Search

The pore space anisotropy of pharmaceutical compacts was evaluated in relation to the mechanical property anisotropy. The 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. The 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. Except 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.

International audience; Purpose - The purpose of this paper is to investigate the local feature of driven granular gases in event-driven molecular dynamic simulation, in order to achieve spatial profiles of local velocity distribution and granular temperature, and the local state with various coefficients of restitution.Design/methodology/approach - Event-driven molecular dynamic simulation is performed to study a vibro-fluidized granular gas system. Triangular-wave vibration is adopted in the simulation. The authors focus on the steady state of a driven granular gas.Findings - The simulation finds the local velocity distribution is asymmetric along vibration direction in this driven granular gas system, which agrees with the experimental results obtained in micro-gravity. A nonlinear spatial profile of the skewness of local velocity distribution in vibration direction is found in the simulation. Furthermore, it is found that the value of skewness increases with the system dissipation. It is also found that the two temperature components T+ and T- differ from each other. This shows breakdown of energy equipartition. The ratio between them drops exponentially along y direction in various coefficients of restitution. All results confirm that the bulk boundary effect relates to the dissipation properties of granular gases.Originality/value - This is the first MD simulation that investigates the bulk boundary effect to the local velocity distribution. The spatial profiles of the skewness of local velocity distribution are also investigated when changing the coefficient of restitution to study the influence of the system dissipative nature.

Simple axi-symmetric uni-axial compression tests have been realized on dry loose samples of glass beads (diameters d: d = 0.2 +/- 0.05 mm, 0.75 +/- 0.1 mm, or 3 mm) and on Hostun sand under small lateral confinement, sigma(3) < 60 kPa, using different sample sizes. The experiments with the two smallest spheres (d = 0.2 and 0.75 mm) exhibit stick-slips, which are characterized by (i) a rapid release Deltaq of the deviatoric stress q and by (ii) the strain Deltaepsilon(1) separating two events. The samples which exhibit stick-slip also present a weakening of strength q(epsilon(1)) as the rate of deformation depsilon(1)/dt is increased. No stick-slip is generated during the first part of the q - epsilon(1) curve, i.e. when q grows fast with epsilon(1). Four different parameters helped us determine the statistics of Deltaq and Deltaepsilon: the lateral pressure sigma(3)', the rate of deformation depsilon(1)/dt, the sample height H, and the diameter D. The statistics do not depend on rate history. They look like exponentials in small samples and/or in (large sample + fast depsilon(1)/dt), and they look like Poissonian or Gaussian in (Large sample + small depsilon(1)/dt). This change in statistics is attributed to a varying of triggering process starting from a single random event in small samples to multiple random events. We have interpreted this change of statistics as due to some finite size effect so that the representative elementary volume shall contain at least (200)(3) grains. Localization of deformation is visible at the end of compression but cannot be detected from stick-slip statistics nor from q vs epsilon curve.

Magnetic Resonance Imaging (MRI) was used to characterize the kinematics of mixing and size segregation of dry binary mixtures (diameters d min and d max ) in a Turbula® shaker-mixer. It was found that the filling level F of the cylindrical container should not exceed 80%; otherwise, a dead zone appears in the centre of the cell. When F =66% and the two different species ( d min ≠ d max ) are in equivalent proportion, segregation is observed when R = d max / d min is greater than 1.1. Furthermore, the slower the rotation, the larger the segregation. Moreover, it is demonstrated that this blender is very efficient for dry materials within the three following conditions: (i) the rotation speed is fast enough, (ii) one tries to mix a little amount of small particles in a sea of large ones, and (iii) the concentration of the smaller particles does not exceeds 10%. Otherwise, large particles segregate quite fast towards the container walls. A segregation index S , based on density fluctuation, has been defined. When studied as a function of the number of rotations, S allows to define a characteristic time that is much shorter (1.4 rotations) for segregation than for mixing (10.7 rotations). However, it is demonstrated that this index S is not sufficient to study the real segregation mechanism and the flow pattern. It is also shown that segregation in Turbula® results from both surface and bulk segregation mechanisms. The surface effect is related to shear percolation during flow close to the free surface and it is observed whatever the rotation speed is. On the other hand, the bulk effect disappears when sample rotation is large enough since “it averages the gravity force at zero”. At last, it is proved that a low concentration system can be understood via a self-consistent approach with a single small particle in a “sea” of large ones.

The average dynamics of two immiscible fluids of different densities in a rectangular cavity oscillating horizontally with a high frequency are investigated experimentally. The fluids are characterized by a small surface tension coefficient. The regularities of the quasi-steady spatial relief formation on the fluid interface are studied. It is shown that, in addition to the capillary and vibrational parameters, the pattern excitation threshold is determined by the dimensionless vibration frequency. In the limit of high dimensionless frequency, good agreement with the well-known theoretical results is obtained.

The dynamics of a granular medium in a cavity filled with incompressible viscous fluid under harmonic vertical vibration are studied experimentally. The sand is fluidized in a relatively thin sublayer of the granular layer near the interface between the media. The fluidization is of the threshold type and is accompanied by intense parametric oscillations of the interface. For viscous fluids, the transition of the sand from a quasi-solid to a fluidized state and the reverse transition associated with a decrease in the oscillation rate occur with hysteresis. The nondimensional governing parameters determining the sand dynamics are established. The analysis is focused on the case of low nondimensional frequencies.

Tridimensional Magnetic Resonance Imaging (MRI) was used to study the mixing and segregation processes in a Turbula mixer using binary mixtures of sugar beads. A segregation index S was defined to study the homogeneity and the kinetics of the mixing/segregation processes. When the ratio of bead diameters dmax/dmin is approximately 1, the mixing process is observed, but segregation occurs as soon as dmax/dmin is greater than 1.1. Moreover, the segregation appears as a faster process than mixing in the Turbula blender.

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...

It is found experimentally that vertical-stress field in a conic pile depends on gravity level, building process, and loading story. For instance, a conic pile with inclined strata does exhibit a minimum of stress in the center, whereas conic pile with horizontal strata does not; both piles exhibit an arching effect, which increases with gravity. This questions the assumptions of radius stress field scaling. Amplitude of the stress dip is found to be 10%, which is much smaller than what was found in previous experiments.

We used the liquid-vapor equilibrium of ${\mathrm{CO}}_{2}$ near its critical point ${(T}_{C}\ensuremath{-}T=1 \mathrm{to}\mathrm{ }150\mathrm{mK})$ in order to study the stability of an interface between a gas and a liquid having close densities ${\ensuremath{\rho}}_{L}\ensuremath{\simeq}{\ensuremath{\rho}}_{V}$ when submitted to high frequency f (3--57.5 Hz) horizontal vibrations (of amplitude a from 0.1 to 2.5 mm). Above a given velocity threshold $(2\ensuremath{\pi}\mathrm{af}{)}_{0}$ we observed a ``frozen wave,'' corresponding to an interface profile of sinelike shape which is stationary in the reference frame of the vibrated sample cell. By varying the vibration parameters, the surface tension, and the density difference between the two phases via the temperature, it was found that the wavelength and the amplitude of the stationary profile are both increasing functions of the frequency and of the amplitude of the vibration and that they are proportional to the capillary length. Our measurements are consistent with a model of inviscid and incompressible flow averaging the effect of the vibration over a period and leading to a Kelvin-Helmholtz-like instability mechanism due to the relative motion of the two fluids.

Resume La repartition des pressions verticales dans un silo rempli de materiau granulaire a ete decrite jadis (a partir de deux postulats) par Janssen. L'un de nous (P. E.) a estime le coefficient phenomenologique K J introduit par Janssen en utilisant, dans la colonne, des lois de comportement soit elastique simple, soit plastique. Nous discutons ici i) la definition precise des deplacements, ii) la friction aux parois: elle n'est completement mobilisee que si le deplacement local excede une certaine ≪ longueur d'ancrage ≫ Δ, de l'ordre du micron. A partir de ce critere, on peut definir une hauteur caracteristique H * (Δ), au-dessous de laquelle l'analyse de Janssen ne s'applique plus.

The mean dynamics of a "thick" sand bed in a closed cell filled with liquid and subjected to vertical vibration is reported at different amplitudes b and frequencies Ω/2π of vibration for different grain sizes. The generation of a quasi-steady relief made of a 2D regular system of heaps of relatively small size is found. The gradual transition from rest to relief formation and after it to liquefaction and parametrical oscillations of the sand surface with increasing vibration intensity is studied. The dimensionless vibrational parameters governing these transitions are determined.

An event driven molecular dynamics simulation of granular gases in a rectangle container in the high frequency boundary vibration limit is performed. The local velocity distribution spatial profiles under various vibration velocities are presented. Two peaks of local velocity distribution in the marginal layers are observed. To quantify the spatial transformation of the local velocity distribution, we fit the major peak by a Gaussian function(with the mean ξ and the standard deviation σ). The results show that the fitting parameters of the major peaks, such as ξ and σ, can be well scaled by the vibration velocity.

En depit de certaines approches, les deformations jouent un role important dans la determination des contraintes dans les milieux granulaires. Nous reexaminons la theorie de Janssen des silos, qui postule la proportionnalite (σ v = k siloσh ) entre contraintes verticale (σ v ) et horizontale (σh), en introduisant les deformations pour determiner k silo . Apres un examen des differentes theories possibles, nous proposons une nouvelle methode de calcul de k silo , qui tient compte de la relation fondamentale de Rowe reliant la dilatance a l'etat de contrainte. Nous comparons cette nouvelle valeur a la loi dite de Jaky (k jaky = 1 - sinφ, ou φ est l'angle de frottement solide) qui est un des meilleurs fits experimentaux.

Sand liquefaction has been generated by horizontal vibration of a sand-liquid mixture. The pattern formation of the sand-liquid interface was found at large vibration intensity. The vibro-convective nature of this relief generation is proved. We demonstrate that the only controlling parameter is W = (bΩ)2/gD (radian frequency Ω, amplitude b, cell diameter D, gravity g). An analogy is made with the vibro-convective relief generation of the interface between two immiscible liquids in a closed cell submitted to high-frequency horizontal vibration. Hence, most of the results are similar to those obtained with a liquid-liquid interface as shown in this paper; nevertheless we emphasize some peculiarities of sand behavior.

A 1d Boltzmann equation is introduced to describe the speed distribution function in granular gas system with local collision dissipation. It leads to introduce a new term, equivalent to an acceleration This term was always assumed to be 0, but it is not zero in general, even when the system is steady (i.e. when local mean flow equals 0). This shows that the flow (+ boundary) exerts a force on any extra steady particle (or plane) that drives it to the center. This result is analyzed, compared and interpreted using the Lagrangian & Eulerian view points of the mechanics; it demonstrates that classic view point of hydrodynamics does not hold anymore. The paper investigates different cases and gives experimental evidences of the features: it explains while local speed distribution f(v,r) of granular gas in a box subjected to vibration is non symmetric in the direction of vibration, while the system is stationary (mean local speed equals 0). Papers giving local experimental or simulated distributions are quote...

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.

The frictional motion of a linear array of parallel identical cylinders on a horizontal plane is studied both experimentally and analytically. An ``irregular'' stick-slip motion is observed in experiments. However, statistics on the forces before and after each slip show stable average behavior. We find that global dynamic and static coefficients of friction of the system increase with the number of particles. The organization of the rotations of particles appears as regions with characteristic lengths intermediate between the particle size and the size of the system. The mechanisms leading to these spatial patterns are studied analytically and are shown to be related to the interplay of the Coulombic friction law and the geometerical frustration of rotations. A simple argument based on the variation of the global friction force with the applied force on the array is proposed to account for the slip amplitude distributions observed in experiments.

Recently, a tremendous amount of works has been performed to investigate properties of granular gas (see [Goldhirsch 2003] for a review). This problem is fundamental because it is a frontier of statistical mechanics when dissipation becomes dominant; hence it asks the problem of what dissipation changes in the behavior of a statistical ensemble of particles in interaction: within which limits can one use the analogue of thermodynamics concepts to describe the behavior of these systems?

We have investigated the mean flow of a hourglass submitted to vertical vibrations as function of the amplitude a and frequency f=Ω/2π of the vibration (5Hz≤f≤100Hz) . We find that the time constant of the flow dynamics is longer than 0.2s, that the flow rate is weakly sensitive to vibrations as far as these ones have a small enough amplitude (aΩ22) . When aΩ2 becomes larger than g and when the frequency is located inside a resonance domain (10Hz2 and when 40Hz

International audience; The nonlinear bulk compressibility of entangled multiwalled carbon nanotubes is studied. The analogy with textile fibre assemblies is explored by means of the well established van Wyk model. In view of the small diameter of the nanotubes, the possible effect of adhesive van der Waals interactions at tube–tube contacts is analysed. It is found, however, that the contribution of adhesive contacts to the bulk stress should be negligible. Compression experiments are performed on multi-walled carbon nanotubes and show that van Wyk's model is able to describe the response, although the values of the dimensionless parameter k of van Wyk's model were lower than expected. There is indeed no indication that van der Waals interactions play any significant role.

International audience; We proposed to evaluate the contact resistance between carbon nanotubes from bulk measurement on their tangle. Compression tests with simultaneous measurement of the ohmic resistance were performed on carbon nanotube tangles. The experimental data were analyzed using a contact network model to get an estimate of the contact resistance between carbon nanotubes. It was found that in some cases the contact resistance decreased by up to one order of magnitude and reached values in the order of 100 kOhms.

The compaction of pharmaceutical tablets at high pressure (250 MPa) is a complex process that depends on the nature of the chemical compound. The purpose of this work is to characterize the porous structure of tablets obtained by uniaxial compaction, the most used process in pharmaceutical technology. First, three pharmaceutical excipients (microcrystalline cellulose, lactose and anhydrous calcium phosphate) were compacted and their compressibility properties determined. Secondly, the study of the self‐diffusion process of a molecular fluid inside the pore space was performed by using pulsed‐gradient stimulated‐echo (PGSTE) NMR method, for tablets compacted under various pressure, in the directions perpendicular and parallel to the compaction axis. The results are used to determine the tortuosity factor and the anisotropy of the porous space of such compacted materials.

Three pharmaceutical excipients and their binary mixtures were compacted to form compacts of various mean porosities. The mechanical properties (Young’s modulus, tensile strength and Brinell hardness) of the binary mixtures were not proportional to the mixture composition expressed in mass. More, for all the properties, a negative deviation was always observed from this linear relationship. Secondly, a predictive model based on a statistical approach was proposed for the Young’s modulus and the tensile strength. Finally, the X‐ray tomography technique allowed explaining the non linear relationship of the different mechanical properties results observed on these binary mixtures.

In pharmaceutical field, the percolation theory is used to describe the change of tablet’s properties with the relative density. It defines critical tablet densities from which the mechanical properties start to change. The exponent in the law is expected to be universal for a mechanical property and numerical values are proposed in the literature. In this work, the percolation model was applied to the tensile strength and the reduced modulus of elasticity of three compacted pharmaceutical excipients. This work showed that the exponent seems not universal and that the model must be used carefully.

International audience; 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.

Dynamics of quasi-2D dissipative granular gas is studied in micro-gravity condition (of the order of 10 − 4 g) in the limit of Knudsen regime. The gas, made of 4 spheres, is confined in a square cell enforced to follow linear sinusoidal vibration in ten different vibration modes. The trajectory of one of the particles is followed for 2 hours, and is reconstructed from video data by particle tracking. From statistical analysis, we find that (i) loss due to wall friction is small, (ii) trajectory looks ergodic in space, and (iii) distribution ρ(ν) of speed follows an exponential distribution, i.e., $\rho (v) \approx \exp \left[ {{-\nu } \mathord{\left/ {\vphantom {{-\nu } {\left( {\nu _{x_0 ,y_0 } } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {\nu _{x_0 ,y_0 } } \right)}} \right]$ , with $\nu _{x_0 ,y_0 } $ being a characteristic velocity along a direction parallel (y) or perpendicular (x) to vibration direction. This law deviates strongly from the Boltzmann distribution of speed in molecular gas. Comparisons of this result with previous measurements in earth environment, and what was found in 3D cell (Falcon et al., Europhys Lett 74:830, 2006) performed in environment of about ±5 ×10 − 2 g are given.

A theory which predicts the size of sandpile avalanches is given. It is based on the so-called Granta Gravel model which assumes rigid grains, plastic yielding and friction losses; it also takes into account dilatancy effects. According to our model, the avalanche size is controlled by the difference between the real pile density d and a critical density d c : macroscopic avalanches (i.e. first order process) are obtained when d>d c , since the slope of the pile becomes unstable for an angle larger than the friction angle but critical fluctuations of avalanches sizes (i.e. second order process) are expected when d=dic. This theory makes a link between the theory of Self-Organized Criticality of sand avalanches and experimental results En nous inspirant du modele de «Granta Gravel», nous proposons une approche theorique des avalanches de billes ou de sable qui postule des grains rigides, des pertes par frottement solide, des deformations plastiques et des effets de dilatance. On montre en particulier, que la taille des avalanches est controlee par la difference entre la densite d de l'empilement et une densite critique d c . Lorsque d=d c , les pertes peuvent etre dissipees localement et le processus d'avalanche peut presenter des fluctuations critiques. Lorsque d>d c , la theorie predit des avalanches macroscopiques et un phenomene du premier ordre. Notre description jette un pont entre la theorie d'etat critique auto-organise de P. Bak et al. et les resultats experimentaux

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.

Percolation theory has been applied to several mechanical properties of pharmaceutical tablets. This power law describes the change of tablet's properties with the relative density. It defines critical tablet densities from which the mechanical properties start to change. The exponent in the law is expected to be universal for a mechanical property and numerical values are proposed in the literature. In this work, the percolation model was applied to the tensile strength and the reduced modulus of elasticity (obtained from surface indentation test) of three compacted pharmaceutical excipients (a microcrystalline cellulose, a lactose and an anhydrous calcium phosphate). Two approaches were proposed. First, the exponent was kept constant and equal to the values used in the literature (2.7 for the tensile strength and 3.9 for the reduced modulus of elasticity). Secondly, the critical tablet density (i.e. the percolation threshold) and the exponent were determined from the model. In the first approach, the percolation thresholds were higher than the relative tapped density. Using the second approach, the experimentally determined exponents were not close to the values of the literature and the critical relative densities were higher than the relative tapped density or equal to zero. Then, this study showed that the exponent seems not universal and that the model must be used carefully.

Three pharmaceutical excipients (microcrystalline cellulose, lactose, anhydrous calcium phosphate) and their binary mixtures were compacted to form compacts of various mean porosities. Some mechanical properties (Young's modulus, tensile strength and Brinell hardness) were studied on these compacts. The mechanical properties of the binary mixtures were not proportional to the mixture composition expressed in mass. More, for all the properties, a negative deviation was always observed from this linear relationship. In reference to a composition percolation phenomenon, critical mass fractions were detected from the graph mechanical property vs. mass composition of a mixture. The results obtained with Brinell hardness differed from the results of the Young's modulus and the tensile strength, i.e. the most plastic material in the binary mixture controlled the mixture behaviour. Secondly, a predictive model based on a statistical approach was proposed for the Young's modulus and the tensile strength. The validity of this model was verified on experimental data, and an interaction parameter used to characterize the affinity of the two compounds was calculated. Finally, the X-ray tomography technique was applied to the compacts of cellulose/phosphate mixtures to obtain cross-sections images of the compacts. The analysis of the cross-sections images allowed explaining the no linear relationship of the different mechanical properties results observed on these binary mixtures.

International audience; We report on an experimental study of a dilute gas of steel spheres colliding inelastically and excited by a piston performing sinusoidal vibration, in low gravity. Using improved experimental apparatus, here we present some results concerning the collision statistics of particles on a wall of the container. We also propose a simple model where the non-classical statistics obtained from our data are attributed to the boundary condition playing the role of a 'velostat' instead of a thermostat. The significant differences from the kinetic theory of usual gas are related to the inelasticity of collisions.

Direct compaction is a complex process that results in a density distribution inside the tablets which is often heterogeneous. Therefore, the density variations may affect the compact properties. A quantitative analysis of this phenomenon is still lacking. Recently, X-ray microtomography has been successfully used in pharmaceutical development to study qualitatively the impact of tablet shape and break-line in the density of pharmaceutical tablets. In this study, we evaluate the density profile in microcrystalline cellulose (Vivapur 12®) compacts obtained at different mean porosity (ranging from 7.7% to 33.5%) using X-ray tomography technique. First, the validity of the Beer–Lambert law is studied. Then, density calibration is performed and density maps of cylindrical tablets are obtained and visualized using a process with colour-scale calibration plot which is explained. As expected, important heterogeneity in density is observed and quantified. The higher densities in peripheral region were particularly investigated and appraised in regard to the lower densities observed in the middle of the tablet. The results also underlined that in the case of pharmaceutical tablets, it is important to differentiate the mechanical properties representative of the total volume tablet and the mechanical properties that only characterize the tablet surface like the Brinell hardness measurements.

The compressibility of three pharmaceutical excipients (microcrystalline cellulose, lactose and anhydrous calcium phosphate) and their binary mixtures was studied. The aim of this work was to observe the impact of the mass composition of the mixture on the compressibility. The single-compound materials and their mixtures were compacted using instrumented presses. It allowed obtaining compression cycles (i.e., force–displacement curves) which were associated with energy measurements (specific compaction energy, Esp cp and specific expansion energy, Esp exp). It was observed that for the mixtures studied, the change of Esp cp with the mass composition could be fitted using a linear relationship (it was not the case with Esp exp). A linear relationship between the porosity of mixture’s compacts and the mass composition was also obtained. Heckel’s plots were then obtained for the three excipients and the mixtures. The mean yield pressure was calculated with the “in-die-method” and the “out-of-die method”. A proportional relationship was not valid for the mean yield pressures. But, a predictive approach was proposed in order to obtain indirectly the mean yield pressure of a binary mixture if the data of the single materials were known. It used the linear mixing rule observed with the porosity. The validity was verified and compared with the experimental values. This comparison showed that it was possible to predict the mean yield pressure of binary mixtures from the accessible data of the single excipients.

This paper is a short comment about the paper "stress propagation and arching in static sandpiles" by Wittmer, Cates and Claudin iii. It concern8 the validity of the radial stress field (RSF) scaling assumption used to calculate the stress distribution in a conic granular material and its agreement with different experimental data.

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 trends 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.

Can vibrations act in space as an artificial gravity? We investigate here the role of high frequency vibrations to accelerate the dynamics of phase transition of gas and liquid in space. Hydrogen is studied near its critical point (Tc =33 K). Gravity effects are compensated in a high magnetic field gradient as provided by a 10 T superconducting coil. The experiments are performed in the temperature range [0.17 – 1.1] mK from Tc, at critical and off-critical densities. The pattern shows up as interconnected gas-liquid domains or bubbles. When the domain size becomes larger than the viscous boundary layer, growth is accelerated and the domains eventually elongate in the direction perpendicular to the vibration (interconnected pattern case) or align in periodic planes in the same direction perpendicular to vibration (bubble pattern case). We explain the experimental findings by the presence of inertial velocity gradients between the vapor and liquid domains, which favor coalescence and fast domain growth.

International audience; Recent vibration experiments (amplitude A, frequency f=ω/2π) in microgravity have demonstrated that the "granular-gas" state exists only in the Knudsen regime. The excitation was "supersonic" and the probability density function of the pressure of the gas scaled as (Aω)3/2. This paper draw some analogy with i) the ideal-gas theory and (ii) the thermodynamics of a single particle in a 1d box. The anomalous scaling of pressure fluctuations (Aω)3/2is explained by the crossover from a single-collision regime during the sampling time, which imposes p ~ (Aω)2 at small speed, to a multiple-collision regime imposing p ~ (Aω)2. The effects of air and g-jitter are discussed and quantified. Grain-grain collisions are introduced and their effect on the speed distribution discussed. The second part of the paper addresses the general problem of pattern formation under vibration and in weightlessness condition, using the example of sedimentation.

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=dref/di) 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.

Here granular suspensions refer to very concentrated suspensions of particles within a Newtonian fluid. Under certain conditions given in the paper, the bulk stresses mainly result from the combination of frictional and collisional interactions at the particle scale. The corresponding flow regime is called the frictional-collisional regime. The constitutive equation adapted to this regime is not well known. We propose a constitutive model based on the balance between frictional and collisional interactions. We have applied this model to granular flow down an inclined channel. It is shown that the mass flow rate is proportional to the flow depth.

Magnetic Resonance Imaging (MRI) technique was used to study the mixing and segregation processes of granular materials in a sophisticated tumbling blender (Turbula® mixer) using binary mixtures of sugar beads of different diameters d. Its motion generates mixtures with complex patterns. Effects of some parameters (beads diameter ratio, rotation speed, mixing time) were checked on segregation and mixing processes. We report in this paper, a qualitative and quantitative analysis of these phenomena. A segregation index S was defined to study the homogeneity and the kinetics of the mixing/segregation processes. When the ratio of bead diameters dmax/dmin is approximately 1, mixing process is observed but segregation occurs as soon as dmax/dmin is greater than 1.1.

Magnetic Resonance Imaging (MRI) techniques have been used to study the mixing and segregation processes of granular materials in Turbula mixer using binary mixtures of sugar beads of different diameters d. When the ratio R of bead diameters is approximatively R = 1 mixing process is observed, but segregation occurs as soon as R > 1.1 or R < 0.9. Furthermore, segregation develops faster than mixing and is induced by surface effect. We report in this paper, a qualitative analysis of these phenomena. Effects of some parameters (beads diameter ratio, speed rotation, mixing time, concentration) have been checked on segregation and mixing processes.

First, a non linear incremental modelling is proposed to describe rheological behaviour of granular material under different simple (i.e. triaxial-, oedometric-, undrained-) stress-strain paths. Validity of isotropic-response assumption is demonstrated whatever the stress ratio as far as deformation range remains small (ε1

The clustering behavior of a mono-disperse granular gas is experimentally studied in an asymmetric two-compartment setup. Unlike the random clustering in either compartment in the case of symmetric configuration when lowering the shaking strength to below a critical value, the directed clustering is observed, which corresponds to an imperfect pitchfork bifurcation. Numerical solutions of the flux equation using a modified simple flux function show qualitative agreements with the experimental results. The potential application of this asymmetric structure is discussed.

The motion of a single bead on an inclined "line" made up of juxtaposed identical beads is analytically investigated. Initially, an entirely analytical method is presented in some detail: the problem is tractable with the usual analytical tools as long as any slip motion is ignored. Under these conditions, we show (i) the existence of a steady regime within a certain range of line slopes and (ii) that the mean velocity of the mobile bead may be calculated by induction. When compared to all the series of experiments (after the adjustment of the collisional parameter), this approach reflects well all the features displayed by experiments. The influence of slip is then numerically investigated, but, unfortunately, the unicity of solution to motion equations cannot be proved. Despite this uncertainty, energy considerations show that the main dissipation process is due to collisions. The analytical model is then compared to three alternative types of approach namely a phenomenological approach, an heuristical model, and one based on molecular-dynamics model. The comparison throws light on the role of (solid) friction and collisions in granular materials: here, it is found that the macroscopic coefficient of friction (bulk resistance) is mainly due to geometrical characteristics and collisional effects., Des approches microstructurelles ont largement été développées ces dernières années pour modéliser des écoulements granulaires ; ces méthodes consistent à déduire le comportement macroscopique à partir du comportement local de l'écoulement. Cependant, le caractère fortement non-linéaire et le grand nombre des phénomènes impliqués rendent difficile l'analyse des éventuelles divergences constatées entre les prédictions théoriques et les résultats expérimentaux. Il est donc intéressant d'étudier un système physique le plus simple possible pour pouvoir comparer les différentes approches. A cet effet, on étudie le mouvement d'une seule bille sur une rangée droite de billes accolées et identiques (entre elles). Dans un premier temps, on présente en détail une méthode qui donne une solution entièrement analytique à condition que l'on puisse négliger le glissement entre billes. Dans ce cas on montre d'une part (i) que la bille en mouvement peut atteindre un régime stationnaire, tant que l'inclinaison de la rangée est comprise dans un certain intervalle, dont les frontières ne dépendent que de la taille des grains et de la loi collisionnelle et d'autre part (ii) que la vitesse en régime permanent peut être calculée par récurrence. Ces deux point sont en accord avec les résultats expérimentaux à condition de caler le paramètre de la loi collisionnelle. Dans un second temps, on cherche à tenir compte du glissement, mais malheureusement le cadre de la mécanique des corps rigides ne permet pas d'assurer l'unicité de la solution ; pour cela, il faudrait analyser en détail les déformations et contraintes durant le contact de trois billes. Enfin, on compare les résultats de notre étude théorique avec trois autres types de modèle : un modèle phénoménologique, un modèle heuristique et un dernier modèle basé sur la dynamique moléculaire.