Turbophoresis in forced inhomogeneous turbulence

We show, by direct numerical simulations, that heavy inertial particles (characterized by Stokes number $\St$) in inhomogeneously forced statistically stationary isothermal turbulent flows cluster at the minima of mean-square turbulent velocity. Two turbulent transport processes, turbophoresis and turbulent diffusion together determine the spatial distribution of the particles. If the turbulent diffusivity is assumed to scale with turbulent root mean square velocity, as is the case for homogeneous turbulence, the turbophoretic coefficient can be calculated. Indeed, for the above assumption, the non-dimensional product of the turbophoretic coefficient and the rms velocity is shown to increase with $St$ for small $St$, reach a maxima for $St\approx 10$ and decrease as $\sim St^{-0.33}$ for large $St$.