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 $0.1\leqslant {\it\phi}\leqslant 0.5$. The wall region shows particle layers with a 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 ${\it\phi}\lessapprox 0.4$, wall-induced layering has a moderate impact on the 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 $|{\it\Sigma}_{xx}^{c}|$ (where $x$ is the velocity direction) because of particle layering in the wall region.