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Large deformations of soft elastic beads spinning at high angular velocity in a denser background fluid are investigated theoretically, numerically, and experimentally using millimeter-size polyacrylamide hydrogel particles introduced in a spinning drop tensiometer. We determine the equilibrium shapes of the beads from the competition between the centrifugal force and the restoring elastic and surface forces. Considering the beads as neo-Hookean up to large deformations, we show that their elastic modulus and surface energy constant can be simultaneously deduced from their equilibrium shape. Also, our results provide further support to the scenario in which surface energy and surface tension coincide for amorphous polymer gels., Comment: 8 figures, 10 pages

Changes in the mechanical properties of granular materials, induced by variations in the intrinsic compressibility of the particles, are investigated by means of numerical simulations based on the combination of the Finite Element and Contact Dynamics methods. Assemblies of athermal 2D particles are subjected to quasi-static uni-axial compactions up to packing fractions close to $1$. Inspired by the contact mechanics in the Hertz's limit, we show that the effect of the compressibility of the particles both on the global and the local stresses, can be described by considering only the packing fraction of the system. This result, demonstrated in the whole range of accessible packing fractions in case of frictionless particles, remains relevant for moderate inter-particles coefficients of friction. The small discrepancies observed with frictional particles originate from irreversible local reorganizations in the system, the later being facilitated by the compressibility of the particles.

Dicing soft solids with a sharp knife is quicker and smoother if the blade is sliding rapidly parallel to its edge in addition to the normal squeezing motion. We explain this common observation with a consistent theory suited for soft gels and departing from the standard theories of elastic fracture mechanics developed for a century. The gel is assumed to locally fail when submitted to stresses exceeding a threshold $\sigma_1$. The changes in its structure generate a liquid layer coating the blade and transmitting the stress through viscous forces. The driving parameters are the ratio $U/W$ of the normal to the tangential velocity of the blade, and the characteristic length $\eta W/\sigma_1$, with $\eta$ the viscosity of the liquid. The existence of a maximal value of $U/W$ for a steady regime explains the crucial role of the tangential velocity for slicing biological and other soft materials.

Deformations of heavy elastic cylinders with their axis in the direction of earth's gravity field are investigated. The specimens, made of polyacrylamide hydrogels, are attached from their top circular cross section to a rigid plate. An equilibrium configuration results from the interplay between gravity that tends to deform the cylinders downwards under their own weight, and elasticity that resists these distortions. The corresponding steady state exhibits fascinating shapes which are measured with lab-based micro-tomography. For any given initial radius to height ratio, the deformed cylinders are no longer axially symmetric beyond a critical value of a control parameter that depends on the volume force, the height and the elastic modulus: lateral wrinkling hierarchy develops, and holes appear at the bottom surface of the shallowest samples. We show that these patterns are the consequences of elastic instabilities.

We investigate freely expanding sheets formed by ultrasoft gel beads, and liquid and viscoelastic drops, produced by the impact of the bead or drop on a silicon wafer covered with a thin layer of liquid nitrogen that suppresses viscous dissipation thanks to an inverse Leidenfrost effect. Our experiments show a unified behaviour for the impact dynamics that holds for solids, liquids, and viscoelastic fluids and that we rationalize by properly taking into account elastocapillary effects. In this framework, the classical impact dynamics of solids and liquids as far as viscous dissipation is negligible, appears as the asymptotic limits of a universal theoretical description. A novel material-dependent characteristic velocity that includes both capillary and bulk elasticity emerges from this unified description of the physics of impact., Comment: to appear in PRL

We investigate the nucleation and propagation of cracks in self-assembled viscoelastic fluids, which are made of surfactant micelles reversibly linked by telechelic polymers. The morphology of the micelles can be continuously tuned, from spherical to rod-like to wormlike, thus producing transient double networks when the micelles are sufficiently long and entangled, and transient single networks otherwise. For a single network, we show that cracks nucleate when the sample deformation rate involved is comparable to the relaxation time scale of the network. For a double network, by contrast, significant rearrangements of the micelles occur as a crack nucleates and propagates. We show that birefringence develops at the crack tip over a finite length, $\xi$, which corresponds to the length scale over which micelles alignment occur. We find that $\xi$ is larger for slower cracks, suggesting an increase of ductility., Comment: 10 pages, 4 figures

Extra-large deformations in ultra-soft elastic materials are ubiquitous, yet systematic studies and methods to understand the mechanics of such huge strains are lacking. Here we investigate this complex problem systematically with a simple experiment: by introducing a heavy bead of radius $a$ in an incompressible ultra-soft elastic medium. We find a scaling law for the penetration depth ($\delta$) of the bead inside the softest gels as $\delta \sim a^{3/2}$. While this result is inconsistent with an ideal neo-Hookean model of elastic deformation, according to which the displacement fields must diverge, it is vindicated by an original asymptotic analytic model developed in this article. This model demonstrates that the observed relationship is precisely at the demarcating boundary of what would be required for the field variables to either diverge or converge. This correspondence between a unique mathematical prediction and the experimental observation ushers in new insights into the behavior of the deformations of strongly non-linear materials.

We explore the influence of particle softness and internal structure on both the bulk and interfacial rheological properties of colloidal suspensions. We probe bulk stresses by conventional rheology, by measuring the flow curves, shear stress vs strain rate, for suspensions of soft, deformable microgel particles and suspensions of near hard-sphere-like silica particles. A similar behavior is seen for both kind of particles in suspensions at concentrations up to the random close packing volume fraction, in agreement with recent theoretical predictions for sub-micron colloids. Transient interfacial stresses are measured by analyzing the patterns formed by the interface between the suspensions and their own solvent, due to a generalized Saffman-Taylor hydrodynamic instability. At odd with the bulk behavior, we find that microgels and hard particle suspensions exhibit vastly different interfacial stress properties. We propose that this surprising behavior results mainly from the difference in particle internal structure (polymeric network for microgels vs compact solid for the silica particles), rather than softness alone., Comment: 20 pages, 8 figures

Surface tension tends to minimize the area of interfaces between pieces of matter in different thermodynamic phases, be they in the solid or the liquid state. This can be relevant for the macroscopic shape of very soft solids, and lead to a roughening of initially sharp edges. We calculate this effect for a neo-Hookean elastic solid, with assumptions corresponding to actual experiments, namely the case where an initially sharp edge is rounded by the effect of surface tension felt when the fluid surrounding the soft solid (and so surface tension) is changed at the solid/liquid boundary. We consider two opposite limits where the analysis can be carried to the end, the one of a shallow angle and the one of a very sharp angle. Both cases yield a discontinuity of curvature in the state with surface tension although the initial state had a discontinuous slope.

We demonstrate the instability of the free surface of a soft elastic solid facing downwards. Experiments are carried out using a gel of constant density $\rho$, shear modulus $\mu$, put in a rigid cylindrical dish of depth $h$. When turned upside down, the free surface of the gel undergoes a normal outgoing acceleration $g$. It remains perfectly flat for $\rho g h/\mu<\alpha^* $ with $\alpha^*\simeq 6$, whereas a steady pattern spontaneously appears in the opposite case. This phenomenon results from the interplay between the gravitational energy and the elastic energy of deformation, which reduces the Rayleigh waves celerity and vanishes it at the threshold.

We consider a dilute system of small hard beads or hard fibers immersed in a very soft gel able to withstand large elastic deformations. Because of its low to very low shear modulus, this system is very sensitive to small forces. We calculate the local deformation induced by a constant volume force, the inclusion weight. We explain how this deformation could be put in evidence by using techniques similar to the PIV method (particle image velocimetry) used to show complex velocity fields in transparent fluids.

We study the fingering instability of the interface between two miscible fluids, a colloidal suspension and its own solvent. The temporal evolution of the interface in a Hele-Shaw cell is found to be governed by the competition between the non-linear viscosity of the suspension and an off-equilibrium, effective surface tension $\Gamma_e$. By studying suspensions in a wide range of volume fractions, $\Phi_\mathrm{C}$, we show that $\Gamma_e \sim \Phi_\mathrm{C}^2$, in agreement with Korteweg's theory for miscible fluids. The surface tension exhibits an anomalous increase with particle size, which we account for using entropy arguments., Comment: 5 pages, 5 figures + supplementary material

Fracture processes are ubiquitous in soft materials, even in complex fluids, subjected to stresses. To investigate these processes in a simple geometry, we use a model self-assembled transient gel and study the instability patterns obtained in a radial Hele-Shaw cell when a low viscosity oil pushes the more viscous transient gel. Thanks to an analysis of the morphology of the patterns, we find a discontinuous transition between the standard Saffman-Taylor fingering instability and a fracturing instability as the oil injection rate increases. Our data suggest that the flow properties of the gel ahead of the finger tip controls the transition towards fracturing. By analyzing the displacement field of the gel in the vicinity of the fingers and cracks, we show that in the fingering regime, the oil gently pushes the gel, whereas in the fracturing regime, the crack tears apart the gel, resulting in a strong drop of the gel velocity ahead of the crack tip as compared to the tip velocity. We find a unique behavior for the whole displacement field of a gel around a crack, which is drastically different from that around a finger, and reveals the solid-like behavior of the gel at short time. Our experiments and analysis provide quantitative yet simple tools to unambiguously discriminate a finger from a crack in a visco-elastic material., Comment: to appear in Soft Matter

We present a comprehensive review of the current state of fracture phenomena in transient networks, a wide class of viscoelastic fluids. We will first define what is a fracture in a complex fluid, and recall the main structural and rheological properties of transient networks. Secondly, we review experimental reports on fractures of transient networks in several configurations: shear-induced fractures, fractures in Hele-Shaw cells and fracture in extensional geometries (filament stretching rheometry and pendant drop experiments), including fracture propagation. The tentative extension of the concepts of brittleness and ductility to the fracture mechanisms in transient networks is also discussed. Finally, the different and apparently contradictory theoretical approaches developed to interpret fracture nucleation will be addressed and confronted to experimental results. Rationalized criteria to discriminate the relevance of these different models will be proposed., Comment: Review; Rheologica Acta 2013 published on line

The effect of silica nanoparticles on transient microemulsion networks made of microemulsion droplets and telechelic copolymer molecules in water is studied, as a function of droplet size and concentration, amount of copolymer, and nanoparticle volume fraction. The phase diagram is found to be affected, and in particular the percolation threshold characterized by rheology is shifted upon addition of nanoparticles, suggesting participation of the particles in the network. This leads to a peculiar reinforcement behaviour of such microemulsion nanocomposites, the silica influencing both the modulus and the relaxation time. The reinforcement is modelled based on nanoparticles connected to the network via droplet adsorption. Contrast-variation Small Angle Neutron Scattering coupled to a reverse Monte Carlo approach is used to analyse the microstructure. The rather surprising intensity curves are shown to be in good agreement with the adsorption of droplets on the nanoparticle surface.

Model microemulsion networks of oil droplets stabilized by non ionic surfactant and telechelic polymer C18-PEO(10k)-C18 have been studied for two droplet-to-polymer size ratios. The rheological properties of the networks have been measured as a function of network connectivity and can be described in terms of simple percolation laws. The network structure has been characterised by Small Angle Neutron Scattering. A Reverse Monte Carlo approach is used to demonstrate the interplay of attraction and repulsion induced by the copolymer. These model networks are then used as matrix for the incorporation of silica nanoparticles (R=10nm), individual dispersion being checked by scattering. A strong impact on the rheological properties is found for silica volume fractions up to 9%.