Softening of edges of solids by surface tension

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

Elasto-buoyant heavy spheres: a unique way to test non-linear elasticity

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

Bulk and interfacial stresses in suspensions of soft and hard colloids

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 figure

Buckling of a compliant hollow cylinder attached to a rotating rigid shaft

International audienceBifurcations in the equilibrium shape of a thick elastic layer attached to a circular rigid cylinder rotating about its axis are investigated analytically and numerically. The centrifugal force breaks the symmetry of the system leading to deformations invariant along the axis as the result of an instability. The instability threshold depends at linear order on the relative thickness of the compliant layer, and on a dimensionless control parameter based on the elastic modulus, the angular velocity and the outer radius. A weakly non linear analysis, carried out for layers following the Mooney-Rivlin constitutive law, points out the discon-tinuous (sub-critical) features of the bifurcation, except for relative thickness laying in a very narrow range in which the bifurcation is super-critical. Numerical simulations in the fully post-buckled regime yield the absolute instability threshold, and the order in the rotational symmetry of the developed equilibrium shape

Quand solides et liquides s'imitent

Elastic materials surface tension effects are characterized by a length scale. They must be taken into account as soon as this level is not microscopic, which is exactly the case of "soft" materials such as gels, elastomers, and several biological materials.We have highlighted a series of new physical phenomena, as the absence of edges and angles in this "soft matter", existence of a Rayleigh-Plateau instability in a elastic cylinder of sufficiently small diameter, presence of a zone reversible elastic very stretched fracture head by masked area plastic deformations for harder materials. We have alsostudied the effect of elastic energy in the unstable Saffman-Taylor, and showed that the surface tension allows to regularize the Biot instability of a compressed solid. The field of applications of this work extends mechanics biological media to the design and construction of objects microscopic controlled geometry.Les effets de la tension superficielle des matériaux élastiques sont caractérisés par une échelle de longueur. Ils doivent être pris en compte dès que cette échelle n'est pas microscopique, ce qui est précisément le cas de matériaux « mous » comme les gels, les élastomères, et plusieurs matériaux biologiques. Nous avons ainsi mis en évidence une série de phénomènes physiques nouveaux, comme l'absence d'arêtes et d'angles dans cette « matière molle », l'existence d'une instabilité de Rayleigh-Plateau dans un cylindre élastique de diamètre suffisamment petit, la présence d'une zone élastique réversible très étirée en tête de fracture, zone masquée par des déformations plastiques pour les matériaux plus durs. Nous avons aussiétudié l'effet d'une énergie élastique sur l'instabilité de Saffman-Taylor, et montré que la tension superficielle permet de régulariser l'instabilité de Biot d'un solide comprimé. Le champ d'applications de ces travaux s'étend de la mécanique des milieux biologiques à la conception et la réalisation d'objets microscopiques de géométrie contrôlée

The shape of hanging elastic cylinders

International audienceDeformations 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: self-similar wrinkling hierarchies develop, and dimples appear at the bottom surface of the shallowest samples. We show that these patterns are the consequences of elastic instabilities

Microemulsion nanocomposites: phase diagram, rheology and structure using a combined small angle neutron scattering and reverse Monte Carlo approach

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