# Turbulence modulation in heavy-loaded suspensions of tiny particles

## TL;DR

This paper investigates how tiny particles in heavy-loaded suspensions influence turbulence, revealing a new energy spectrum scaling law and demonstrating the impact on energy transfer and particle clustering through a robust regularised model and numerical simulations.

## Contribution

It introduces a physically-based regularisation approach to describe small-scale turbulence modulation by tiny particles, capturing the $k^{-4}$ energy spectrum scaling and energy exchange mechanisms.

## Key findings

- Particles modify the energy spectrum to follow a $k^{-4}$ scaling law.
- The regularised model accurately captures small-scale turbulence physics.
- Particle clustering at small scales is reduced, affecting collision dynamics.

## Abstract

The features of turbulence modulation produced by a heavy loaded suspension of small solid particles or liquid droplets are discussed by using a physically-based regularisation of particle-fluid interactions. The approach allows a robust description of the small scale properties of the system exploiting the convergence of the statistics with respect to the regularisation parameter. It is shown that sub-Kolmogorov particles/droplets modify the energy spectrum leading to a scaling law, $E(k)\propto k^{-4}$, that emerges at small scales where the particle forcing balances the viscous dissipation. This regime is confirmed by Direct Numerical Simulation data of a particle-laden statistically steady homogeneous shear flow, demonstrating the ability of the regularised model to capture the relevant small-scale physics. The energy budget in spectral space, extended to account for the inter-phase momentum exchange, highlights how the particle provide an energy sink in the production range that turns into a source at small scales. Overall, the dissipative fluid-particle interaction is found to stall the energy cascade processes typical of Newtonian turbulent flows. In terms of particle statistics, clustering at small scale is depleted, with potential consequences for collision models.