Strain-rate frequency superposition: a rheological probe of structural relaxation in soft materials

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.

Nonlinear viscoelasticity and shear localization at complex fluid interfaces

Foams and emulsions are often exposed to strong external fields, resulting in large interface deformations far beyond the linear viscoelastic regime. Here, we investigate the nonlinear and transient interfacial rheology of adsorption layers in large-amplitude oscillatory shear flow. As a prototypical material forming soft-solid-type interfacial adsorption layers, we use Acacia gum (i.e., gum arabic), a protein/polysaccharide hybrid. We quantify its nonlinear flow properties at the oil/water interface using a biconical disk interfacial rheometer and analyze the nonlinear stress response under forced strain oscillations. From the resulting Lissajous curves, we access quantitative measures recently introduced for nonlinear viscoelasticity, including the intracycle moduli for both the maximum and zero strains and the degree of plastic energy dissipation upon interfacial yielding. We demonstrate using in situ flow visualization that the onset of nonlinear viscoelasticity coincides with shear localization at the interface. Finally, we address the nonperiodic character of this flow transition using an experimental procedure based on opposing stress pulses, allowing us to extract additional interfacial properties such as the critical interfacial stress upon yielding and the permanent deformation.

Mechanical responses and stress fluctuations of a supercooled liquid in a sheared non-equilibrium state

A steady shear flow can drive supercooled liquids into a non-equilibrium state. Using molecular dynamics simulations under steady shear flow superimposed with oscillatory shear strain for a probe, non-equilibrium mechanical responses are studied for a model supercooled liquid composed of binary soft spheres. We found that even in the strongly sheared situation, the supercooled liquid exhibits surprisingly isotropic responses to oscillating shear strains applied in three different components of the strain tensor. Based on this isotropic feature, we successfully constructed a simple two-mode Maxwell model that can capture the key features of the storage and loss moduli, even for highly non-equilibrium state. Furthermore, we examined the correlation functions of the shear stress fluctuations, which also exhibit isotropic relaxation behaviors in the sheared non-equilibrium situation. In contrast to the isotropic features, the supercooled liquid additionally demonstrates anisotropies in both its responses and its correlations to the shear stress fluctuations. Using the constitutive equation (a two-mode Maxwell model), we demonstrated that the anisotropic responses are caused by the coupling between the oscillating strain and the driving shear flow. Due to these anisotropic responses and fluctuations, the violation of the fluctuation-dissipation theorem (FDT) is distinct for different components. We measured the magnitude of this violation in terms of the effective temperature. It was demonstrated that the effective temperature is notably different between different components, which indicates that a simple scalar mapping, such as the concept of an effective temperature, oversimplifies the true nature of supercooled liquids under shear flow. An understanding of the mechanism of isotropies and anisotropies in the responses and fluctuations will lead to a better appreciation of these violations of the FDT, as well as certain consequent modifications to the concept of an effective temperature.

Thermodynamic interpretation of soft glassy rheology models

Mesoscopic models play an important role in our understanding of the deformation and flow of amorphous materials. One such description, based on the shear transformation zone theory, has recently been reformulated within a nonequilibrium thermodynamics framework and found to be consistent with it. We show here that a similar interpretation can be made for the soft glassy rheology (SGR) model. Conceptually this means that the "noise temperature" x, proposed phenomenologically in the SGR model to control the dynamics of a set of slow mesoscopic degrees of freedom, can consistently be interpreted as their actual thermodynamic temperature. (Because such modes are slow to equilibrate, this generally does not coincide with the temperature of the fast degrees of freedom and/or heat bath.) If one chooses to make this interpretation, the thermodynamic framework significantly constrains extensions of the SGR approach to models in which x is a dynamical variable. We assess in this light some such extensions recently proposed in the context of shear banding.

Yielding and structural relaxation in soft materials: evaluation of strain-rate frequency superposition data by the stress decomposition method

Rheological properties of soft materials are often investigated in oscillatory shear and characterized by the storage and loss modulus, G' and G'', respectively. Unfortunately, the relaxation dynamics of most soft materials is too slow to be directly probed by commercial rheometers. Recently, it was shown by Wyss et al. [Phys. Rev. Lett. 98, 238303 (2007)] that the application of an oscillating strain-rate drives such soft materials and shifts the structural relaxation to higher times. They called this experimental technique strain-rate frequency superposition (SRFS). The great benefit of SRFS is the extremely extended frequency range. As viscoelastic measures, Wyss et al. proposed the familiar storage and loss modulus. Using these moduli results in a serious drawback: When the material yields, nonlinearities appear and the physical interpretation of the storage and loss modulus breaks down. Thus, SRFS as proposed by Wyss et al. is limited to the linear regime and the benefit of the extended frequency regime vanishes. In the present work, we validate an alternative data analysis technique, recently established as the stress decomposition method [K. S. Cho et al., J. Rheol. 49, 747 (2005); R. H. Ewoldt et al., J. Rheol. 52, 1427 (2008)], for combination with SRFS. Use of the stress decomposition method provides a physical interpretation of linear and nonlinear SRFS data in terms of strain stiffening and softening as well as shear thickening and thinning.

Rheology of attractive emulsions

We show how attractive interactions dramatically influence emulsion rheology. Unlike the repulsive case, attractive emulsions below random close packing, φ(RCP), can form soft gel-like elastic solids. However, above φ(RCP), attractive and repulsive emulsions have similar elasticities. Such compressed attractive emulsions undergo an additional shear-driven relaxation process during yielding. Our results suggest that attractive emulsions begin to yield at weak points through the breakage of bonds, and, above φ(RCP), also undergo droplet configurational rearrangements.

Experimental studies of the jamming behaviour of triblock copolymer solutions and triblock copolymer-anionic surfactant mixtures

Photon correlation spectroscopy and rheological measurements are performed to investigate the microscopic dynamics and mechanical responses of aqueous solutions of triblock copolymers and aqueous mixtures of triblock copolymers and anionic surfactants. Increasing the concentration of triblock copolymers results in a sharp increase in the magnitude of the complex moduli characterising the samples. This is understood in terms of the changes in the aggregation and packing behaviours of the copolymers and the constraints imposed upon their dynamics due to increased close packing. The addition of suitable quantities of an anionic surfactant to a strongly elastic copolymer solution results in a decrease in the complex moduli of the samples by several decades. It is argued that the shape anisotropy and size polydispersity of the micelles comprising mixtures cause dramatic changes in the packing behaviour, resulting in sample unjamming and the observed decrease in complex moduli. Finally, a phase diagram is constructed in the temperature-surfactant concentration plane to summarise the jamming-unjamming behaviour of aggregates constituting triblock copolymer-anionic surfactant mixtures.

Strain-accelerated dynamics of soft colloidal glasses

We have investigated strain-accelerated dynamics of soft glasses theoretically and experimentally. Mechanical rheology measurements performed on a variety of systems reveal evidence for the speeding-up of relaxation at modest shear strains in both step and oscillatory shear flows. Using the soft glassy rheology (SGR) model framework, we show that the observed behavior is a fundamental, but heretofore unexplored attribute of soft glasses.

Emergence of airway smooth muscle functions related to structural malleability

The function of a complex system such as a smooth muscle cell is the result of the active interaction among molecules and molecular aggregates. Emergent macroscopic manifestations of these molecular interactions, such as the length-force relationship and its associated length adaptation, are well documented, but the molecular constituents and organization that give rise to these emergent muscle behaviors remain largely unknown. In this minireview, we describe emergent properties of airway smooth muscle that seem to have originated from inherent fragility of the cellular structures, which has been increasingly recognized as a unique and important smooth muscle attribute. We also describe molecular interactions (based on direct and indirect evidence) that may confer malleability on fragile structural elements that in turn may allow the muscle to adapt to large and frequent changes in cell dimensions. Understanding how smooth muscle works may hinge on how well we can relate molecular events to its emergent macroscopic functions.

Nonlinear response of dense colloidal suspensions under oscillatory shear: mode-coupling theory and Fourier transform rheology experiments

Using a combination of theory, experiment, and simulation we investigate the nonlinear response of dense colloidal suspensions to large amplitude oscillatory shear flow. The time-dependent stress response is calculated using a recently developed schematic mode-coupling-type theory describing colloidal suspensions under externally applied flow. For finite strain amplitudes the theory generates a nonlinear response, characterized by significant higher harmonic contributions. An important feature of the theory is the prediction of an ideal glass transition at sufficiently strong coupling, which is accompanied by the discontinuous appearance of a dynamic yield stress. For the oscillatory shear flow under consideration we find that the yield stress plays an important role in determining the nonlinearity of the time-dependent stress response. Our theoretical findings are strongly supported by both large amplitude oscillatory experiments (with Fourier transform rheology analysis) on suspensions of thermosensitive core-shell particles dispersed in water and Brownian dynamics simulations performed on a two-dimensional binary hard-disk mixture. In particular, theory predicts nontrivial values of the exponents governing the final decay of the storage and loss moduli as a function of strain amplitude which are in good agreement with both simulation and experiment. A consistent set of parameters in the presented schematic model achieves to jointly describe linear moduli, nonlinear flow curves, and large amplitude oscillatory spectroscopy.

Rheology and structure formation in diluted mixed particle-surfactant systems

In the present work, we focus on the bulk rheology of mixtures consisting of surfactant modified silica nanoparticles in water. Depending on the ratio of surfactant and nanoparticle concentrations, significant modifications in the measured rheology are evidenced. A domain where the dispersions behave like viscoelastic media is observed. Outside this domain, the dispersions exhibit viscous properties. The changes in the bulk rheology characteristics are discussed in terms of interaction effects between the surfactant and the particles. The results obtained are seen in the context of diluted emulsions' properties and characteristics.

Relaxation dynamics at different time scales in electrostatic complexes: time-salt superposition

In this Letter we show that in the rheology of electrostatically assembled soft materials, salt concentration plays a similar role as temperature for polymer melts, and as strain rate for soft solids. We rescale linear and nonlinear rheological data of a set of model electrostatic complexes at different salt concentrations to access a range of time scales that is otherwise inaccessible. This provides new insights into the relaxation mechanisms of electrostatic complexes, which we rationalize in terms of a microscopic mechanism underlying salt-enhanced activated processes.

Remodeling of integrated contractile tissues and its dependence on strain-rate amplitude

Here we investigate the origin of relaxation times governing the mechanical response of an integrated contractile tissue to imposed cyclic changes of length. When strain-rate amplitude is held constant as frequency is varied, fast events are accounted for by actomyosin cross-bridge cycling, but slow events reveal relaxation processes associated with ongoing cytoskeletal length adaptation. Although both relaxation regimes are innately nonlinear, these regimes are unified and their positions along the frequency axis are set by the imposed strain-rate amplitude.

A direct numerical simulation method for complex modulus of particle dispersions

We report an extension of the smoothed profile method (SPM) (Y. Nakayama, K. Kim, and R. Yamamoto, Eur. Phys. J. E 26, 361 (2008)), a direct numerical simulation method for calculating the complex modulus of the dispersion of particles, in which we introduce a temporally oscillatory external force into the system. The validity of the method was examined by evaluating the storage G'(ω) and loss G"(ω) moduli of a system composed of identical spherical particles dispersed in an incompressible Newtonian host fluid at volume fractions of Φ = 0 , 0.41, 0.46, and 0.51. The moduli were evaluated at several frequencies of shear flow; the shear flow used here has a zigzag profile, as is consistent with the usual periodic boundary conditions. The simulation results were compared with several experiments for colloidal dispersions of spherical particles.

Internal relaxation time in immersed particulate materials

We study the dynamics of the static-to-flow transition in a model material made of elastic particles immersed in a viscous fluid. The interaction between particle surfaces includes their viscous lubrication, a sharp repulsion when they get closer than a tuned steric length, and their elastic deflection induced by those two forces. We use soft dynamics to simulate the dynamics of this material when it experiences a step increase in the shear stress and a constant normal stress. We observe a long creep phase before a substantial flow eventually establishes. We measure the change in volume (dilatancy) and find that during the creep phase, it does not change significantly. We find that the typical creep time relies on an internal relaxation process, namely, the separation of two particles driven by the applied stress and resisted by the viscous friction. The present mechanism should be relevant for granular pastes, living cells, emulsions, and wet foams.

Soft glass rheology in liquid crystalline gels formed by a monodisperse dipeptide

Thermal and extensive rheological characterization of a nematic liquid crystal gelated with a novel monodisperse dipeptide, also a liquid crystal, has been carried out. For certain concentrations, the calorimetric scans display a two-peak profile across the chiral nematic-isotropic (N*-I) transition, a feature reminiscent of the random-dilution to random-field crossover observed in liquid crystal gels formed with aerosil particles. All samples show shear thinning behavior without a Newtonian plateau region at lower shear rates. Small deformation oscillatory data at lower frequencies exhibit a frequency dependence of the storage (G') and loss (G'') moduli that can be described by a weak power-law, characteristic of soft glassy rheological systems. At higher frequencies, while lower concentration composites have a strong frequency dependence with a trend for possible crossover from viscoelastic solid to viscoelastic liquid behavior, the higher-concentration gels show frequency-independent rheograms of entirely elastic nature G' > G''. The plateau modulus of G' is described by a power-law with an exponent again common to soft materials, such as foams, slurries, etc. Other features which are a hallmark of such materials observed in the present study are: (i) above a critical strain, a strain softening of the moduli with a peak in the loss modulus, (ii) power-law variation of the storage modulus in the nonlinear viscoelastic regime, and (iii) absence of Cox-Merz superposition for the complex viscosity. An attractive feature of these gels is the fast recovery upon removal of large strain and qualitatively different temporal behavior of the recovery between the low and high concentration composites, with the latter indicating the presence of two characteristic time scales.

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.

Viscoelastic properties of silica nanoparticle monolayers at the air-water interface

We have investigated the rheological behaviour of silica nanoparticle layers at the air-water interface. Both compressed and deposited layers have been studied in Langmuir troughs and with a bicone rheometer. The compressed layers are more homogeneous and rigid, and the elastic response to continuous, step and oscillatory compression are similar, provided the compression is fast enough and relaxation is prevented. The deposited layers are less rigid and more viscoelastic. Their shear moduli deduced from the oscillatory uniaxial compression are much smaller than those deduced from pure shear deformation suggesting that the effective shear rate is smaller than expected in the compression measurements.

Shear melting of a colloidal glass

We use confocal microscopy to explore shear melting of colloidal glasses, which occurs at strains of approximately 0.08, coinciding with a strongly non-Gaussian step size distribution. For larger strains, the particle mean square displacement increases linearly with strain and the step size distribution becomes Gaussian. The effective diffusion coefficient varies approximately linearly with shear rate, consistent with a modified Stokes-Einstein relationship in which thermal energy is replaced by shear energy and the length scale is set by the size of cooperatively moving regions consisting of approximately 3 particles.

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.

The ages in a self-suspended nanoparticle liquid

Telomers ionically tethered to nanometer-sized particles yield self-suspended, nanoparticle-laden liquids with unusual dynamical features. By subjecting these suspensions to controlled, modest shear strains, we find that their flow behaviors observed using experiments performed on time scales of tens of seconds can be projected to obtain maps of their dynamical response on geological time scales. That such extraordinarily slow dynamic processes can be uncovered from real-time measurements by simply stretching a system provides a simple but powerful tool for interrogating extremely slow motions in other jammed physical states.

Soft Dynamics simulation. 2. Elastic spheres undergoing a T(1) process in a viscous fluid

Robust empirical constitutive laws for granular materials in air or in a viscous fluid have been expressed in terms of timescales based on the dynamics of a single particle. However, some behaviours such as viscosity bifurcation or shear localization, observed also in foams, emulsions, and block copolymer cubic phases, seem to involve other micro-timescales which may be related to the dynamics of local particle reorganizations. In the present work, we consider a T(1) process as an example of a rearrangement. Using the Soft Dynamics simulation method introduced in the first paper of this series, we describe theoretically and numerically the motion of four elastic spheres in a viscous fluid. Hydrodynamic interactions are described at the level of lubrication (Poiseuille squeezing and Couette shear flow) and the elastic deflection of the particle surface is modeled as Hertzian. The duration of the simulated T(1) process can vary substantially as a consequence of minute changes in the initial separations, consistently with predictions. For the first time, a collective behaviour is thus found to depend on a parameter other than the typical volume fraction of particles.

Relaxation processes of PGPR at the water/oil interface inferred by oscillatory or transient viscoelasticity measurements

The rheological properties of PolyGlycerol PolyRicinoleate (PGPR) at the oil/water interface were studied using a drop-shaped tensiometer. Small deformation oscillations of the drop area allow the measurement of the interfacial viscoelasticity spectrum, that is, the elastic and viscous moduli as a function of frequency. Another way to obtain such a spectrum is to perform a transient relaxation measurement from which the relaxation modulus as a function of time is deduced and interpreted. Several models containing one or more relaxation times were considered, and their resulting spectra were compared to the oscillatory ones. Similar results suggest that one could in principle use oscillatory or transient relaxations indifferently. However, the transient relaxation technique proved to be more adapted for the determination of the relaxation times. At low PGPR concentrations in oil, the behavior is controlled by long relaxation times, whereas short ones take over when approaching and exceeding the saturation interfacial concentration. This was understood as a shift from a diffusion-dominated regime to a rearrangements-dominated regime.

Viscoelastic properties of nanocrystalline films of semiconducting chalcogenides at liquid/liquid interface

The interfacial shear rheological properties of a continuous single-crystalline film of CuS and a 3D particulate gel of CdS nanoparticles (3-5 nm in diameter) formed at toluene-water interfaces have been studied. The ultrathin films (approximately 50 nm in thickness) are formed in situ in the shear cell through a reaction at the toluene-water interface between a metal-organic compound in the organic layer and an appropriate reagent for sulfidation in the aqueous layer. Linear viscoelastic spectra of the nanofilms reveal solid-like rheological behavior with the storage modulus higher than the loss modulus over the range of angular frequencies probed. Large strain amplitude sweep measurements on the CdS nanofilms formed at different reactant concentrations suggest that they form a weakly flocculated gel. Under steady shear, the films exhibit a yield stress, followed by a steady shear thinning at high shear rates. The viscoelastic and flow behavior of these films that are in common with those of many 3D "soft" materials like gels, foams, and concentrated colloidal suspensions can be described by the "soft" glassy rheology model.

Universality in oscillating flows

We show that oscillating flow of a simple fluid in both the Newtonian and the non-Newtonian regime can be described by a universal function of a single dimensionless scaling parameter omega tau, where omega is the oscillation (angular) frequency and tau is the fluid relaxation time; geometry and linear dimension bear no effect on the flow. Energy dissipation of mechanical resonators in a rarefied gas follows this universality closely in a broad linear dimension (10(-6) m < L < 10(-2) m) and frequency (10(5) Hz < omega/2pi < 10(8) Hz) range. Our results suggest a deep connection between flows of simple and complex fluids.

Is cell rheology governed by nonequilibrium-to-equilibrium transition of noncovalent bonds?

A living cell deforms or flows in response to mechanical stresses. A recent report shows that dynamic mechanics of living cells depends on the timescale of mechanical loading, in contrast to the prevailing view of some authors that cell rheology is timescale-free. Yet the molecular basis that governs this timescale-dependent behavior is elusive. Using molecular dynamics simulations of protein-protein noncovalent interactions, we show that multipower laws originate from a nonequilibrium-to-equilibrium transition: when the loading rate is faster than the transition rate, the power-law exponent alpha(1) is weak; when the loading rate is slower than the transition rate, the exponent alpha(2) is strong. The model predictions are confirmed in both embryonic stem cells and differentiated cells. Embryonic stem cells are less stiff, more fluidlike, and exhibit greater alpha(1) than their differentiated counterparts. By introducing a near-equilibrium frequency f(eq), we show that all data collapse into two power laws separated by f/f(eq), which is unity. These findings suggest that the timescale-dependent rheology in living cells originates from the nonequilibrium-to-equilibrium transition of the dynamic response of distinct, force-driven molecular processes.

Shear stresses of colloidal dispersions at the glass transition in equilibrium and in flow

We consider a model dense colloidal dispersion at the glass transition, and investigate the connection between equilibrium stress fluctuations, seen in linear shear moduli, and the shear stresses under strong flow conditions far from equilibrium, viz., flow curves for finite shear rates. To this purpose, thermosensitive core-shell particles consisting of a polystyrene core and a cross-linked poly(N-isopropylacrylamide) shell were synthesized. Data over an extended range in shear rates and frequencies are compared to theoretical results from integrations through transients and mode coupling approaches. The connection between nonlinear rheology and glass transition is clarified. While the theoretical models semiquantitatively fit the data taken in fluid states and the predominant elastic response of glass, a yet unaccounted dissipative mechanism is identified in glassy states.

Rheology of gelling and yielding soft matter systems

Yielding and gelling soft matter materials are ubiquitous throughout biological and geological systems, the most commonly encountered examples being in food and other household products. In this Highlight, we attempt to summarise the rheological properties that are characteristic of structured soft matter systems, including their universal flow behaviour and viscoelastic response as well as appropriate methods of characterisation. We also discuss how the mechanical response depends on the materials' microstructure. Soft matter of this nature is typically in a non-equilibrium state, which means that it can be modified during processing and storage (aging) to obtain new structural states and rheologies. Several universal features have recently been observed experimentally for the linear and non-linear response of structured soft matter, and such developments are assisting in the development of suitable models to characterise their behaviour.

Phase behavior and dynamics of a micelle-forming triblock copolymer system

Synperonic F-108 (generic name, "pluronic") is a micelle forming triblock copolymer of type ABA , where A is polyethylene oxide (PEO) and B is polypropylene oxide (PPO). At high temperatures, the hydrophobicity of the PPO chains increase, and the pluronic molecules, when dissolved in an aqueous medium, self-associate into spherical micelles with dense PPO cores and hydrated PEO coronas. At appropriately high concentrations, these micelles arrange in a face centered cubic lattice to show inverse crystallization, with the samples exhibiting high-temperature crystalline and low-temperature fluidlike phases. By studying the evolution of the elastic and viscous moduli as temperature is increased at a fixed rate, we construct the concentration-temperature phase diagram of Synperonic F-108. For a certain range of temperatures and at appropriate sample concentrations, we observe a predominantly elastic response. Oscillatory strain amplitude sweep measurements on these samples show pronounced peaks in the loss moduli, a typical feature of soft solids. The soft solidlike nature of these materials is further demonstrated by measuring their frequency-dependent mechanical moduli. The storage moduli are significantly larger than the loss moduli and are almost independent of the applied angular frequency. Finally, we perform strain rate frequency superposition experiments to measure the slow relaxation dynamics of this soft solid.

Aging in a colloidal glass in creep flow: time-stress superposition

We study the aging behavior of aqueous laponite suspension, a model soft glassy material, in creep. We observe that the viscoelastic behavior is time dependent and is strongly influenced by the deformation field; the effect is known to arise due to aging and rejuvenation. We show that irrespective of the strength of the deformation field (shear stress) and age, when the imposed time scale is normalized with a dominating relaxation mode of the system, universal aging behavior is obtained, demonstrating time-stress superposition, a phenomenon that may be generic in a variety of soft materials.

Nonlinear viscoelasticity of sorbitan tristearate monolayers at liquid/gas interface

The interfacial rheology of sorbitan tristearate monolayers formed at the liquid/air interface reveal a distinct nonlinear viscoelastic behavior under oscillatory shear usually observed in many 3D metastable complex fluids with large structural relaxation times. At large strain amplitudes (gamma), the storage modulus (G') decreases monotonically whereas the loss modulus (G'') exhibits a peak above a critical strain amplitude before it decreases at higher strain amplitudes. The power law decay exponents of G' and G'' are in the ratio 2:1. The peak in G'' is absent at high temperatures and low concentration of sorbitan tristearate. Strain-rate frequency sweep measurements on the monolayers do indicate a strain-rate dependence on the structural relaxation time. The present study on sorbitan tristearate monolayers clearly indicates that the nonlinear viscoelastic behavior in 2D Langmuir monolayers is more general and exhibits many of the features observed in 3D complex fluids.

An elastic, plastic, viscous model for slow shear of a liquid foam

We suggest a scalar model for deformation and flow of an amorphous material such as a foam or an emulsion. To describe elastic, plastic and viscous behaviours, we use three scalar variables: elastic deformation, plastic deformation rate and total deformation rate; and three material-specific parameters: shear modulus, yield deformation and viscosity. We obtain equations valid for different types of deformations and flows slower than the relaxation rate towards mechanical equilibrium. In particular, they are valid both in transient or steady flow regimes, even at large elastic deformation. We discuss why viscosity can be relevant even in this slow shear (often called "quasi-static") limit. Predictions of the storage and loss moduli agree with the experimental literature, and explain with simple arguments the non-linear large amplitude trends.