Sign of turbulence modulation by heavy particles smaller than eddies
In plain words
Tiny heavy particles, smaller than the smallest eddies, can either drain energy from the turbulence that carries them or feed it, depending on their inertia and how many there are. No theory predicts which happens.
Precise statement
Heavy point particles (diameter $d << \eta$, eta the Kolmogorov length) with Stokes number St and mass loading $\Phi_m$ (particle-to-fluid mass ratio) of order 0.1 to 1 in homogeneous turbulence with two-way coupling. Determine the sign and magnitude of the change in carrier turbulent kinetic energy and dissipation rate as functions of $\mathrm{St}, \Phi_m, \mathrm{Sv}\text{ and }\mathrm{Re}_\lambda$, including the scale-by-scale energy exchange between phases. Answer: a predictive relation validated for St from about 0.1 to 10.
What would settle it
Two-way coupled point-particle DNS with converged coupling schemes, checked against experiments with sub-Kolmogorov particles at matched St and $\Phi_m$.