Pressure threshold for inhibition of dense granular film opening

Controlling the stability of a granular film is essential in a wide range of industrial applications, from aerated building materials to recovering ore by flotation and treating wastewater. We therefore carry out experiments of granular film opening where particles of hundred of micrometers above random close packing zip the two interfaces of a soap film which liquid pressure is controlled. We create a hole at the center of this dense granular film and, surprisingly, we observe that the opening is not always inhibited. Different behaviours are identified: total bursting of the granular film, intermittent opening and jammed state for which the hole does not evolve. The liquid pressure drives the transition from one opening behaviour to another. Lower is the liquid pressure, more jammed is the system. The critical pressure transition scales as the surface tension over the particle size until the finite size of the granular film is only few tens of the particle size. Ultimately we evidence that spontaneous hole in thin film between particle do not lead to the granular film failure.

Daisy-shaped liquid bridges in foam-filled granular packings

HYPOTHESIS

Many applications of liquid foams use them to fill the porosity of various granular media. How is the liquid distributed in such foam-filled systems, in which the geometry of the bubble assembly can be strongly constrained by pore confinement?

EXPERIMENTS

We study how the liquid is distributed in a grain packing filled with liquid foam, as a function of both liquid content and bubble-to-grain size ratio. Moreover, Surface Evolver simulations are carried out at the scale of a single bubble confined into a tetrahedral pore.

FINDINGS

We reveal that foam-filled granular assemblies exhibit a robust pendular-like regime, which is reminiscent of the pendular regime in unsaturated media. The main difference is that here the liquid bridges are daisy-shaped, i.e. with a liquid core bounded by bubbly petals. A simple theoretical model is proposed to describe the foam liquid bridges between contacting grains. In the case of large bubbles, the model is compared with the Surface Evolver simulation. The model is also applied to the case of wall liquid bridge, which is compared with the experimental observation. Beyond their geometrical characteristics, the presence of these liquid bridges, which can represent almost 25% of the liquid contained in the porosity, makes it possible to imagine a new approach (binder foam-based) to bind granular assemblies and turn them to solid materials.

Well-controlled foam-based solid coatings

Foam-based solid coatings appear to be a simple solution for giving new properties to solid surfaces. An efficient method is presented for producing open-cell foam coatings having a tunable pore radius distribution (i.e. monodisperse within the range 100-1000 μm, bidisperse or fully polydisperse), tunable thickness, and tunable bulk and surface porosities. This is achieved by mixing a precursor aqueous foam and particle suspension (here a micrometer-sized polyurethane dispersion), and by spreading with a nozzle the resulting particle-loaded foam on the solid surface to be coated. It is shown that the bubble size distribution of the precursor foam can be preserved in the final solid coating. This is highlighted by using a monodisperse aqueous foam, for which coatings showed a polycrystalline structure, as well as bidisperse or fully polydisperse foams. As a major advantage of our method, the bubble size and solid volume fraction are shown to be independent parameters, allowing the size of the microstructural elements to be tuned easily, and so the expected functional properties of the coating. Results obtained with the studied polyurethane dispersion are expected to be reproduced with other dispersions.

Permeability of solid foam: Effect of pore connections

In this paper, we study how the permeability of solid foam is modified by the presence of membranes that close partially or totally the cell windows connecting neighboring pores. The finite element method (FEM) simulations computing the Stokes problem are performed at both pore and macroscopic scales. For foam with fully interconnected pores, we obtain a robust power-law relationship between permeability and aperture size. This result is due to the local pressure drop mechanism through the aperture as described by Sampson for fluid flow through a circular orifice in a thin plate. Based on this local law, pore-network simulation of simple flow is used and is shown to reproduce FEM results. Then this low computational cost method is used to study in detail the effect of an open window fraction on the percolation properties of the foam pore space. The results clarify the effect of membranes on foam permeability. Finally, Kirkpatrick's model is adapted to provide analytical expressions that allow for our simulation results to be successfully reproduced.

Elasticity of particle-loaded liquid foams

Mixing solid particles with liquid foam is a common process used in industry for manufacturing aerated materials. Desire for improvement of involved industrial processes and optimization of resulting foamed materials stimulates fundamental research on those complex mixtures of grains, bubbles and liquid. In this paper, we generate well-controlled particle-loaded liquid foams and we determine their elastic behavior as a function of particle size (6-3000 μm) and particle volume fraction (0-6%). We focus on both the elastic modulus exhibited by the material at small strain and the strain marking the end of the linear elastic regime. Results reveal the existence of a critical particle-to-bubble size ratio triggering a sharp transition between two well-defined regimes. For small size ratios, the behavior is governed by the mechanical properties of the solid grains, which have been proved to pack in the shape of a foam-embedded granular skeleton. In contrast, bubbles elasticity prevails in the second regime, where isolated large particles contribute only weakly to the rheological behavior of the foamed material. The modeling of elasticity for each regime allows for this transition to be normalized and compared with previously reported particle size-induced effects for foam drainage (Haffner et al. J. Colloid Interface Sci., 2015, 458, 200-208) and solid foam mechanics (Khidas et al., Compos. Sci. Technol., 2015, 119, 62-67). This highlights that rheology and the other properties of particle-loaded foams are subjected to the same size-induced morphological transition.

Optimal strengthening of particle-loaded liquid foams

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.

Foam clogging

To what extent are aqueous foams prone to clogging? Foam permeability is measured as a function of particulate loading (trapped hydrophilic particles) under conditions where the particle to bubble size ratio is allowed to increase when the number of particles per bubble is fixed. In addition to experiments performed on the foam scale, we investigated experimentally and numerically the hydrodynamic resistance of a single foam node loaded with one particle. It is shown that, with respect to solid porous media, aqueous foams clog more efficiently due to two reasons: (i) the deformation of interfaces allows for larger particles to be incorporated within the interstitial network and (ii) the interfacial mobility contributes to lowering of the reduced permeability.

Capture-induced transition in foamy suspensions

We investigate the drainage behaviour of foamy granular suspensions. Results reveal large fluctuations in the drainage velocity as bubble size, particle size and gas volume fraction are varied for a given particle volume fraction. Particle capture is proved to control the overall drainage behaviour through the parameter λ, which compares the particle size to the size of passage through constrictions within the foam pore space. λ highlights a sharp transition: for λ < 1 particles are free to drain with the liquid, which involves the shear of the suspension in foam interstices, for λ > 1 particles are trapped and the resulting drainage velocity is strongly reduced. A phenomenological model is proposed to describe this behaviour.

Flow and jamming of granular suspensions in foams

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 φ(p) increases. The suspensions jam--and therefore drainage stops--for values φ*(p) which reveal a strong effect of the particle size. In accounting for the particular geometry of the foam, we show that φ*(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 φ*(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.

Probing the shear-band formation in granular media with sound waves

We investigate the mechanical responses of dense granular materials, using a direct shear box combined with simultaneous acoustic measurements. Measured shear wave speeds evidence the structural change of the material under shear, from the jammed state to the flowing state. There is a clear acoustic signature when the shear band is formed. Subjected to cyclic shear, both shear stress and wave speed show the strong hysteretic dependence on the shear strain, likely associated with the geometry change in the packing structure. Moreover, the correlation function of configuration-specific multiply scattered waves reveals an intermittent behavior before the failure of material.

Anisotropic nonlinear elasticity in a spherical-bead pack: influence of the fabric anisotropy

Stress-strain measurements and ultrasound propagation experiments in glass bead packs have been simultaneously conducted to characterize the stress-induced anisotropy under uniaxial loading. These measurements realized, respectively, with finite and incremental deformations of the granular assembly, are analyzed within the framework of the effective-medium theory based on the Hertz-Mindlin contact theory. Our work shows that both compressional and shear wave velocities and consequently the incremental elastic moduli agree fairly well with an effective-medium model developed by Johnson [J. Appl. Mech. 65, 380 (1998)] for the oedometric test, but the anisotropic stress ratio resulting from finite deformation does not at all. As indicated by numerical simulations, the discrepancy may arise from the fact that the model does not properly allow the grains to relax from the affine motion approximation. Here we find that the interaction nature at the grain contact could also play a crucial role for the relevant prediction by the model; indeed, such discrepancy can be significantly reduced if the frictional resistance between grains is removed. Another main experimental finding is the influence of the inherent anisotropy of granular packs, realized by different protocols of the sample preparation. Our results reveal that compressional waves are more sensitive to the stress-induced anisotropy, whereas the shear waves are more sensitive to the fabric anisotropy.

Origin of the slow linear viscoelastic response of aqueous foams

We have studied the slow linear viscoelastic response of wet aqueous foams by macroscopic creep compliance measurements, combined to a diffusing-wave spectroscopy investigation of the local dynamics. The data strongly suggest that this rheological response arises from two distinct relaxation mechanisms: The first is due to the coarsening induced bubble rearrangements and governs the steady-state creep; the second results from the interplay between surface tension and surface viscosity of the gas-liquid interfaces and gives rise to a transient relaxation.

Friction and rotation modes in a packing of cylinders under shear stress

We study the influence of collective processes such as rotations on the effective friction of sheared granular media made of two-dimensional array of cylinders. An original experimental device allows us to measure simultaneously grain rotations and the global friction force between the packing and the basal plane. It is shown that the correlation between these two quantities can be analyzed at two different time scales: 1. Averaging over the duration of a whole experiment, the mean sliding behavior of the first row on the base of the packing describes satisfactorily the global friction force. 2. At short-time, description of this correlation requires the knowledge of the propagation of rotation perpendicularly to the shear direction.

Collective response of an array of rotating particles to fluctuating confining forces

We study the influence of fluctuations of confining forces on the rotation patterns in a dense array of cylinders. Our theoretical studies are motivated by new results from detailed time-resolved experimental measurements. In order to calculate the system's evolution in time at each moment, a molecular-dynamics code adapted to the system is developed. The numerical procedure is tested by a comparison with rigorous predictions derived analytically. The chain's reaction on oscillating confining forces is analyzed numerically for different typical cases. Our theoretical results reproduce the striking features of the experimental data. A quantitative analysis of the experimental data is performed by a computation of their power spectrum and of spatial and temporal correlation functions. From our comparison of the theoretical and experimental results we conclude that the experimental rotation patterns result of random superpositions of different steady-state patterns ("collective random walk").