Two-state model to describe the rheological behavior of vibrated granular matter

In this paper, we present a model aimed at predicting the rheological response of a 3D dry granular system to nonstationary mechanical solicitations, subjected or not to vibrations. This model is based on a phenomenological two-state approach related to the inherent bimodal behavior of chain forces in granular packing. It is set up from a kinetic equation describing the dynamics of the contact network. To allow experimental assessment, the kinetic equation is transformed into a differential constitutive equation, relating stress to strain, from which rheological properties can be derived. Its integration allows predicting and describing several rheological behaviors, in stationary and nonstationary conditions, including viscous (Newtonian) and frictional (Coulombian) regimes, as well as elastic linear (Hookean and Maxwellian) and nonlinear behaviors. Despite its simplicity, since it involves only three independent parameters, the model is in very close agreement with experiments. Moreover, within experimental errors, the values of these parameters are independent of the type of test used to determine them, evidence of the self-consistency of the model.

Rheological study of two-dimensional very anisometric colloidal particle suspensions: from shear-induced orientation to viscous dissipation

In the present study, we investigate the evolution with shear of the viscosity of aqueous suspensions of size-selected natural swelling clay minerals for volume fractions extending from isotropic liquids to weak nematic gels. Such suspensions are strongly shear-thinning, a feature that is systematically observed for suspensions of nonspherical particles and that is linked to their orientational properties. We then combined our rheological measurements with small-angle X-ray scattering experiments that, after appropriate treatment, provide the orientational field of the particles. Whatever the clay nature, particle size, and volume fraction, this orientational field was shown to depend only on a nondimensional Péclet number (Pe) defined for one isolated particle as the ratio between hydrodynamic energy and Brownian thermal energy. The measured orientational fields were then directly compared to those obtained for infinitely thin disks through a numerical computation of the Fokker-Plank equation. Even in cases where multiple hydrodynamic interactions dominate, qualitative agreement between both orientational fields is observed, especially at high Péclet number. We have then used an effective approach to assess the viscosity of these suspensions through the definition of an effective volume fraction. Using such an approach, we have been able to transform the relationship between viscosity and volume fraction (ηr = f(φ)) into a relationship that links viscosity with both flow and volume fraction (ηr = f(φ, Pe)).

Taylor-Couette instability in anisotropic clay suspensions measured using small-angle X-ray scattering

In this Letter, we propose an original and novel experimental method to characterize both the onset and morphology of Taylor-Couette instability occurring in a non-Newtonian cylindrical Couette flow. Using synchrotron-based rheological small angle x-ray scattering experiments, we jointly investigate the shear-thinning behavior of natural swelling clays suspensions and the associated anisotropy developing in such media. Combined with a linear stability analysis for power law fluids, a destabilizing effect is shown both numerically and experimentally and the vortices morphology is found to be dependent on the fluid index. Still, the strong destabilizing effect and large vortex size can not be assigned to shear-thinning only, which clearly evidences the impact of medium anisotropy on Taylor-Couette instability.

Vibration-induced liquefaction of granular suspensions

We investigate the mechanical behavior of granular suspensions subjected to coupled vibrations and shear. At high shear stress, whatever the mechanical vibration energy and bead size, the system behaves like a homogeneous suspension of hard spheres. At low shear stress, in addition to a dependence on bead size, vibration energy drastically influences the viscosity of the material that can decrease by more than 2 orders of magnitude. All experiments can be rationalized by introducing a hydrodynamical Peclet number defined as the ratio between the lubrication stress induced by vibrations and granular pressure. The behavior of vibrated wet and dry granular materials can then be unified by assimilating the hookean stress in dry media to the lubrication stress in suspensions.

Anisotropy on the collective dynamics of water confined in swelling clay minerals

Collective excitations of water confined in the interlayer space of swelling clay minerals were studied by means of inelastic neutron scattering. The effect of bidimensional confinement on the dynamics of the interlayer water was investigated by using a synthetic Na-saponite sample with a general formula of Si(7.3)Al(0.7)Mg(6)O(20)(OH)(4)Na(0.7) in a bilayer hydration state. Experimental results reveal two inelastic signals, different from those described for bulk water with a clear anisotropy on the low-energy excitation of the collective dynamics of interlayer water, this difference being stronger in the perpendicular direction. Results obtained for the parallel direction follow the same trend as bulk water, and the effect of the confinement is mainly manifested from the fact that clay interlayer water is more structured than bulk water. Data obtained in the perpendicular direction display a nondispersive behavior below a cutoff wavenumber value, Q(c), indicating a nonpropagative excitation below that value. Molecular dynamics simulations results agree qualitatively with the experimental results.

Rheo-SAXS investigation of shear-thinning behaviour of very anisometric repulsive disc-like clay suspensions

Aqueous suspensions of swelling clay minerals exhibit a rich and complex rheological behaviour. In particular, these repulsive systems display strong shear-thinning at very low volume fractions in both the isotropic and gel states. In this paper, we investigate the evolution with shear of the orientational distribution of aqueous clay suspensions by synchrotron-based rheo-SAXS experiments using a Couette device. Measurements in radial and tangential configurations were carried out for two swelling clay minerals of similar morphology and size, Wyoming montmorillonite and Idaho beidellite. The shear evolution of the small angle x-ray scattering (SAXS) patterns displays significantly different features for these two minerals. The detailed analysis of the angular dependence of the SAXS patterns in both directions provides the average Euler angles of the statistical effective particle in the shear plane. We show that for both samples, the average orientation is fully controlled by the local shear stress around the particle. We then apply an effective approach to take into account multiple hydrodynamic interactions in the system. Using such an approach, it is possible to calculate the evolution of viscosity as a function of shear rate from the knowledge of the average orientation of the particles. The viscosity thus recalculated almost perfectly matches the measured values as long as collective effects are not too important in the system.

Changes in humic acid conformation during coagulation with ferric chloride: implications for drinking water treatment

Electrophoretic mobility, pyrene fluorescence, surface tension measurements, transmission electron microscopy on resin-embedded samples, and X-ray microscopy (XRM) were combined to characterize the aggregates formed from humic colloids and hydrolyzed-Fe species under various conditions of pH and mixing. We show that, at low coagulant concentration, the anionic humic network is reorganized upon association with cationic coagulant species to yield more compact structures. In particular, spheroids about 80nm in size are evidenced by XRM at pH 6 and 8 just below the optimal coagulant concentration. Such reorganization of humic colloids does not yield surface-active species, and maintains negative functional groups on the outside of humic/hydrolyzed-Fe complex. We also observe that the humic network remains unaffected by the association with coagulant species up to the restabilization concentration. Upon increasing the coagulant concentration, restructuration becomes limited: indeed, the aggregation of humic acid with hydrolyzed-Fe species can be ascribed to a competition between humic network reconformation rate and collision rate of destabilized colloids. A decrease in stirring favors the shrinkage of humic/hydrolyzed-Fe complexes, which then yields a lower sediment volume. Elemental analyses also reveal that the iron coagulant species are poorly hydrolyzed in the destabilization range. This suggests that destabilization mechanisms such as sweep flocculation or adsorption onto a hydroxyde precipitate are not relevant to our case. A neutralization/complexation destabilization mechanism accompanied by a restructuration of flexible humic network is then proposed to occur in the range of pHs investigated.

Role of exchangeable cations on geometrical and energetic surface heterogeneity of kaolinites

Textural and energetic proprieties of kaolinite were studied by low-pressure argon adsorption at 77 K. The heterogeneity of four kaolinites (two low-defect and two high-defect samples) modified on their surface by cation exchange with Li+, Na+, or K+ was studied by DIS analysis of the derivative argon adsorption isotherms. The comparison between the derivative adsorption isotherms shows that the nature of the surface cation influences the adsorption phenomena on edge and basal faces. In the case of basal faces, two adsorption domains are observed: for the first one, argon adsorption is slightly sensitive to the nature of the surface cation; for the second one, argon adsorption energy depends on the nature of surface cation suggesting their presence on theoretically uncharged basal faces. This study also shows that the shape of elementary particles, as derived from basal and edge surface areas, changes with the nature of cation. This anomalous result is due to the decrease of edge surface area with increasing the size of the cation. This surface cation dependence can be accounted for the area occupied by the edge surface cations in the first argon monolayer.