Foam trapping in a 3D porous medium: in situ observations by ultra-fast X-ray microtomography.

One of the challenges in the study of foam transport in 3D porous media is to have an adequate spatial and temporal resolution to get a better understanding of the local phenomenon at the pore scale in a non-destructive way. We present an experimental study in which ultra-fast X-ray microtomography is used to investigate the foam trapping while the foam is flowing in a 3D porous medium. Preformed aqueous foam is injected into a rotating cell containing a 3D granular medium made of silica grains. The use of rotating seals allows the cell to rotate continuously at a rate of one revolution per second, compatible with the fast X-ray tomography at SOLEIL synchrotron. We visualize the foam flow and track the trapping of bubbles with an acquisition time of about one second and a spatial resolution of a few microns (pixel size of one micron). This allows us to extract the characteristics and reliable statistics about trapped bubbles inside the granular medium and to observe their local behavior. With this setup and technique we obtain access to the dynamics of foam trapping during the flow and the texture variations of the foam in the trapped zones. These local trapping events are well correlated with the macroscopical measurement of the pressure gradient over the cell.

Characterization of foam flowing in a granular medium in the presence of oil by small angle neutron scattering.

We present an experimental study of foam-flow characterization inside a 3D granular medium packed in a cell. The foam is formed by coinjecting a surfactant solution and gas inside a cell filled with silica grains. The porous medium is initially saturated with dodecane and water before the gas-surfactant coinjection. To simplify the interpretation of the measurements, a contrast matching methodology has been applied in order to obtain a two phase system regarding the scattering length density values. The combination of transmission and incoherent scattering allows us to estimate the volume fractions of each phase, whereas the coherent scattering is used to estimate the surface to volume ratio S/V related to water-oil and water-gas interfaces. Considering the evolution of S/V ratio, volume fractions and pressure difference, we infer some mechanisms of foam generation and transportation as well as oil removal.

Dynamic effective mass of granular media.

We develop the concept of frequency dependent effective mass, M[over ](omega), of jammed granular materials which occupy a rigid cavity to a filling fraction of 48%, the remaining volume being air of normal room condition or controlled humidity. The dominant features of M[over ](omega) provide signatures of the dissipation of acoustic modes, elasticity, and aging effects in the granular medium. We perform humidity controlled experiments and interpret the data in terms of a continuum model and a "trap" model of thermally activated capillary bridges at the contact points. The results suggest that attenuation of acoustic waves in granular materials can be influenced significantly by the kinetics of capillary condensation between the asperities at the contacts.

Dynamic effective mass of granular media and the attenuation of structure-borne sound.

We report a theoretical and experimental investigation into the fundamental physics of why loose granular media are effective deadeners of structure-borne sound. Here, we demonstrate that a measurement of the effective mass, M(omega), of the granular medium is a sensitive and direct way to answer the question: what is the specific mechanism whereby acoustic energy is transformed into heat? Specifically, we apply this understanding to the case of the flexural resonances of a rectangular bar with a grain-filled cavity within it. The pore space in the granular medium is air of varying humidity. The dominant features of M(omega) are a sharp resonance and a broad background, which we analyze within the context of simple models. We find that: (a) on a fundamental level, dampening of acoustic modes is dominated by adsorbed films of water at grain-grain contacts, not by global viscous dampening or by attenuation within the grains. (b) These systems may be understood, qualitatively, in terms of a height-dependent and diameter-dependent effective sound speed [approximately 100-300 (m.s-1)] and an effective viscosity [approximately 5x10(4) Poise]. (c) There is an acoustic Janssen effect in the sense that, at any frequency, and depending on the method of sample preparation, approximately one-half of the effective mass is borne by the side walls of the cavity and one-half by the bottom. (d) There is a monotonically increasing effect of humidity on the dampening of the fundamental resonance within the granular medium which translates to a nonmonotonic, but predictable, variation in dampening within the grain-loaded bar.

Granular packings: nonlinear elasticity, sound propagation, and collective relaxation dynamics.

Experiments on isotropic compression of a granular assembly of spheres show that the shear and bulk moduli vary with the confining pressure faster than the 1/3 power law predicted by Hertz-Mindlin effective medium theories of contact elasticity. Moreover, the ratio between the moduli is found to be larger than the prediction of the elastic theory by a constant value. The understanding of these discrepancies has been a long-standing question in the field of granular matter. Here we perform a test of the applicability of elasticity theory to granular materials. We perform sound propagation experiments, numerical simulations, and theoretical studies to understand the elastic response of a deforming granular assembly of soft spheres under isotropic loading. Our results for the behavior of the elastic moduli of the system agree very well with experiments. We show that the elasticity partially describes the experimental and numerical results for a system under compressional loads. However, it drastically fails for systems under shear perturbations, particularly for packings without tangential forces and friction. Our work indicates that a correct treatment should include not only the purely elastic response but also collective relaxation mechanisms related to structural disorder and nonaffine motion of grains.