On the relation between preferential concentration and radial relative velocity of inertial particles in homogeneous isotropic turbulence

\parindent = 0 pt{} The radial distribution function (RDF, a statistical measure of preferential concentration) and the PDF of the radial relative velocity ($w_r$) are the two statistical inputs to the collision kernel for inertial particles, which determines their collision rate in a turbulent flow. Although the relative velocity between the particles drives their spatial distribution (and hence the RDF), the relation between the two is not yet well-established. In this paper, we investigate this relationship using direct numerical simulation (DNS) of particle-laden homogeneous isotropic turbulence, with and without filtering. We show that the spatio-temporal variation of the skewness of the PDF of $w_r$ is qualitatively similar to that of the RDF. We then apply a low-pass sharp spectral filter to the DNS velocity field and use the filtered velocity field to calculate the RDF and the PDF of $w_r$. The first and second moments of $w_r$ are found to decrease monotonically with filtering for all separation distances irrespective of the particle Stokes number ($St$), whereas the skewness decreases with filtering for low $St$ and increases with filtering for high $St$. This non-monotonic response of the skewness to filtering is qualitatively similar to the response of the RDF to filtering, and points towards a connection between them.