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.

Coupled elasticity in soft solid foams.

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.

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.

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").