transition is a nonequilibrium critical phenomenon, which governs characteristic mechanical properties of jammed soft materials, such as pastes, emulsions, and granular matters. Both experiments and theory of jammed soft materials have revealed that the complex modulus measured by conventional macrorheology exhibits a characteristic frequency dependence. Microrheology is a new type of method to obtain the complex modulus, which transforms the microscopic motion of probes to the complex modulus through the generalized Stokes relation (GSR). Although microrheology has been applied to jammed soft materials, its theoretical understanding is limited. In particular, the validity of the GSR near the jamming transition is far from obvious since there is a diverging length scale lc, which characterizes the heterogeneous response of jammed particles. Here, we study the microrheology of jammed particles by theory and numerical simulation. First, we develop a linear response formalism to calculate the response function of the probe particle, which is transformed to the complex modulus via the GSR. Then, we apply our formalism to a numerical model of jammed particles and find that the storage and loss modulus follow characteristic scaling laws near the jamming transition. Importantly, the observed scaling law coincides with that in macrorheology, which indicates that the GSR holds even near the jamming transition. We rationalize this equivalence by asymptotic analysis of the obtained formalism and numerical analysis on the displacement field of jammed particles under a local perturbation.

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.

Activity-dependent glassy cell mechanics Ⅰ: Mechanical properties measured with active microrheology

Active microrheology was conducted in living cells by applying an optical-trapping force to vigorously fluctuating tracer beads with feedback-tracking technology. The complex shear modulus G(ω)=G'(ω)-iG″(ω) was measured in HeLa cells in an epithelial-like confluent monolayer. We found that G(ω)∝(-iω)1/2 over a wide range of frequencies (1 Hz < ω/2π < 10 kHz). Actin disruption and cell-cycle progression from G1 to S and G2 phases only had a limited effect on G(ω) in living cells. On the other hand, G(ω) was found to be dependent on cell metabolism; ATP-depleted cells showed an increased elastic modulus G'(ω) at low frequencies, giving rise to a constant plateau such that G(ω)=G0+A(-iω)1/2. Both the plateau and the additional frequency dependency ∝(-iω)1/2 of ATP-depleted cells are consistent with a rheological response typical of colloidal jamming. On the other hand, the plateau G0 disappeared in ordinary metabolically active cells, implying that living cells fluidize their internal states such that they approach the critical jamming point.

Building block properties govern granular hydrogel mechanics through contact deformations

Granular hydrogels have been increasingly exploited in biomedical applications, including wound healing and cardiac repair. Despite their utility, design guidelines for engineering their macroscale properties remain limited, as we do not understand how the properties of granular hydrogels emerge from collective interactions of their microgel building blocks. In this work, we related building block features (stiffness and size) to the macroscale properties of granular hydrogels using contact mechanics. We investigated the mechanics of the microgel packings through dynamic oscillatory rheology. In addition, we modeled the system as a collection of two-body interactions and applied the Zwanzig and Mountain formula to calculate the plateau modulus and viscosity of the granular hydrogels. The calculations agreed with the dynamic mechanical measurements and described how microgel properties and contact deformations define the rheology of granular hydrogels. These results support a rational design framework for improved engineering of this fascinating class of materials.

Microscopic dynamics underlying the stress relaxation of arrested soft materials

Arrested soft materials such as gels and glasses exhibit a slow stress relaxation with a broad distribution of relaxation times in response to linear mechanical perturbations. Although this macroscopic stress relaxation is an essential feature in the application of arrested systems as structural materials, consumer products, foods, and biological materials, the microscopic origins of this relaxation remain poorly understood. Here, we elucidate the microscopic dynamics underlying the stress relaxation of such arrested soft materials under both quiescent and mechanically perturbed conditions through X-ray photon correlation spectroscopy. By studying the dynamics of a model associative gel system that undergoes dynamical arrest in the absence of aging effects, we show that the mean stress relaxation time measured from linear rheometry is directly correlated to the quiescent superdiffusive dynamics of the microscopic clusters, which are governed by a buildup of internal stresses during arrest. We also show that perturbing the system via small mechanical deformations can result in large intermittent fluctuations in the form of avalanches, which give rise to a broad non-Gaussian spectrum of relaxation modes at short times that is observed in stress relaxation measurements. These findings suggest that the linear viscoelastic stress relaxation in arrested soft materials may be governed by nonlinear phenomena involving an interplay of internal stress relaxations and perturbation-induced intermittent avalanches.

Delayed elastic contributions to the viscoelastic response of foams

We show that the slow viscoelastic response of a foam is that of a power-law fluid with a terminal relaxation. Investigations of the foam mechanics in creep and recovery tests reveal that the power-law contribution is fully reversible, indicative of a delayed elastic response. We demonstrate how this contribution fully accounts for the non-Maxwellian features observed in all tests, probing the linear mechanical response function. The associated power-law spectrum is consistent with soft glassy rheology of systems with mechanical noise temperatures just above the glass transition [Fielding et al., J. Rheol. 44, 323 (2000)] and originates from a combination of superdiffusive bubble dynamics and stress diffusion, as recently evidenced in simulations of coarsening foam [Hwang et al., Nat. Mater. 15, 1031 (2016)].

Shear-enhanced elasticity in the cubic blue phase I

We present results of the linear and nonlinear rheology of the cubic blue phase I (BPI). The elasticity of BPI is dominated by double-twist cylinders assembled in a body-centered cubic lattice, which can be specified by disclination lines. We find that the elasticity of BPI is enhanced by an order of magnitude by applying pre-shear. The shear-enhanced elasticity is attributed to a rearrangement of the disclination lines that are arrested in a metastable state. Our results are relevant for the understanding of the dynamics of disclinations in the cubic blue phases.

Self-motion and heterogeneous droplet dynamics in moderately attractive dense emulsions

We show that diffusing wave spectroscopy (DWS) is sensitive to the presence of a moderate short-range attraction between droplets in uniform fractionated colloidal emulsions near and below the jamming point associated with monodisperse hard spheres. This moderate interdroplet attraction, induced by micellar depletion, has an energy of about ∼2.4k_BT, only somewhat larger than thermal energy. Although changes in the mean free path of optical transport caused by this moderate depletion attraction are small, DWS clearly reveals an additional secondary decay-to-plateau in the intensity autocorrelation function at long times that is not present when droplet interactions are nearly hard. We hypothesize that this secondary decay-to-plateau does not reflect the average self-motion of individual droplets experiencing Brownian excitations, but instead results from heterogeneous dynamics involving a sub-population of droplets that still experience bound motion yet with significantly larger displacements than the average. By effectively removing the contribution of this secondary decay-to-plateau, which is linked to greater local heterogeneity in droplet structure caused by the moderate attraction, we obtain self-motion mean square displacements (MSDs) of droplets that reflect only the initial primary decay-to-plateau. Moreover, we show that droplet self-motion primary plateau MSDs can be interpreted using the generalized Stokes-Einstein relation of passive microrheology, yielding quantitative agreement with plateau elastic shear moduli measured mechanically.

Investigation of the swollen state of Carbopol molecules in non-aqueous solvents through rheological characterization

We explore how different types of solvent influence the rheological properties of non-aqueous Carbopol dispersions from the dilute to the jammed state. In novel non-aqueous formulations, polar solvents are used more and more frequently, because they can form Carbopol microgels without the need of any neutralizing agents. However, the swelling behaviour of Carbopol molecules in the absence of water, when ionic forces are weak, is still poorly understood. To this end, we study the swelling behaviour of Carbopol 974P NF in different polar solvents, i.e. glycerol, PEG400 and mixtures of the two solvents, by mapping the rheological behaviour of Carbopol suspensions from very dilute to highly concentrated conditions. The rheological study reveals that the onset of the jamming transition occurs at different critical polymer concentrations depending on the solvents used. Nevertheless, once the jammed state is reached, both elastic and yielding behaviours are scalable with the particle volume fraction. These results suggest that the type of solvent influences the final volume of the single Carbopol particles but does not alter the interactions between the particles. The final radius of the swollen particles is estimated from shear rheology measurements in dilute conditions, showing a decrease of the final swelling ratio of Carbopol molecules of almost 50% for PEG400 solutions, a result that confirms the shift to higher values of the critical jamming concentration obtained from linear viscoelasticity for the same solutions.

Acoustic resonance in periodically sheared glass: damping due to plastic events

Using molecular dynamics simulation, we study acoustic resonance in a low-temperature model glass by applying a small periodic shear at a boundary wall. Shear wave resonance occurs as the frequency ω approaches ωl = πc⊥l/L (l = 1, 2…). Here, c⊥ is the transverse sound speed and L is the cell width. At resonance, large-amplitude sound waves appear after many cycles even if the applied strain γ0 is very small. They then induce plastic events, which are heterogeneous on the mesoscopic scale and intermittent on timescales longer than the oscillation period tp = 2π/ω. We visualize them together with the extended elastic strains around them. These plastic events serve to damp sounds. We obtain the nonlinear damping Q-1 = tan δ due to the plastic events near the first resonance at ω ≅ ω1, which is linear in γ0 and independent of ω. After many resonant cycles, we observe an increase in the shear modulus (measured after switching-off the oscillation). We also observe catastrophic plastic events after a very long time (∼103tp), which induce system-size elastic strains and cause a transition from resonant to off-resonant states. At resonance, stroboscopic diffusion becomes detectable.

Relationship between rheology and structure of interpenetrating, deforming and compressing microgels

Thermosensitive microgels are widely studied hybrid systems combining properties of polymers and colloidal particles in a unique way. Due to their complex morphology, their interactions and packing, and consequentially the viscoelasticity of suspensions made from microgels, are still not fully understood, in particular under dense packing conditions. Here we study the frequency-dependent linear viscoelastic properties of dense suspensions of micron sized soft particles in conjunction with an analysis of the local particle structure and morphology based on superresolution microscopy. By identifying the dominating mechanisms that control the elastic and dissipative response, we can explain the rheology of these widely studied soft particle assemblies from the onset of elasticity deep into the overpacked regime. Interestingly, our results suggest that the friction between the microgels is reduced due to lubrification mediated by the polymer brush-like corona before the onset of interpenetration.

Diffusing wave microrheology of highly scattering concentrated monodisperse emulsions

Motivated by improvements in diffusing wave spectroscopy (DWS) for nonergodic, highly optically scattering soft matter and by cursory treatment of collective scattering effects in prior DWS microrheology experiments, we investigate the low-frequency plateau elastic shear moduli [Formula: see text] of concentrated, monodisperse, disordered oil-in-water emulsions as droplets jam. In such experiments, the droplets play dual roles both as optical probes and as the jammed objects that impart shear elasticity. Here, we demonstrate that collective scattering significantly affects DWS mean-square displacements (MSDs) in dense colloidal emulsions. By measuring and analyzing the scattering mean free path as a function of droplet volume fraction φ, we obtain a φ-dependent average structure factor. We use this to correct DWS MSDs by up to a factor of 4 and then calculate [Formula: see text] predicted by the generalized Stokes-Einstein relation. We show that DWS-microrheological [Formula: see text] agrees well with mechanically measured [Formula: see text] over about three orders of magnitude when droplets are jammed but only weakly deformed. Moreover, both of these measurements are consistent with predictions of an entropic-electrostatic-interfacial (EEI) model, based on quasi-equilibrium free-energy minimization of disordered, screened-charge-stabilized, deformable droplets, which accurately describes prior mechanical measurements of [Formula: see text] made on similar disordered monodisperse emulsions over a wide range of droplet radii and φ. This very good quantitative agreement between DWS microrheology, mechanical rheometry, and the EEI model provides a comprehensive and self-consistent view of weakly jammed emulsions. Extensions of this approach may improve DWS microrheology on other systems of dense, jammed colloids that are highly scattering.

Linear and nonlinear rheology and structural relaxation in dense glassy and jammed soft repulsive pNIPAM microgel suspensions

We present an integrated experimental and quantitative theoretical study of the mechanics of self-crosslinked, slightly charged, repulsive pNIPAM microgel suspensions over a very wide range of concentrations (c) that span the fluid, glassy and putative "soft jammed" regimes. In the glassy regime we measure a linear elastic dynamic shear modulus over 3 decades which follows an apparent power law concentration dependence G' ∼ c5.64, a variation that appears distinct from prior studies of crosslinked ionic microgel suspensions. At very high concentrations there is a sharp crossover to a nearly linear growth of the modulus. To theoretically understand these observations, we formulate an approach to address all three regimes within a single conceptual Brownian dynamics framework. A minimalist single particle description is constructed that allows microgel size to vary with concentration due to steric de-swelling effects. Using a Hertzian repulsion interparticle potential and a suite of statistical mechanical theories, quantitative predictions under quiescent conditions of microgel collective structure, dynamic localization length, elastic modulus, and the structural relaxation time are made. Based on a constant inter-particle repulsion strength parameter which is determined by requiring the theory to reproduce the linear elastic shear modulus over the entire concentration regime, we demonstrate good agreement between theory and experiment. Testable predictions are then made. We also measured nonlinear rheological properties with a focus on the yield stress and strain. A theoretical analysis with no adjustable parameters predicts how the quiescent structural relaxation time changes under deformation, and how the yield stress and strain change as a function of concentration. Reasonable agreement with our observations is obtained. To the best of our knowledge, this is the first attempt to quantitatively understand structure, quiescent relaxation and shear elasticity, and nonlinear yielding of dense microgel suspensions using microscopic force based theoretical methods that include activated hopping processes. We expect our approach will be useful for other soft polymeric particle suspensions in the core-shell family.

Universal glass-forming behavior of in vitro and living cytoplasm

Physiological processes in cells are performed efficiently without getting jammed although cytoplasm is highly crowded with various macromolecules. Elucidating the physical machinery is challenging because the interior of a cell is so complex and driven far from equilibrium by metabolic activities. Here, we studied the mechanics of in vitro and living cytoplasm using the particle-tracking and manipulation technique. The molecular crowding effect on cytoplasmic mechanics was selectively studied by preparing simple in vitro models of cytoplasm from which both the metabolism and cytoskeletons were removed. We obtained direct evidence of the cytoplasmic glass transition; a dramatic increase in viscosity upon crowding quantitatively conformed to the super-Arrhenius formula, which is typical for fragile colloidal suspensions close to jamming. Furthermore, the glass-forming behaviors were found to be universally conserved in all the cytoplasm samples that originated from different species and developmental stages; they showed the same tendency for diverging at the macromolecule concentrations relevant for living cells. Notably, such fragile behavior disappeared in metabolically active living cells whose viscosity showed a genuine Arrhenius increase as in typical strong glass formers. Being actively driven by metabolism, the living cytoplasm forms glass that is fundamentally different from that of its non-living counterpart.

Feedback-tracking microrheology in living cells

Living cells are composed of active materials, in which forces are generated by the energy derived from metabolism. Forces and structures self-organize to shape the cell and drive its dynamic functions. Understanding the out-of-equilibrium mechanics is challenging because constituent materials, the cytoskeleton and the cytosol, are extraordinarily heterogeneous, and their physical properties are strongly affected by the internally generated forces. We have analyzed dynamics inside two types of eukaryotic cells, fibroblasts and epithelial-like HeLa cells, with simultaneous active and passive microrheology using laser interferometry and optical trapping technology. We developed a method to track microscopic probes stably in cells in the presence of vigorous cytoplasmic fluctuations, by using smooth three-dimensional (3D) feedback of a piezo-actuated sample stage. To interpret the data, we present a theory that adapts the fluctuation-dissipation theorem (FDT) to out-of-equilibrium systems that are subjected to positional feedback, which introduces an additional nonequilibrium effect. We discuss the interplay between material properties and nonthermal force fluctuations in the living cells that we quantify through the violations of the FDT. In adherent fibroblasts, we observed a well-known polymer network viscoelastic response where the complex shear modulus scales as G* ∝ (-iω)3/4. In the more 3D confluent epithelial cells, we found glassy mechanics with G* ∝ (-iω)1/2 that we attribute to glassy dynamics in the cytosol. The glassy state in living cells shows characteristics that appear distinct from classical glasses and unique to nonequilibrium materials that are activated by molecular motors.

Advances and challenges in the rheology of concentrated emulsions and nanoemulsions

We review advances that have been made in the rheology of concentrated emulsions and nanoemulsions, which can serve as model soft materials that have highly tunable viscoelastic properties at droplet volume fractions near and above the glass transition and jamming point. As revealed by experiments, simulations, and theoretical models, interfacial and positional structures of droplets can depend on the applied flow history and osmotic pressure that an emulsion has experienced, thereby influencing its key rheological properties such as viscoelastic moduli, yield stress and strain, and flow behavior. We emphasize studies of monodisperse droplets, since these have led to breakthroughs in the fundamental understanding of dispersed soft matter. This review also covers the rheological properties of attractive emulsions, which can exhibit a dominant elasticity even at droplet volume fractions far below maximal random jamming of hard spheres.

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.

Atomic-scale origin of dynamic viscoelastic response and creep in disordered solids

Viscoelasticity has been described since the time of Maxwell as an interpolation of purely viscous and purely elastic response, but its microscopic atomic-level mechanism in solids has remained elusive. We studied three model disordered solids: a random lattice, the bond-depleted fcc lattice, and the fcc lattice with vacancies. Within the harmonic approximation for central-force lattices, we applied sum rules for viscoelastic response derived on the basis of nonaffine atomic motions. The latter motions are a direct result of local structural disorder, and in particular, of the lack of inversion symmetry in disordered lattices. By defining a suitable quantitative and general atomic-level measure of nonaffinity and inversion symmetry, we show that the viscoelastic responses of all three systems collapse onto a master curve upon normalizing by the overall strength of inversion-symmetry breaking in each system. Close to the isostatic point for central-force lattices, power-law creep G(t)∼t^{-1/2} emerges as a consequence of the interplay between soft vibrational modes and nonaffine dynamics, and various analytical scalings, supported by numerical calculations, are predicted by the theory.

Beyond linear elasticity: jammed solids at finite shear strain and rate

The shear response of soft solids can be modeled with linear elasticity, provided the forcing is slow and weak. Both of these approximations must break down when the material loses rigidity, such as in foams and emulsions at their (un)jamming point - suggesting that the window of linear elastic response near jamming is exceedingly narrow. Yet precisely when and how this breakdown occurs remains unclear. To answer these questions, we perform computer simulations of stress relaxation and shear start-up tests in athermal soft sphere packings, the canonical model for jamming. By systematically varying the strain amplitude, strain rate, distance to jamming, and system size, we identify characteristic strain and time scales that quantify how and when the window of linear elasticity closes, and relate these scales to changes in the microscopic contact network.

Elasticity of frictionless particles near jamming

We study the linear elastic response of harmonic disk packings near jamming via three types of probes: (i) point forcing, (ii) constrained homogeneous deformation of subregions of large systems, and (iii) unconstrained deformation of the full system subject to periodic boundary conditions. For the point forcing, our results indicate that the transverse component of the response is governed by a lengthscale ξT, which scales with the confining pressure, p, as ξT∼p-0.25, while the longitudinal component is governed by ξL, which scales as ξL∼p-0.4. The former scaling is precisely the transverse lengthscale, which has been invoked to explain the structure of normal modes near the density of states anomaly in sphere packings, while the latter is much closer to the rigidity length, l*∼p-0.5, which has been invoked to describe the jamming scenario. For the case of constrained homogeneous deformation, we find that μ(R), the value of the shear modulus measured in boxes of size R, gives a value much higher than the continuum result for small boxes and recedes to its continuum limit only for boxes bigger than a characteristic length, which scales like p-0.5, precisely the same way as l*. Finally, for the case of unconstrained homogeneous deformation, we find displacement fields with power spectra, which are consistent with independent, uncorrelated Eshelby transformations. The transverse sector is amazingly invariant with respect to p and very similar to what is seen in Lennard-Jones glasses. The longitudinal piece, however, is sensitive to p. It develops a plateau at long wavelength, the start of which occurs at a length that grows in the p→0 limit. Strikingly, the same behavior is observed both for applied shear and dilation.

Physical chemistry of highly concentrated emulsions

This review explores the physics underlying the rheology of highly concentrated emulsions (HCEs) to determine the relationship between elasticity and HCE stability, and to consider whether it is possible to describe all physicochemical properties of HCEs on the basis of a unique physical approach. We define HCEs as emulsions with a volume fraction above the maximum closest packing fraction of monodisperse spheres, φm=0.74, even if droplets are not of polyhedron shape. The solid-like rheological behavior of HCEs is characterized by yield stress and elasticity, properties which depend on droplet polydispersity and which are affected by caging at volume fractions about the jamming concentration, φj. A bimodal size distribution in HCEs diminishes caging and facilitates droplet movement, resulting in HCEs with negligible yield stress and no plateau in storage modulus. Thermodynamic forces automatically move HCEs toward the lowest free energy state, but since interdroplet forces create local minimums - points beyond which free energy temporarily increases before it reaches the global minimum of the system - the free energy of HCEs will settle at a local minimum unless additional energy is added. Several attempts have been undertaken to predict the elasticity of HCEs. In many cases, the elastic modulus of HCEs is higher than the one predicted from classical models, which only take into account spatial repulsion (or simply interfacial energy). Improved models based on free energy calculation should be developed to consider the disjoining pressure and interfacial rheology in addition to spatial repulsion. The disjoining pressure and interfacial viscoelasticity, which result in the deviation of elasticity from the classical model, can be regarded as parameters for quantifying the stability of HCEs.

Affine and nonaffine motions in sheared polydisperse emulsions

We study dense and highly polydisperse emulsions at droplet volume fractions ϕ≥0.65. We apply oscillatory shear and observe droplet motion using confocal microscopy. The presence of droplets with sizes several times the mean size dramatically changes the motion of smaller droplets. Both affine and nonaffine droplet motions are observed, with the more nonaffine motion exhibited by the smaller droplets which are pushed around by the larger droplets. Droplet motions are correlated over length scales from one to four times the mean droplet diameter, with larger length scales corresponding to higher strain amplitudes (up to strains of about 6%).

Rheology of soft colloids across the onset of rigidity: scaling behavior, thermal, and non-thermal responses

We study the rheological behavior of colloidal suspensions composed of soft sub-micron-size hydrogel particles across the liquid-solid transition. The measured stress and strain-rate data, when normalized by thermal stress and time scales, suggest our systems reside in a regime wherein thermal effects are important. In a different vein, critical point scaling predictions for the jamming transition, typical in athermal systems, are tested. Near dynamic arrest, the suspensions exhibit scaling exponents similar to those reported in Nordstrom et al., Phys. Rev. Lett., 2010, 105, 175701. The observation suggests that our system exhibits a glass transition near the onset of rigidity, but it also exhibits a jamming-like scaling further from the transition point. These observations are thought-provoking in light of recent theoretical and simulation findings, which show that suspension rheology across the full range of microgel particle experiments can exhibit both thermal and athermal mechanisms.

Laser-speckle-visibility acoustic spectroscopy in soft turbid media

We image the evolution in space and time of an acoustic wave propagating along the surface of turbid soft matter by shining coherent light on the sample. The wave locally modulates the speckle interference pattern of the backscattered light, which is recorded using a camera. We show both experimentally and theoretically how the temporal and spatial correlations in this pattern can be analyzed to obtain the acoustic wavelength and attenuation length. The technique is validated using shear waves propagating in aqueous foam. It may be applied to other kinds of acoustic waves in different forms of turbid soft matter such as biological tissues, pastes, or concentrated emulsions.

Shear shocks in fragile networks

A minimal model for studying the mechanical properties of amorphous solids is a disordered network of point masses connected by unbreakable springs. At a critical value of its mean connectivity, such a network becomes fragile: it undergoes a rigidity transition signaled by a vanishing shear modulus and transverse sound speed. We investigate analytically and numerically the linear and nonlinear visco-elastic response of these fragile solids by probing how shear fronts propagate through them. Our approach, which we tentatively label shear front rheology, provides an alternative route to standard oscillatory rheology. In the linear regime, we observe at late times a diffusive broadening of the fronts controlled by an effective shear viscosity that diverges at the critical point. No matter how small the microscopic coefficient of dissipation, strongly disordered networks behave as if they were overdamped because energy is irreversibly leaked into diverging nonaffine fluctuations. Close to the transition, the regime of linear response becomes vanishingly small: the tiniest shear strains generate strongly nonlinear shear shock waves qualitatively different from their compressional counterparts in granular media. The inherent nonlinearities trigger an energy cascade from low to high frequency components that keep the network away from attaining the quasi-static limit. This mechanism, reminiscent of acoustic turbulence, causes a superdiffusive broadening of the shock width.

Supershear Rayleigh waves at a soft interface

We report on the experimental observation of waves at a liquid foam surface propagating faster than the bulk shear waves. The existence of such waves has long been debated, but the recent observation of supershear events in a geophysical context has inspired us to search for their existence in a model viscoelastic system. An optimized fast profilometry technique allows us to observe on a liquid foam surface the waves triggered by the impact of a projectile. At high impact velocity, we show that the expected subshear Rayleigh waves are accompanied by faster surface waves that can be identified as supershear Rayleigh waves.

Advanced rheological characterization of soft colloidal model systems

The complex flow behavior of polymer-based soft colloidal model systems was investigated using steady and oscillatory shear to prove new concepts for advanced rheological characterization. In the very dilute regime we investigated high molecular weight polybutadiene star polymers to quantify the internal relaxation time arising from the polymeric nature of these ultra-soft colloids. The observed shear-induced brush deformation is interpreted in terms of the internal Zimm time τ(z). The observed dependence of τ(z) on matrix viscosity can be explained by shrinkage of the star polymer due to an increasing incompatibility with increasing matrix molecular weight. The influence of the polymeric nature on the characteristic structural relaxation time in the concentrated regime was investigated using non-linear rheology following Wyss et al (SRFS) (2007 Phys. Rev. Lett. 98 238303). Here we used star-like block copolymer micelles to systematically tune the 'softness' of the colloids by variation of the block ratio. A master curve with proper scaling parameters could be generated independent of the degree of colloidal 'softness'. However, the obtained strain-rate independent structural relaxation time τ(0) was not observed in the linear regime. In addition, a high frequency discrepancy was clearly found in all our experimental data. Both reflect the shortcomings of the SRFS approach.

Nonaffine measures of particle displacements in sheared colloidal glasses

The nonaffine motion of particles is central to the relaxation and flow of glasses. It is usually assumed in plasticity theories that nonaffine rearrangements are localized and uncorrelated. Here we present evidence that this assumption may not hold. We investigate and compare systematically different measures of nonaffinity in a sheared colloidal glass by tracking the motion of the individual particles directly with confocal microscopy. We show that besides differences in the appearance and degree of localization of nonaffine displacements, the nature of their fluctuations is very similar. At intermediate times, all spatial correlation functions display robust power-law behavior, clearly demonstrating long-range correlations and critical behavior of the driven glass, in contrast to the assumptions of plasticity theories. We show that on long-time scales, correlations become finite and plasticity theories may apply.

Bulk and shear moduli of compressed microgel suspensions

We independently determine the bulk and shear moduli of compressed microgel suspensions and the bulk modulus of individual microgel particles and find that the elastic behavior of the suspension reflects the degree of compression of the particles. This feature, which is distinct from other soft materials such as emulsions or foams, can give rise to an unusually large difference between the bulk and shear moduli of the suspension. Our results extend our understanding of soft materials to systems based on compressible objects, opening up possibilities for engineering materials with drastically different responses to shear and compression.

Relaxations and rheology near jamming

We determine the form of the complex shear modulus G* in soft sphere packings near jamming. Viscoelastic response at finite frequency is closely tied to a packing's intrinsic relaxational modes, which are distinct from the vibrational modes of undamped packings. We demonstrate and explain the appearance of an anomalous excess of slowly relaxing modes near jamming, reflected in a diverging relaxational density of states. From the density of states, we derive the dependence of G* on the frequency and distance to the jamming transition, which is confirmed by numerics.

Investigating acoustic-induced deformations in a foam using multiple light scattering

We have studied the effect of an external acoustic wave on bubble displacements inside an aqueous foam. The signature of the acoustic-induced bubble displacements is found using a multiple light scattering technique, and occurs as a modulation on the photon correlation curve. Measurements for various sound frequencies and amplitudes are compared to analytical predictions and numerical simulations. These comparisons finally allow us to elucidate the nontrivial acoustic displacement profile inside the foam; in particular, we find that the acoustic wave creates a localized shear in the vicinity of the solid walls holding the foam, as a consequence of inertial contributions. This study of how bubbles "dance" inside a foam as a response to sound turns out to provide new insights on foam acoustics and sound transmission into a foam, foam deformation at high frequencies, and analysis of light scattering data in samples undergoing nonhomogeneous deformations.

Fast relaxations in foam

Aqueous foams present an anomalous macroscopic viscoelastic response at high frequency, previously shown to arise from collective relaxations in the disordered bubble packing. We demonstrate experimentally how these mesoscopic dynamics are in turn tuned by physico-chemical processes on the scale of the gas-liquid interfaces. Two specific local dissipation processes are identified, and we show how the rigidity of the interfaces selects the dominant one, depending on the choice of the surfactant.

Strain-rate frequency superposition in large-amplitude oscillatory shear

In a recent work, Wyss [Phys. Rev. Lett. 98, 238303 (2007)] have noted a property of "soft solids" under oscillatory shear, the so-called strain-rate frequency superposition. We extend this study to the case of soft solids under large-amplitude oscillatory shear (LAOS). We show results from LAOS studies in a monodisperse hydrogel suspension, an aqueous gel, and a biopolymer suspension and show that constant strain-rate frequency sweep measurements with soft solids can be superimposed onto master curves for higher harmonic moduli with the same shift factors as for the linear viscoelastic moduli. We show that the behavior of higher harmonic moduli at low frequencies in constant strain-rate frequency sweep measurements is similar to that at large strain amplitude in strain-amplitude sweep tests. We show surface plots of the harmonic moduli and the energy dissipation rate per unit volume in LAOS for soft solids and show experimentally that the energy dissipated per unit volume depends on the first harmonic loss modulus alone, in both the linear and the nonlinear viscoelastic regime.

Shearing particle monolayers: strain-rate frequency superposition

We report surface shear rheological measurements on monolayers of silica nanoparticles at the air-water interface. We have used the method of strain-rate frequency superposition (SRFS) to characterize the structural relaxation. We show that the rheological properties of the layers have the same universal linear and nonlinear behavior as three-dimensional soft materials. We also discuss the original healing properties of these monolayers.

Re-entrant phase behavior of a concentrated anionic surfactant system with strongly binding counterions

The phase behavior of the anionic surfactant sodium dodecyl sulfate (SDS) in the presence of the strongly binding counterion p-toluidine hydrochloride (PTHC) has been examined using small-angle X-ray diffraction and polarizing microscopy. A hexagonal-to-lamellar transition on varying the PTHC to SDS molar ratio (alpha) occurs through a nematic phase of rodlike micelles (Nc) --> isotropic (I) --> nematic of disklike micelles (N(D)) at a fixed surfactant concentration (phi). The lamellar phase is found to coexist with an isotropic phase (I') over a large region of the phase diagram. Deuterium nuclear magnetic resonance investigations of the phase behavior at phi = 0.4 confirm the transition from N(C) to N(D) on varying alpha. The viscoelastic and flow behaviors of the different phases were examined. A decrease in the steady shear viscosity across the different phases with increasing alpha suggests a decrease in the aspect ratio of the micellar aggregates. From the transient shear stress response of the N() and N(D) nematic phases in step shear experiments, they were characterized to be tumbling and flow aligning, respectively. Our studies reveal that by tuning the morphology of the surfactant micelles strongly binding counterions modify the phase behavior and rheological properties of concentrated surfactant solutions.

Flow in linearly sheared two-dimensional foams: From bubble to bulk scale

We probe the flow of two-dimensional (2D) foams, consisting of a monolayer of bubbles sandwiched between a liquid bath and glass plate, as a function of driving rate, packing fraction, and degree of disorder. First, we find that bidisperse, disordered foams exhibit strongly rate-dependent and inhomogeneous (shear-banded) velocity profiles, while monodisperse ordered foams are also shear banded but essentially rate independent. Second, we adapt a simple model [E. Janiaud, D. Weaire, and S. Hutzler, Phys. Rev. Lett. 97, 038302 (2006)] based on balancing the averaged drag forces between the bubbles and the top plate F[over ]_{bw} and the averaged bubble-bubble drag forces F[over ]_{bb} by assuming that F[over ]_{bw} approximately v;{2/3} and F[over ]_{bb} approximately ( partial differential_{y}v);{beta} , where v and ( partial differential_{y}v) denote average bubble velocities and gradients. This model captures the observed rate-dependent flows for beta approximately 0.36 , and the rate independent flows for beta approximately 0.67 . Third, we perform independent rheological measurements of F[over ]_{bw} and F[over ]_{bb} , both for ordered and disordered systems, and find these to be fully consistent with the forms assumed in the simple model. Disorder thus leads to a modified effective exponent beta . Fourth, we vary the packing fraction phi of the foam over a substantial range and find that the flow profiles become increasingly shear banded when the foam is made wetter. Surprisingly, the model describes flow profiles and rate dependence over the whole range of packing fractions with the same power-law exponents-only a dimensionless number k that measures the ratio of the prefactors of the viscous drag laws is seen to vary with packing fraction. We find that k approximately (phi-phi_{c});{-1} , where phi_{c} approximately 0.84 corresponds to the 2D jamming density, and suggest that this scaling follows from the geometry of the deformed facets between bubbles in contact. Overall, our work shows that the presence of disorder qualitatively changes the effective bubble-bubble drag forces and suggests a route to rationalize aspects of the ubiquitous Herschel-Bulkley (power-law) rheology observed in a wide range of disordered materials.

Dissipation in a sheared foam: from bubble adhesion to foam rheology

The link between the rheology of 3D aqueous foam and the adhesion of neighboring bubbles is tested by confronting experiments at two different length scales. On the one hand, the dynamics of adhesion are probed by measuring how the shape of two bubbles in contact changes as their center-to-center distance is modulated. On the other hand, the linear viscoelastic behavior of 3D foam prepared with the same soapy solution is characterized by its complex shear modulus. To connect the two sets of data, we present a model of foam viscoelasticity taking into account bubble adhesion.

Rate dependence and role of disorder in linearly sheared two-dimensional foams

The shear flow of two-dimensional foams is probed as a function of shear rate and disorder. Disordered, bidisperse foams exhibit strongly shear rate dependent velocity profiles. This behavior is captured quantitatively in a simple model based on the balance of the time-averaged drag forces in the system, which are found to exhibit power-law scaling with the foam velocity and strain rate. Disorder makes the scaling of the bulk drag forces different from that of the local interbubble drag forces, which we evidence by rheometrical measurements. In monodisperse, ordered foams, rate independent velocity profiles are found, which lends further credibility to this picture.