  Preferential concentration is thought to play a key role in promoting
particle growth, which is crucial to processes such as warm rain formation in
clouds, planet formation, and industrial sprays. In this work, we investigate
preferential concentration using 3D Direct Numerical Simulations adopting the
Eulerian-Eulerian two-fluid approach, where the particles are treated as a
continuum field with its own momentum and mass conservation laws. We consider
particles with Stokes number $St \lesssim O(0.01)$ in moderately turbulent
flows with fluid Reynolds number $Re \leq 600$. In our previous work (Nasab &
Garaud, Physical Review Fluids. doi: 10.1103/PhysRevFluids.5.114308, 2020), we
established scaling laws to predict maximum and typical particle concentration
enhancements in the context of the particle-driven convective instability. Here
we verify that the same results apply when turbulence is externally driven,
extending the relevance of our model to a wider class of particle-laden flows.
We find in particular that (i) the maximum particle concentration enhancement
above the mean scales as $u_{rms}^2 \tau_p / \kappa_p$, where $u_{rms}$ is the
rms fluid velocity, $\tau_p$ is the particle stopping time, and $\kappa_p$ is
the assumed particle diffusivity from the two-fluid equations; (ii) the typical
particle concentration enhancement over the mean scales as $(u_{rms}^2 \tau_p /
\kappa_p)^{1/2}$; and (iii) the probability distribution function of the
particle concentration enhancement over the mean has an exponential tail whose
slope scales like $(u_{rms}^2 \tau_p /\kappa_p)^{-1/2}$. We conclude by
discussing the caveats of our model and its implications in a relevant cloud
application.
