Stéphane Rodts

Local determination of the constitutive law of a dense suspension of noncolloidal particles through magnetic resonance imaging

We investigate the flowing behavior of dense suspensions of noncolloidal particles, by coupling macroscopic rheometric experiments and local velocity and concentration measurements through magnetic resonance imaging (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 light of these local observations. We show that the short time response to a velocity step allows dense suspensions to be characterized locally: they have a purely viscous behavior, without any observable influence of granular friction. In the “jammed” zone, there may be a contact network, whereas in the sheared zone there are only hydrodynamic interactions: localization consists of a change in configuration at the grain scale. From the concentration and velocity profiles, we provide for the first time local measurements of the concentration dependence of viscosity, and find a Krieger-Dough...

Flow of Wet Granular Materials

The transition from frictional to lubricated flows of a dense suspension of non-Brownian particles is studied. The pertinent parameter characterizing this transition is the Leighton number Le=eta(s)gamma / sigma, the ratio of lubrication to frictional forces. 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 and the velocity profile has a 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.

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, with droplet size ranging from 0.3to40microm , in a wide-gap Couette geometry. We couple macroscopic rheometric experiments and local velocity measurements through magnetic resonance imaging (MRI) techniques. As concentration heterogeneities are expected in the wide-gap Couette flows of multiphase materials, we also 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 in wide-gap Couette flows, 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. The existence of a constitutive law accounting for all flows contrasts with previous results obtained within a microchannel by Goyon [Nature (London) 454, 84 (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 Bécu [Phys. Rev. Lett. 96, 138302 (2006)]. We also evidence the existence of discrepancies between a perfect Herschel-Bulkley behavior and the observed local behavior 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.

Proton NMR relaxation as a probe for setting cement pastes

We report a 20-MHz proton nuclear magnetic resonance T1 relaxation study of cement paste hydration in the early stages of setting, using different centimeter-sized samples of cements of various origins and different water-to-cement ratios. In every sample, during the first few minutes of hydration, it is found that inverse Laplace processing of inversion-recovery measurements systematically exhibits at least two T1 values: a long one, around 100 ms, whose value correlates well with water content and which may be attributed to bulk water surrounding cement grains; and a short one, around 2 ms, which is quite insensitive to water-to-cement ratio and which may be attributed to water embedded in floculated cement grains before setting occurs. The time evolution of the longest T1 value for several hours is also shown to exhibit a characteristic five-stage behavior that is well correlated with known stages of the hydration process: initial reaction, induction period, acceleration period, deceleration period and slow hydration reaction. These results are compared with calorimetric measurements and electrical conductivity literature.

A Grand Canonical Monte-Carlo Simulation Study of Xenon Adsorption in a Vycor-like Porous Matrix

We have performed atomistic Grand Canonical Monte-Carlo (GCMC) simulations of adsorption of xenon in a Vycor-like matrix at 195 K. The disordered mesoporous network is obtained by applying a numerical 3D off-lattice reconstruction procedure to a simulation box originally containing silicon and oxygen atoms of a non-porous silica solid. In order to reduce the computational cost, we have applied a homothetic decrease of the simulation box dimensions which preserves the morphology and the topology of the pore network (the average pore dimension is then around 30 Å). The surface chemistry is obtained in a realistic fashion by saturating all dangling bonds with hydrogen atoms. Small angle scattering spectra calculated on different numerical samples have evidenced a departure from Porods law due to surface roughness. The simulated isotherms calculated on such disordered connected porous networks, show the capillary condensation phenomenon. The shape of the adsorption curves differs from that obtained for simple pore geometries. The analysis of the adsorbed quantity distribution indicates partial molecular-film formation depending on the local surface curvature and roughness.

New technique for reconstructing instantaneous velocity profiles from viscometric tests: Application to pasty materials

We present a new technique for reconstructing the instantaneous velocity profiles during creep, dynamic, or ramp tests under controlled stress in wide-gap Couette flows, from a series of similar tests under smaller stress amplitudes. This approach is based on a rigourous theory, and since it requires that the fluid does not flow close to the outer cylinder, it is particularly suitable for yield stress fluids. The interest of this reconstruction technique is that it is simpler than direct techniques (nuclear magnetic resonance, light scattering, particle imaging velocimetry, etc.) and has almost no limitations in time and space resolution. Thus, one can obtain the velocity profiles under steady-state and transient flows. We show that for a commercial hair gel the velocity profile obtained with this technique is in excellent agreement with that found from magnetic resonance imaging rheometry within the range of measurement (four decades of velocity). From other tests with a mustard and a kaolin–water suspen...

Boundary layer (shear-band) in frustrated viscoplastic flows

We show that frustrated creep flows of yield stress fluids give rise to a boundary layer, which takes the form of a liquid region of uniform significant thickness separating two solid regions. In this boundary layer the shear rate is approximately constant for a given flow rate and the layer thickness varies extremely slowly with the flow rate.

Structure of the two-dimensional relaxation spectra seen within the eigenmode perturbation theory and the two-site exchange model.

The form of the two-dimensional (2D) NMR-relaxation spectra--which allow to study interstitial fluid dynamics in diffusive systems by correlating spin-lattice (T(1)) and spin-spin (T(2)) relaxation times--has given rise to numerous conjectures. Herein we find analytically a number of fundamental structural properties of the spectra: within the eigen-modes formalism, we establish relationships between the signs and intensities of the diagonal and cross-peaks in spectra obtained by various 1 and 2D NMR-relaxation techniques, reveal symmetries of the spectra and uncover interdependence between them. We investigate more specifically a practically important case of porous system that has sets of T(1)- and T(2)-eigenmodes and eigentimes similar to each other by applying the perturbation theory. Furthermore we provide a comparative analysis of the application of the, mathematically more rigorous, eigen-modes formalism and the, rather more phenomenological, first-order two-site exchange model to diffusive systems. Finally we put the results that we could formulate analytically to the test by comparing them with computer-simulations for 2D porous model systems. The structural properties, in general, are to provide useful clues for assignment and analysis of relaxation spectra. The most striking of them--the presence of negative peaks--underlines an urgent need for improvement of the current 2D Inverse Laplace Transform (ILT) algorithm used for calculation of relaxation spectra from NMR raw data.

Structural properties of 2D NMR relaxation spectra of diffusive systems.

Much has been learnt and speculated about the form of 2D NMR relaxation spectra of diffusive systems. Herein we show that the eigen-modes formalism can help to establish a number of fundamental structural properties, i.e. symmetries, overall intensities, signs and relative intensities of the diagonal and cross components, of such spectra, on which one can safely rely in analysing experimental data. More specifically, we prove that the correlation T(1)-T(2) spectra will always have negative peaks, thus making questionable the nowadays wide spread strategy in developing inverse Laplace transformation algorithms.

MRI investigation of granular interface rheology using a new cylinder shear apparatus

The rheology of granular materials near an interface is investigated through proton magnetic resonance imaging. A new cylinder shear apparatus has been inserted in the magnetic resonance imaging device, which allows the control of the radial confining pressure exerted by the outer wall on the grains and the measurement of the torque on the inner shearing cylinder. A multi-layer velocimetry sequence has been developed for the simultaneous measurement of velocity profiles in different sample zones, while the measurement of the solid fraction profile is based on static imaging of the sample. This study describes the influence of the roughness of the shearing interface and of the transverse confining walls on the granular interface rheology.