Microstructure in sheared non-Brownian concentrated suspensions

Abstract

The shear-induced microstructure in non-Brownian suspensions is studied. The Pair Distribution Function in the shear plane is experimentally determined for particle volume fractions ranging from 0.05 to 0.56. Transparent suspensions made of PMMA particles (172µm in diameter) dispersed in a fluorescent index matched Newtonian liquid is sheared in a wide gap Couette rheometer. A thin laser sheet lights the shear plane. The particle positions are recorded and the pair distribution function (PDF) in the shear plane is computed. The PDF at contact is shown to be anisotropic, with a depleted area in the receding side of the reference particle. The angular position of the depleted zone, close to the velocity axis at low particle concentration, is tilted toward the dilatation axis as the volume fraction is increased. At high concentrations (larger than 0.45), the shape of the PDF changes qualitatively with a secondary depleted area in the compressional quadrant of the main flow and a probability peak in the velocity direction.These experimental results are in good agreement with numerical simulations in Stokesian Dynamics where the interaction force between particles has been tuned to reproduce the particle roughness effects.

A new rate-independent tensorial model for suspensions of noncolloidal rigid particles in Newtonian fluids

“…The pair distribution function g(x), i.e. the likelihood of finding pairs of particles at a separation vector x, has been shown to become anisotropic and lose fore-aft symmetry under shear, with development of preferential concentration and depletion orientations that depend on the volume fraction φ [11]. This asymmetry of the microstructure is the hallmark of a loss of reversibility of the system that, again, contradicts expectations based on Stokes equation.…”

“…The α parameter has been already identified for this experimental setup, and its dependence upon φ is given by (11). For each volume fraction, identification of the three other parameters can be performed based on the evolution of the apparent viscosity η app = σ xy /γ during the shear reversals, as illustrated in the previous sensitivity analysis.…”

“…We quantitatively compared our model to the unsteady shear flow experiments of Blanc [39], sec 3.3 (see also [8,11,47]). This author performed shear reversal experiments in a Couette rheometer.…”

“…As an example, Fig. 3 shows, for a suspension at φ = 0.35 submitted to a a stationary shear flow, the experimentallydetermined evolution of g(x) in the shear plane (x, y) [11]. Recall that g(x) is the conditional probability, when there is already a particle in x 0 = 0, to find a particle at any location x ∈ R 2 , normalized by the average particle density φ/(4πa 3 /3) (where a is particle radius).…”

“…1, a key feature of the microstructure of sheared suspensions is the existence of preferential directions along which the average inter-distance between particles varies: particles are closer along the compression axis, and farther apart along the depletion axis. In inertialess systems, these preferential directions depend on the concentration φ, but not on the deformation rate |γ| (see [11]). The rheological model developed in this work is purely macroscopic, and hence no attempt is made at deriving a microscopic evolution equation for the microstructure.…”