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The macroscopic behaviour of foams is deeply related to rearrangements occurring at the bubble scale, which dynamics depends on the mobility of the interstitial phase. In this paper, we resort to drainage experiments to quantify this mobility in particulate foams, where a particle suspension is confined between foam bubbles. Results show a strong dependence on each investigated parameter, i.e. bubble size, particle size and gas volume fraction for a given particle volume fraction. A combination of these parameters has been identified as the control parameter lambda, which compares the particle size to the size of passage through constrictions within the foam pore space. lambda highlights a sharp transition: for lambda < 1 particles are free to drain with the liquid, which involves the shear of the suspension in foam interstices, for lambda > 1 particles are trapped and the mobility of the interstitial phase is strongly reduced.
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Foams made of complex fluids such as particle suspensions have a great potential for the development of advanced aerated materials. In this paper we study the rheological behavior of liquid foams loaded with granular suspensions. We focus on the effect of small particles, i.e. particle-to-bubble size ratio smaller than 0.1, and we measure the complex modulus as a function of particle size and particle volume fraction. With respect to previous work, the results highlight a new elastic regime characterized by unequaled modulus values as well as independence of size ratio. A careful investigation of the material microstructure reveals that particles organize through the network between the gas bubbles and form a granular skeleton structure with tightly packed particles. The latter is proven to be responsible for the reported new elastic regime. Rheological probing performed by strain sweep reveals a two-step yielding of the material: the first one occurs at small strain and is clearly attributed to yielding of the granular skeleton; the second one corresponds to the yielding of the bubble assembly, as observed for particle-free foams. Moreover the elastic modulus measured at small strain is quantitatively described by models for solid foams in assuming that the granular skeleton possesses a bulk elastic modulus of order 100 kPa. Additional rheology experiments performed on the bulk granular material indicate that this surprisingly high value can be understood as soon as the magnitude of the confinement pressure exerted by foam bubbles on packed grains is considered.
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.
We study the steady flow properties of different three-dimensional aqueous foams in a wide gap Couette geometry. From local velocity measurements through Magnetic Resonance Imaging techniques and from viscosity bifurcation experiments, we find that these foams do not exhibit any observable signature of shear banding. This contrasts with two previous results (Rodts et al., Europhys. Lett., 69 (2005) 636 and Da Cruz et al., Phys. Rev. E, 66 (2002) 051305); we discuss possible reasons for this dicrepancy. Moreover, the foams we studied undergo steady flow for shear rates well below the critical shear rate recently predicted (Denkov et al., Phys. Rev. Lett., 103 (2009) 118302). Local measurements of the constitutive law finally show that these foams behave as simple Herschel-Bulkley yield stress fluids.
The drainage of particulate foams is studied under conditions where the particles are not trapped individually by constrictions of the interstitial pore space. The drainage velocity decreases continuously as the particle volume fraction $phi_{p}$ increases. The suspensions jam - and therefore drainage stops - for values $phi_{p}^{*}$ which reveal a strong effect of the particle size. In accounting for the particular geometry of the foam, we show that $phi_{p}^{*}$ accounts for unusual confinement effects when the particles pack into the foam network. We model quantitatively the overall behavior of the suspension - from flow to jamming - by taking into account explicitly the divergence of its effective viscosity at $phi_{p}^{*}$. Beyond the scope of drainage, the reported jamming transition is expected to have a deep significance for all aspects related to particulate foams, from aging to mechanical properties.
Key features of the mechanical response of amorphous particulate materials, such as foams, emulsions, and granular media, to applied stress are determined by the frequency and size of particle rearrangements that occur as the system transitions from one mechanically stable state to another. This work describes coordinated experimental and computational studies of bubble rafts, which are quasi-two dimensional systems of bubbles confined to the air-water interface. We focus on small mechanically stable clusters of four, five, six, and seven bubbles with two different sizes with diameter ratio $sigma_L/sigma_S = 1.4$. Focusing on small bubble clusters, which can be viewed as subsystems of a larger system, allows us to investigate the full ensemble of clusters that form, measure the respective frequencies with which the clusters occur, and determine the form of the bubble-bubble interactions. We emphasize several important results. First, for clusters with N > 5 bubbles, we find using discrete element simulations that short-range attractive interactions between bubbles give rise to a larger ensemble of distinct mechanically stable clusters compared to that generated by long-range attractive interactions. The additional clusters in systems with short-range attractions possess larger gaps between pairs of neighboring bubbles on the periphery of the clusters. The ensemble of bubble clusters observed in experiments is similar to the ensemble of clusters with long-range attractive interactions. We also compare the frequency with which each cluster occurs in simulations and experiments. We find that the cluster frequencies are extremely sensitive to the protocol used to generate them and only weakly correlated to the energy of the clusters.
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