A full Lagrangian method (FLM) is used in direct numerical simulations (DNS) of incompressible homogeneous isotropic and statistically stationary turbulent ﬂow to measure the statistical properties of the segregation of small inertial particles advected with Stokes drag by the ﬂow. Qualitative good agreement is observed with previous kinematic simulations (KS) (IJzermans, Meneguz & Reeks, J. FluidMech., vol. 653, 2010, pp. 99–136): in particular, the existence of singularities in the particle concentration ﬁeld and a threshold value for the particle Stokes number St above which the net compressibility of the particle concentration changes sign (from compression to dilation). A further KS analysis is carried out by examining the distribution in time of the compression of an elemental volume of particles, which shows that it is close to Gaussian as far as the third and fourth moments but non-Gaussian (within the uncertainties of the measurements) for higher-order moments when the contribution of singularities in the tails of the distribution increasingly dominates the statistics. Measurements of the rate of occurrence of singularities show that it reaches a maximum at St 1, with the distribution of times between singularities following a Poisson process. Following the approach used by Fevrier, Simonin & Squires (J. Fluid Mech., vol. 553, 2005, pp. 1–46), we also measured therandom uncorrelated motion (RUM) and mesoscopic components of the compression for St D 1 and show that the non-Gaussian highly intermittent part of the distribution of the compression is associated with the RUM component and ultimately with the occurrence of singularities. This result is consistent with the formation of caustics (Wilkinson et al. Phys. Fluids, vol. 19, 2007, p. 113303), where the activation ofsingularities precedes the crossing of trajectories (RUM). |