# Effects of the finite particle size in turbulent wall-bounded flows of dense suspensions

## TL;DR

This study uses detailed simulations to analyze how particle size influences turbulence and particle behavior in dense suspensions within wall-bounded flows, revealing size-dependent effects on flow statistics and particle dynamics.

## Contribution

It provides new insights into finite-size effects on turbulence and particle dynamics in dense suspensions, especially near walls, extending existing flow scaling laws.

## Key findings

- Particle-wall layer influences suspension micro-structure over a distance proportional to particle size.
- Significant slip velocity and extreme shear stress events occur in the particle-wall layer.
- Finite-size effects are more pronounced for larger particles in the bulk flow.

## Abstract

We use interface-resolved simulations to study finite-size effects in turbulent channel flow of neutrally-buoyant spheres. Two cases with particle sizes differing by a factor of 2, at the same solid volume fraction of 20% and bulk Reynolds number are considered. These are complemented with two reference single-phase flows: the unladen case, and the flow of a Newtonian fluid with the effective suspension viscosity of the same mixture in the laminar regime. As recently highlighted in Costa et al. (PRL 117, 134501), a particle-wall layer is responsible for deviations of the statistics from what is observed in the continuum limit where the suspension is modeled as a Newtonian fluid with an effective viscosity. Here we investigate the fluid and particle dynamics in this layer and in the bulk. In the particle-wall layer, the near wall inhomogeneity has an influence on the suspension micro-structure over a distance proportional to the particle size. In this layer, particles have a significant (apparent) slip velocity that is reflected in the distribution of wall shear stresses. This is characterized by extreme events (both much higher and much lower than the mean). Based on these observations we provide a scaling for the particle-to-fluid apparent slip velocity as a function of the flow parameters. We also extend the flow scaling laws in to second-order Eulerian statistics in the homogeneous suspension region away from the wall. Finite-size effects in the bulk of the channel become important for larger particles, while negligible for lower-order statistics and smaller particles. Finally, we study the particle dynamics along the wall-normal direction. Our results suggest that 1-point dispersion is dominated by particle-turbulence (and not particle-particle) interactions, while differences in 2-point dispersion and collisional dynamics are consistent with a picture of shear-driven interactions.