Shear thinning in non-Brownian suspensions explained by variable friction between particles

Abstract

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.

X-ray radiography of viscous resuspension

“…It suggests that the contact contribution to stress scales asγ 0.76 , which is broadly consistent with particle stresses scaling aṡ γ 0.7 in resuspension experiments [Equation (13)]. Altogether, these observations point to non-Coulomb friction between our glass particles, as recently proposed by Chatté et al 12 and by Lobry et al 14 . This means that the resuspension properties of non-Brownian particles should depend much on the exact nature of the particles and on the way their friction coefficient varies with load and velocity.…”

“…For φ = 50%, the apparent viscosity follows a scaling η ∝γ −0.17 . Similar shear-thinning at high particle concentration has already been reported in a number of other non-Brownian suspensions [10][11][12][13][14] .…”

“…In all these works, a viscous scaling of all stresses is assumed, which is theoretically justified for ideal rate-independent Coulomb friction between the particles 9 . Many experimental results, however, show the emergence of a shear-thinning viscosity at high volume fraction in non-Brownian suspensions [10][11][12][13][14] . This has been proposed to originate from a velocity-weakening friction between the particles 13 or from non-Coulomb friction 12,14 as evidenced experimentally by Chatté et al 12 .…”

Effect of Particle Specific Surface Area on the Rheology of Non-Brownian Silica Suspensions

“…In our previous work [ 12 ], we showed that the strong shear thinning behaviour of the PS52 suspensions, as opposed to that of GS2, can be attributed to the surface asperities being elastically deformed due to the frictional contacts between the former particles. According to a theory introduced by Chatté et al [ 36 ] and Lobry et al [ 28 ], this leads to a decrease in the microscopic friction coefficient and shear thinning. The shear thinning of the glass spheres is, however, suppressed due to the presence of a solvation layer as the hydroxyl groups (-OH) of the glycerol molecules bind onto the inherently hydrophilic silicas through hydrogen bonding.…”

“…The density of the silica particles is different from that of glycerol, as shown in Table 1 , and thus shear stresses above a critical level need be applied during the rheological measurements to exclude any particle sedimentation effects. This stress value can be estimated using the dimensionless Shields parameter [ 28 ]: where is the shear stress (Pa), the particle radius (m), the difference in densities between the particles and the fluid (kg/m 3 ), and the gravitational acceleration (m/s 2 ). in Equation (2) is effectively the ratio of the fluid induced force acting on the particle to the particle weight; a cut off value of is assumed to estimate the critical stress beyond which particle sedimentation can be neglected.…”