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Elasticity of soft materials can be greatly influenced by the presence of air bubbles. Such a capillary effect is expected for a wide range of materials, from polymer gels to concentrated emulsions and colloidal suspensions. Whereas experimental results and theory exist for describing the elasto-capillary behavior of bubbly materials (i.e. with moderate gas volume fractions), foamy systems still require a dedicated study in order to increase our understanding of elasticity in aerated materials over the full range of gas volume fractions. Here we elaborate well-controlled foams with concentrated emulsion and we measure their shear elastic modulus as a function of gas fraction, bubble size and elastic modulus of the emulsion. Such complex foams possess the elastic features of both the bubble assembly and the interstitial matrix. Moreover, their elastic modulus is shown to be governed by two parameters, namely the gas volume fraction and the elasto-capillary number, defined as the ratio of the emulsion modulus with the bubble capillary pressure. We connect our results for foams with existing data for bubbly systems and we provide a general view for the effect of gas bubbles in soft elastic media. Finally, we suggest that our results could be useful for estimating the shear modulus of aqueous foams and emulsions with multimodal size distributions.
This paper discusses the elastic behavior of a very long crosslinked polyelectrolyte chain (Debye-Huckel chain), which is weakly charged. Therefore the response of the crosslinked chain (network) on an external constant force $f$ acting on the ends o
We discuss a class of models for particulate gels in which the particle contacts are described by an effective interaction combining a two-body attraction and a three-body angular repulsion. Using molecular dynamics, we show how varying the model par
The soft-disk model previously developed and applied by Durian [D. J. Durian, Phys. Rev. Lett. 75, 4780 (1995)] is brought to bear on problems of foam rheology of longstanding and current interest, using two-dimensional systems. The questions at issu
In the theory of weakly non-linear elasticity, Hamilton et al. [J. Acoust. Soc. Am. textbf{116} (2004) 41] identified $W = mu I_2 + (A/3)I_3 + D I_2^2$ as the fourth-order expansion of the strain-energy density for incompressible isotropic solids. Su
Assemblies of purely repulsive and frictionless particles, such as emulsions or hard spheres, display very curious properties near their jamming transition, which occurs at the random close packing for mono-disperse spheres. Although such systems do