Effects of the blade shape on the slicing of soft gels.

Slicing soft gels with a knife is eased by rapidly sliding the blade along its edge. This common observation has been recently explained thanks to a model in which the split of the gel results from a failure occurring at a critical stress and consisting of the transformation of the solid gel into a liquid phase (Phys Rev Lett 125:038002, 2020). Here, the cutting process is shown to be independent of the yield criterion of the gel, and the model investigated further by considering the thickness and the shape of the blade. Features of the slicing process converge toward the zero-thickness limit as the sharpness of the blade increases. The model does predict that a thinner edge facilitates the cleavage. In addition, a symmetric cross section of the blade is found to be more efficient than a bevel.

Spinning elastic beads: a route for simultaneous measurements of the shear modulus and the interfacial energy of soft materials.

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 interfacial energy constant can be simultaneously deduced from their equilibrium shape. Also, our results provide further support to the scenario in which interfacial energy and interfacial tension coincide for amorphous polymer gels.

Cutting and Slicing Weak Solids.

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 relied on for a century. The gel is assumed to fail locally when submitted to stresses exceeding a threshold σ_{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 ηW/σ_{1}, with η the viscosity of the liquid layer. 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.

Compaction of elastic granular materials: inter-particles friction effects and plastic events.

The uni-axial compaction of granular materials made of elastic neo-Hookean particles is investigated in the quasi-static regime. Two-dimensional disk assemblies are simulated using the Finite Element model coupled with Contact Dynamics method for dealing both with finite deformations of the particles and contact interactions. Due to large deformations of the particles, the packing fraction of the system increases continuously during the compaction process, reaching values close to 1. The influence of the coefficient of friction between the particles on the macroscopic and micro-structural behaviors of the system is thoroughly discussed.

Numerical simulations of the compaction of assemblies of rubberlike particles: A quantitative comparison with experiments.

Using the contact dymanics method together with the finite element method, we simulate the uniaxial compression of assemblies of elastic cylinders. The numerical model accounts for finite deformations of the particles through the neo-Hookean constitutive equation and solid friction between the particles. A quantitative comparison with experiments carried out with centimetric rubberlike cylinders, with local deformations of the particles determined by image correlation, is proposed. We show that the simulations accurately capture the details of both the microstructure and the macroscopic behavior of the real granular system, demonstrating the relevancy of the numerical approach.

The shape of hanging elastic cylinders.

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: 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.

Rearrangement Zone around a Crack Tip in a Double Self-Assembled Transient Network.

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 rodlike 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, ξ, which corresponds to the length scale over which micelle alignment occurs. We find that ξ is larger for slower cracks, suggesting an increase of ductility.

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.

Gravity driven instability in elastic solid layers.

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 ρ, shear modulus µ, 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 ρgh/µ<α* with α*≃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.

Off-equilibrium surface tension in colloidal suspensions.

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 nonlinear viscosity of the suspension and an off-equilibrium, effective surface tension Γe. By studying suspensions in a wide range of volume fractions, ΦC, we show that Γe∼ΦC2, 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.

Solid drops: large capillary deformations of immersed elastic rods.

Under the effect of surface tension, a blob of liquid adopts a spherical shape when immersed in another fluid. We demonstrate experimentally that soft, centimeter-size elastic solids can exhibit a similar behavior: when immersed into a liquid, a gel having a low elastic modulus undergoes large, reversible deformations. We analyze three fundamental types of deformations of a slender elastic solid driven by surface stress, depending on the shape of its cross section: a circular elastic cylinder shortens in the longitudinal direction and stretches transversally; the sharp edges of a square based prism get rounded off as its cross sections tend to become circular; and a slender, triangular based prism bends. These experimental results are compared to analysis and nonlinear simulations of neo-Hookean solids deformed by surface tension and are found to be in good agreement with each other.

Shape of an elastic loop strongly bent by surface tension: experiments and comparison with theory.

When a very flexible wire is dipped into a soapy solution, it collapses onto itself. We consider the regions of high curvature where the wire folds back onto itself, enclosing a capillary film. The shapes of these end loops are measured in experiments using soap films and compared to a known similarity solution. The sizes of these structures provide a simple and reliable way to measure surface tension.

Capillarity driven instability of a soft solid.

We report the observation of a Plateau instability in a thin filament of solid gel with a very small elastic modulus. A longitudinal undulation of the surface of the cylinder reduces its area thereby triggering capillary instability, but is counterbalanced by elastic forces following the deformation. This competition leads to a nontrivial instability threshold for a solid cylinder. The ratio of surface tension to elastic modulus defines a characteristic length scale. The onset of linear instability is when the radius of the cylinder is one-sixth of this length scale, in agreement with theory presented here.

Specific ion adsorption and short-range interactions at the air aqueous solution interface.

We have investigated the surface composition of alkali-halide aqueous solutions using grazing incidence x-ray fluorescence. Using mixtures of salts as a means to enhance the short-range effects, small differences in concentration over a few angstrom could be resolved, with, for example I- or Br- > Cl-. In order to explain our data, we need to include an effective potential accounting for the short-range (A) solvent mediated couplings, responsible for specific effects together with dispersion forces. This attractive potential (few k{B}T for halides) leads to concentration profiles which are in good agreement with recent numerical simulations.