Pierre Evesque

A theoretical framework for granular suspensions in a steady simple shear flow

We focus our attention on granular suspensions made up of noncolloidal spherical particles within a Newtonian fluid. The main objective of this paper is to provide a general framework for the formulation of the bulk stress tensor. The bulk stress within granular suspensions is mainly generated at the particle level by strong interactions between particles, such as friction, collision, and lubricated contact. The existence of a few local mechanisms is a major cause of behavior complexity at the macroscopic scale. A direct consequence is that the constitutive equation is only known for some flow conditions and given types of mixture. Here we have used a microstructural approach, which consists of considering the mixture as an effective continuum at the macroscopic level and inferring the bulk stress tensor from averaging of local interactions and local stresses. The bulk stress tensor may be split into elementary contributions pertaining to particle interactions. A complementary equation standing for the bu...

Magnetic resonance imaging investigation of the mixing-segregation process in a pharmaceutical blender

Magnetic Resonance Imaging (MRI) was used to study the mixing process of binary mixtures of free flowing sugar beads in a Turbula mixer. In order to make particles MRI-sensitive, some reference beads were doped with an organic oil. Doped and undoped particles were mixed and MRI was used to non-destructively image the particle bed for a given number of mixer rotations (NR), bead diameter ratio (R=d(ref)/d(i)) and rotation speed (V). All the results were quantified on the basis of image analysis to characterise the degree of mixing. Studies showed that for binary mixtures of identical particle size, the mixing was complete after 30 rotations, whereas for beads of different size (R=2.8) a segregated steady state was obtained after nearly 10 rotations. Experiments revealed that segregation appeared as soon as R=0.9. Moreover, the lower the rotation speed, the more segregated the final state was. It appeared that for a filling level greater than 80%, dead regions appeared in the centre of the powder bed. In conclusion, when the particles are non-cohesive, the Turbula blender perfectly mixes identical beads but segregation occurs for beads of different size after just a few rotations.

Examination of the possibility of a fluid‐mechanics treatment of dense granular flows

SUMMARY The aim of this paper is to examine the possibility of a simple fluid-mechanics treatment of rapid dense granular flows. In other words, we examine whether the constitutive equation can be sought in a simple relationship between the strain-rate and stress tensors. With this aim, we first show that an inclined channel is an appropriate device for providing rheological data. Here we provide a complete rheometrical treatment, which allows to infer the shear-stress/shear-rate curve (for simple shear flows) from the flow-depth/mass-flow-rate curve. Experiments performed with glass beads and sand grains revealed an apparent decrease in the shear stress with increasing shear rate. We then demonstrate that this result, although paradoxical, is not unphysical. Moreover, more detailed theoretical analysis shows that the main issues raised by our experiments may be overcome by ‘microstructural’ models. We finally give two examples of models including a single microstructural parameter, which are able to qualitatively account for the main features of our experiments. A large range of flows encountered in industry and nature involve highly concentrated mixtures of discrete solid grains and an interstitial fluid (generally water or air). By ‘dense granular flow’, we refer to any flow involving rapid and very large deformations of bulk solid mixtures, made up of noncolloidal particles and whose solid fraction (volume of solids per unit bulk volume) approaches the maximum packing concentration. Examples in the area of geophysics include rockfalls,’ some rapid landslides and (stony) debris flows;’ in addition, flowing avalanches are sometimes considered as granular In industry, we might quote some technological problems related to processing, transport, and handling of various materials (grains, cereals, sand, coal, pharmaceutical pills, ceramics, etc.).5 An understanding of the dynamics of dense granular flows is of great interest in view of their practical importance, but unfortunately it is far from being complete despite numerous investigations. For instance, as far as we know, no theoretical model is able to correctly predict the macroscopic characteristics (such as depth/mass-flow-rate relations) of dense granular flows in various flow situations. Here we examine the possibility of a fluid-mechanics treatment for dense granular flows. In other words, we shall attempt to determine whether a granular flow can be described using a simple constitutive equation, namely a relationship between the stress and strain-rate tensors. First, we

Breakdown of Energy Equipartition in Vibro-Fluidized Granular Media in Micro-Gravity

We present a micro-gravity experimental study of intermediate number density vibro-fluidized inelastic spheres in a rectangular container. Local velocity distributions are investigated, and are found to deviate measurably from a symmetric distribution for the velocity component of the vibrating direction when dividing particles along the vibration direction into several bins. This feature does not exist in the molecular gas. We further study the hydrodynamic profiles of pressures p and temperatures T in positive and negative components, such as p+y and p−y and T+y and T−y, in accordance with the sign of velocity components of the vibrating direction. Along vibration direction, granular media are found to be not only inhomogeneous and anisotropic, but also different greatly in positive and negative components. Energy equipartition breaks down in this case.

Application of PGSTE-NMR technique to characterize the porous structure of pharmaceutical tablets

Direct compaction of pharmaceutical tablets is a complex process that results in a heterogeneous density distribution inside the compact. In the present study, we have used a non-invasive and non-destructive technique: the pulsed-gradient stimulated-echo (PGSTE) NMR method to access to topological information (connectivity, tortuosity) about the porous structure of the tablets obtained with three different pharmaceutical excipients: the microcrystalline cellulose, the lactose and the anhydrous calcium phosphate. These materials were chosen since their mechanical properties under pressure are highly differentiated. To probe the pore space with the PGSTE-NMR technique, the tablets were initially impregnated with silicone oil that is NMR sensitive (1H NMR). The time-dependent apparent self-diffusion coefficient was measured over a suitable range of diffusion time in the directions perpendicular and parallel to the compression axis, from which the tortuosity factor and the anisotropy of the porous structure can be studied. These results show that the porous structure varies with pressure and depends on the excipient behaviour under pressure. Then, this work demonstrates that PGSTE-NMR could be an alternative and a very interesting technique to obtain useful information on the structural properties of such compacted materials.

Phase transition under forced vibrations in critical CO2

Phase separation is investigated in CO2 under linear harmonic vibrations. The study is performed under weightlessness in a sounding rocket. The fluid is at critical density near its critical point to get benefit from universal behavior. Without vibration, phase separation is characterized by an interconnected pattern of vapor and liquid domains and a near linear growth law. Under vibration, three time regions have been identified. i) When the liquid-vapor domains are smaller than a few viscous boundary layer thickness, growth is unaffected by vibration. ii) Then the Bernoulli pressure across the interfaces makes the domains grow exponentially perpendicularly to the vibration direction while growth parallel to the vibration direction is unaffected. iii) When the domains reach the sample size, the pattern looks as periodic stripes perpendicular to the vibration direction and keep on growing parallel to the vibration direction. A theoretical approach of these phenomena is proposed.

Anisotropic Porous Structure of Pharmaceutical Compacts Evaluated by PGSTE-NMR in Relation to Mechanical Property Anisotropy

ABSTRACTPurposeThe pore space anisotropy of pharmaceutical compacts was evaluated in relation to the mechanical property anisotropy.MethodsThe topology and the pore space anisotropy were characterized by PGSTE-NMR measurements. Parallelepipedical compacts of anhydrous calcium phosphate (aCP) and microcrystalline cellulose (MCC) were tested on top, bottom and side faces. A microindentation and three-point single beam tests were used to measure Brinell hardness, tensile strength and Young’s modulus. All the data were submitted to a statistical analysis to test for significance.ResultsThe porous structure of MCC compacts was anisotropic, contrary to those of aCP. The analysis of the pore space by PGSTE-NMR method showed that its structural anisotropy was controlled by the behaviour under compaction of the excipients. At the same time, the Young’s modulus and the tensile strength were the same whatever the direction of testing. For the aCP compacts, all the faces had the same Brinell hardness. With MCC compacts, only the bottom face showed a lower Brinell hardness.ConclusionsExcept for Brinell hardness measured on MCC compacts, the tested samples were characterized by anisotropic mechanical properties when its porous structures were sometimes anisotropic. Then, there is not a straight link between porosity anisotropy and mechanical properties.

Effect of aging on the reinforcement efficiency of carbon nanotubes in epoxy matrix

The reinforcement efficiency of carbon nanotubes (CNTs) in epoxy matrix was investigated in the elastic regime. Cyclic uniaxial tensile tests were performed at constant strain amplitude and increasing maximum strain. Post-curing of the epoxy and its composite at a temperature close to the glass transition temperature allowed us to explore the effect of aging on the reinforcement efficiency of CNT. It is found that the reinforcement efficiency is compatible with a mean field mixture rule of stress reinforcement by random inclusions. It also diminishes when the maximum strain increased and this effect is amplified by aging. The decrease of elastic modulus with increasing cyclic maximum strain is quite similar to the one observed for filled elastomers with increasing strain amplitude, a phenomenon often referred as the Payne effect.

Granular gas in weightlessness: The limit case of very low densities of non interacting spheres

Experiments on non interacting balls in a vibrated box are reported. In a first experiment with an electromagnetic vibrator on earth or in board of Airbus A300 of CNES, the 1-ball dynamics exhibit little transverse motion and an intermittent quasi periodic motion along the direction parallel to the vibration. This behaviour proves a significant reduction of the phase space dimension of this billiard-like system from 11- d to 3- d or 1- d. It is caused by dissipation, which generates non ergodic dynamics. This experiment exemplifies the coupling between translation and rotation degrees of freedom during the collisions with the walls, due to solid friction at contacts. This eliminates ball rotation and freezes transverse velocity fluctuations. This trend is confirmed by 3d simulations with JJ Moreau discrete element code. A two-ball experiment performed under zero-g conditions in the Maxus 5 flight confirms the trend; the quasi-periodicity is found much greater, which is probably due to an improvement of experimental conditions. The two balls are not in perfect synchronisation showing the effect of small random noise; but the particles has never collided. This is then the normal dynamics of a gas of non-interacting dilute spherical grains in a vibrated container.

Asymmetric velocity distribution in boundary-heating granular gas and a hydrodynamic description

A microgravity experimental study of vibrofluidized granular gas with intermediate number density is performed. Local velocity distributions are investigated, and are found to deviate measurably from a symmetric distribution for the velocity component in the direction of vibration due to the boundary heating mechanism. One generalized granular hydrodynamic theory (GSH) is used for a phenomenological model to describe this extended boundary effect by introducing additional variables to the two-peak distribution profile, which provides an account for the understanding of the bulk boundary effect.