Effect of confinement in wall-bounded non-colloidal suspensions

Abstract

This paper presents three-dimensional numerical simulations of non-colloidal dense suspensions in a wall-bounded shear flow at zero Reynolds number. Simulations rely on a fictitious domain method with a detailed modelling of particle-particle and wall-particle lubrication forces, as well as contact forces including particle roughness and friction. This study emphasizes the effect of walls on the structure, velocity and rheology of a moderately confined suspension (channel gap to particle radius ratio of 20) for a volume fraction range 0.1 ≤ φ ≤ 0.5. The wall region shows particle layers with an hexagonal structure. The size of this layered zone depends on volume fraction and is only weakly affected by friction. This structure implies a wall slip which is in good accordance with empirical models. Simulations show that this wall slip can be mitigated by reducing particle roughness. For φ 0.4, wall-induced layering has a moderate impact on viscosity and second normal stress difference N 2 . Conversely, it significantly alters the first normal stress difference N 1 and can result in positive N 1 , in better agreement with some experiments. Friction enhances this effect, which is shown to be due to a substantial decrease in the contact normal stress |Σ c xx | (where x is the velocity direction) because of particle layering in the wall region.

Stripes instability of an oscillating non-Brownian iso-dense suspension of spheres

“…The analysis of the particle concentration distribution across the gap supports a two steps scenario of the instability: migration of the particles towards the cell walls followed by an instability due to the concentration gradient across the gap. Recent measurements of the first normal stresses difference [13,14] and the theory of longitudinal instability due to the first normal stresses difference [6] account reasonably for our experimental observations. More quantitative comparisons will require further measurements of the concentration across the gap as well as of the particle distribution function in order to estimate N 1 (z).…”

Fully developed and transient concentration profiles of particulate suspensions sheared in a cylindrical Couette cell

“…According to this scenario, layering should slow down the migration process, as we observed in the present study where, above φ b = 40%, the migration strain scale no longer decreases. Conversely, the numerical simulations of Gallier (2016) indicate that the particle stress (whose divergence in inhomogeneous flow drives the migration) is only slightly affected by the structuration of the suspension. From the latter observation, one would expect the migration dynamics to be unaffected by layering.…”

“…In practice, index matching and direct optical visualization require small systems. Moreover, providing experimental results for such confinement is useful to compare with numerical simulations which, limited by computation time, also investigate systems having similar sizes (Gallier (2016)). Most importantly, for gap /a > 20, previous experiments and numerical simulations both already showed that confinement has a negligible impact on macroscopic quantities such as the suspension viscosity (Maxey (2017)), but also on the fully developed concentration profiles (Snook et al (2016)).…”

Rheology of dense suspensions of non colloidal particles

“…Some experiments using more conventional rheometry find that N 1 is quite small and negative [10][11][12][13], while others report positive values [14]. Some recent studies point to the effect of polydispersity [15] and of confinement [16] which may explain these discrepancies.…”