This paper presents three-dimensional numerical simulations of non-Brownian concentrated suspensions in a Couette flow at zero Reynolds number using a fictitious domain method. Contacts between particles are modelled using a discrete element method (DEM)-like approach, which allows for a more physical description, including roughness and friction. This work emphasizes the effect of friction between particles and its role on rheological properties, especially on normal stress differences. Friction is shown to notably increase viscosity and second normal stress difference $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}|N_2|$ and decrease $|N_1|$, in better agreement with experiments. The hydrodynamic and contact contributions to the overall particle stress are particularly investigated. This shows that the effect of friction is mostly due to the additional contact stress since the hydrodynamic stress remains unaffected by friction. Simulation results are also compared with experiments, such as normal stresses or effective friction coefficient $\mu (I_v)$, and the agreement is improved when friction is accounted for. This suggests that friction is operative in actual suspensions.

International audienceWe present an experimental approach used to measure both normal stress differences and the particle phase contribution to the normal stresses in suspensions of non-Brownian hard spheres. The methodology consists of measuring the radial profile of the normal stress along the velocity gradient direction in a torsional flow between two parallel discs. The values of the first and the second normal stress differences, and , are deduced from the measurement of the slope and of the origin ordinate. The measurements are carried out for a wide range of particle volume fractions (between 0.2 and 0.5). As expected, is measured to be negative but is found to be positive. We discuss the validity of the method and present numerous tests that have been carried out in order to validate our results. The experimental setup also allows the pore pressure to be measured. Then, subtracting the pore pressure from the total stress, , the contribution of the particles to the normal stress is obtained. Most of our results compare well with the different experimental and numerical data present in the literature. In particular, our results show that the magnitude of the particle stress tensor component and their dependence on the particle volume fraction used in the suspension model balance proposed by Morris & Boulay (J. Rheol., vol. 43, 1999, p. 1213) are suitable

Space dependent diffusion of micrometer sized particles has been directly observed using digital video microscopy. The particles were trapped between two nearly parallel walls making their confinement position dependent. Consequently, not only did we measure a diffusion coefficient which depended on the particles' position, but also report and explain a new effect: a drift of the particles' individual positions in the direction of the diffusion coefficient gradient, in the absence of any external force or concentration gradient. PACS number(s): 05.40. Jc, 82.70.Dd, 67.40.Hf (February 1, 2008) Brownian motion of spherical colloidal particles in the vicinity of a wall has been extensively studied, both theoretically and experimentally . It has been shown that the diffusion coefficients parallel or perpendicular to the wall were greatly reduced when the particles were close enough to the obstacle, i.e. within distances comparable to or less than their radius [1]. When the Brownian particles are trapped in a more confined geometry, such as a porous medium, the theory is far more complicated and few experimental studies have been reported in model geometries, where the particles are trapped between two parallel walls [2,3]. In this article, we report some new experimental results concerning the Brownian motion of particles trapped between two nearly parallel walls, so that the confinement, and thus the diffusion coefficient, become space dependent. As a result, we not only measure a diffusion coefficient which varies with the confinement, but also a drift of the particules' individual positions in the direction of the diffusion coefficient gradient, in the absence of any external force or concentration gradient. This drift was not accompanied by any net particle flux, i.e. statistically the same number of particles crossed any imaginary surface in both directions. We first discuss the general problem of a Brownian walker with a spatially dependent diffusion coefficient to explain the origin of the expected drift, and then present the experimental set-up and results.As in our experiment the diffusion coefficient varies in only one direction, say x, we briefly sketch a heuristic derivation of the 1D Brownian walker algorithm. The velocity of a 1D Brownian particle subjected to a random force and a viscous drag follows the Langevin equation,where γ −1 is the velocity relaxation time and Γ(t) the random force per unit mass defined by its mean value Γ(t) = 0 and correlation function Γ(t)Γ(t ′ ) = qδ(t − t ′ ). Using the equipartition theorem it can be shown that q is related to the temperature T and the particle's mass, m, by the standard relation q = 2γkT /m. Discretizing the random function Γ(t) over time intervals ∆t >> γ −1 allows us to drop in Eq.(1) the inertial term, dv/dt, and to replace the velocity v by ∆x/∆t. Choosing for Γ(t) the simplest random function, Γ(t) = ± q/∆t, leads to the well known Brownian walker algorithm,with D = kT /mγ. When the diffusion coefficient D, i.e. when the temperature T and/or t...

We propose to explain shear thinning behaviour observed in most concentrated non-Brownian suspensions by variable friction between particles. Considering the low magnitude of the forces experienced by the particles of suspensions under shear flow, it is first argued that rough particles come into solid contact through one or a few asperities. In such a few-asperity elastic-plastic contact, the friction coefficient is expected not to be constant but to decrease with increasing normal load. Simulations based on the Force Coupling Method and including such a load-dependent friction coefficient are performed for various particle volume fractions. The results of the numerical simulations are compared to viscosity measurements carried out on suspensions of polystyrene particles (40 µm in diameter) dispersed in a Newtonian silicon oil. The agreement is shown to be satisfactory. Furthermore, the comparison between the simulations conducted either with a constant or a load-dependent friction coefficient provides a model for the shearthinning viscosity. In this model the effective friction coefficient µ ef f is specified by the effective normal contact force which is simply proportional to the bulk shear stress. As the shear stress increases, µ ef f decreases and the jamming volume fraction increases, leading to the reduction of the viscosity. At last, using this model, we show that it is possible to evaluate the microscopic friction coefficient for each applied shear stress from the rheometric measurements.