Local determination of the constitutive law of a dense suspension of non-colloidal particles through MRI

We investigate the flowing behavior of dense suspensions of non-colloidal particles, by coupling macroscopic rheometric experiments and local velocity and concentration measurements through MRI techniques. We find that the flow is localized at low velocities, and that the material is inhomogeneous; the local laws inferred from macroscopic rheometric observations must then be reinterpreted in the light of these local observations. We show that the short time response to a velocity step allows to characterize dense suspensions locally: they have a purely viscous behavior, without any observable influence of friction. In the jammed zone, there may be a contact network, whereas in the sheared zone there are only hydrodynamic interactions: localization consists in a change in configuration at the grain scale. From the concentration and velocity profiles, we have provided for the first time local measurements of the concentration dependence of viscosity; we find a Krieger-Dougherty law $\eta(\phi)=\eta_0(1-\phi/0.605)^{-2}$. Shear induced migration is almost instantaneous and seems inconsistent with most observations: it would imply that the diffusion coefficients strongly depend on the concentration. We finally propose a simple constitutive law for dense suspensions, based on a purely viscous behavior, that accounts for all the macroscopic and local observations.Comment: Submitted to the Journal of Rheolog

MRI evidence of nanoparticles migration in drying porous media

Due to the migration of elements they induce imbibition-drying cycles are known to play a major role in the colloid-facilitated transport in many industrials process, for instance for pollutants migration in soils or pores clogging in building materials. We study the drying of a colloidal suspension in a porous media. The critical physical phenomenon at work here is the displacement and redistribution of colloidal particles induced by evaporation of the liquid phase from the porous medium. This can be clearly seen by filling a bead packing with coffee. Indeed after full drying the sample has shaded tones with darker regions around the sample free surface and white regions almost free of particles around the bottom. The mechanisms are not yet fully understood and there is no straightforward observation and simple quantification of the spreading of the elements. To better understand the phenomenon, we perform the same experiment using with a clear scaling separation between the porous structure (glass beads diameter=200 μm) and nanoparticles in suspension in water (diameter = 20 nm). Using a new MRI technique to measure the distributions of water and particles we observe particles rising towards the free surface, as water remains homogenously distributed. The particles aggregation area is very large compare to their volume fraction in the pore volume. But we can quantify how the elements migrate towards the free surface of the sample and accumulate in the remaining liquid films. Our complete understanding of the process makes it possible to establish a simple model predicting the drying rate and the concentration distribution [7]. This opens the way to a control of salt or colloid migration and drying rate of soils and building materials

Flow of wet granular materials

The transition from frictional to lubricated flow of a dense suspension of non-Brownian particles is studied. The pertinent parameter characterizing this transition is the Leighton number $Le = \frac{\eta_s \dot{\gamma}}{\sigma}$, which represents the ratio of lubrication to frictional forces. The Leighton number $Le$ defines a critical shear rate below which no steady flow without localization exists. In the frictional regime the shear flow is localized. The lubricated regime is not simply viscous: the ratio of shear to normal stresses remains constant, as in the frictional regime; moreover the velocity profile has a single universal form in both frictional and lubricated regimes. Finally, a discrepancy between local and global measurements of viscosity is identified, which suggests inhomogeneity of the material under flow.Comment: Accepted for publication by Physical Review Letters (december 2004

Breaking of non-Newtonian character in flows through a porous medium

International audienceFrom NMR measurements we show that the velocity field of a yield stress fluid flowing through a disordered well-connected porous medium is very close to that for a Newtonian fluid. In particular, it is shown that no arrested regions exist even at very low velocities, for which the solid regime is expected to be dominant. This suggests that these results obtained for strongly nonlinear fluid can be extrapolated to any nonlinear fluid. We deduce a generalized form of Darcy's law for such materials and provide insight into the physical origin of the coefficients involved in this expression, which are shown to be moments of the second invariant of the strain rate tensor

Evaporation from a capillary tube: Experiment and modelization

Drying is known to play a major role in soils and buildings materials. Better understanding the physics may help saving cost and energy. Thus control of the drying kinetics is a key factor. In permeable porous media, capillary forces lead to constant curvature of the air/water interface. The value of the curvature and the shape of the interface depend strongly on the pore geometry. Thus small change in their shape may lead to main change of the air/water interface as the medium desaturates. As the surface is supplied with water the drying rate remains at a constant value set by the area of air/water interface close to the surface. A capillary tube of rectangular cross section maintains water layers in its 4 corners and reproduce well the drying regimes of a porous medium. Here we show that a small variation in the shape of the cross section modify drastically the invasion of air due to equilibrium of capillary forces. Moreover not only the corners but a large part of the cross section remains wet in particular at the entrance of the tube allowing a high drying rate. Pore distribution and the opacity of samples make it difficult to locate water and estimate capillary forces with accuracy. Using a simple geometry, we can observe the water distribution and measure the shape of the air/water interface with good resolution in imaging and in time. We observe that the drying rate is constant during the main period of the desaturation even if the air/water interface increases by a factor 10. Using 2D finite element method (FEM), we show that the air inside a large portion of the capillary tube is saturate with water vapor ; thus only a small part of the interface close to the entrance participate to the evaporation flux. More generally we can infer that below one pore diameter air is saturated and the air/water interface does not contribute to drying. The three basic regimes of drying kinetics in porous media assumes that the drying rate will decrease as the capillary forces are no longer able to provide water to the evaporation surface. In our tube, as desaturation goes further, the drying rate decreases even if the capillary flow still supply water to the surface. Again using FEM, we show that as the wetting surface at the entrance decreases the drying rate will decrease even if no receding front progress. In this situation, the air/water interface inside the tube contributing to the drying increase progressively but this is not enough to maintain the initial high rate. Interpreting only the water mass loss as a function of time, we may lead to wrong conclusions considering basics drying regimes. In Porous media with the same porosity and a slight variation in pore shape drying rate may differ by order of magnitude. Our understanding of the drying kinetics of a simple geometry opens way to control the pore distribution to tune the drying rate of porous media in situation where capillary effects are dominant

Wide-gap Couette flows of dense emulsions: Local concentration measurements, and comparison between macroscopic and local constitutive law measurements through magnetic resonance imaging

Flows of dense emulsions show many complex features among which long range nonlocal effects pose a problem for macroscopic characterization. In order to get around this problem, we study the flows of several dense emulsions in a wide-gap Couette geometry. We couple macroscopic rheometric experiments and local velocity measurements through MRI techniques. As concentration heterogeneities can be expected, we designed a method to measure the local droplet concentration in emulsions with a MRI device. In contrast to dense suspensions of rigid particles where very fast migration occurs under shear, we show that no migration takes place in dense emulsions even for strains as large as 100 000 in our systems. As a result of the absence of migration and of finite size effect, we are able to determine very precisely the local rheological behavior of several dense emulsions. As the materials are homogeneous, this behavior can also be inferred from purely macroscopic measurements. We thus suggest that properly analyzed purely macroscopic measurements in a wide-gap Couette geometry can be used as a tool to study the local constitutive laws of dense emulsions. All behaviors are basically consistent with Herschel-Bulkley laws of index 0.5, but discrepancies exist at the approach of the yield stress due to slow shear flows below the apparent yield stress in the case of a strongly adhesive emulsion. The existence of a constitutive law accounting for all flows contrasts with previous results obtained within a microchannel by Goyon et al. (2008): the use of a wide-gap Couette geometry is likely to prevent here from nonlocal finite size effects; it also contrasts with the observations of B\'ecu et al. (2006)

Couette Flow of Two-Dimensional Foams

We experimentally investigate flow of quasi two-dimensional disordered foams in Couette geometries, both for foams squeezed below a top plate and for freely floating foams. With the top-plate, the flows are strongly localized and rate dependent. For the freely floating foams the flow profiles become essentially rate-independent, the local and global rheology do not match, and in particular the foam flows in regions where the stress is below the global yield stress. We attribute this to nonlocal effects and show that the "fluidity" model recently introduced by Goyon {\em et al.} ({\em Nature}, {\bf 454} (2008)) captures the essential features of flow both with and without a top plate.Comment: 6 pages, 5 figures, revised versio

Water transfer and crack regimes in nano-colloidal gels

International audienceDirect observations of the surface and shape of model nano-colloidal gels associated with measurements of the spatial distribution of water content during drying show that air starts to significantly penetrate the sample when the material stops shrinking. We show that whether the material fractures or not during desiccation, as air penetrates the porous body, the water saturation decreases but remains almost homogeneous throughout the sample. This air-invasion is at the origin of another type of fracture due to capillary effects; these results provide a new insight in the liquid dynamics at the nano-scale. PACS number(s): 47.56.+r, 68.03.Fg, 81.40.N

L'IRM s'aventure hors des sentiers du monde médical

National audienceL'agroalimentaire et le génie civil constituent deux domaines d'applications très particuliers pour l'imagerie par résonance magnétique (IRM). Essentiellement axées sur les problèmes d'élaboration, de conditionnement et d'évolution de produits et de matériaux en contexte industriel, les études doivent souvent être menées sur des échantillons massifs. Elles mettent en oeuvre des imageurs de grande taille et réclament le développement de méthodologies spécifiques par rapport aux applications médicales. Des systèmes originaux d'instrumentation et de sollicitation in situ des matériaux ont pu être conçus dans ce cadre, nourris par des collaborations étroites entre différents corps de métiers. Deux laboratoires, l'Unité Technologie des équipements agroalimentaires de l'Irstea et le Laboratoire Navier de l'Université Paris-Est, livrent leur témoignage, fruit de plusieurs années d'expertise. Food-processing and civil engineering are very particular application fields for magnetic resonance imaging (MRI). Studies mainly focus on preparation, packaging, and further evolution of products and materials in industry. They are often carried out on massive samples. They involve the use of large MRI facilities, and require the development of specific methodology as compared with routine medical studies. Stimulating close collaborations between various technical specialties, they saw the raise of original experimental setups for in situ measurements and sample solicitations. Two French laboratories, the " Technologie des équipements agroalimentaires " Unity at Irstea and " Laboratoire Navier " at Paris-Est University, report on their long standing expertise