Modeling a dilute suspension of particles in a polykinetic Eulerian framework is described using the conditional quadrature method of moments (CQMOM). The particular regimes of interest are multiphase flows comprised of particles with diameters small compared to the smallest length scale of the turbulent carrier flow and particle material densities much larger than that of the fluid. These regimes correspond to moderate granular Knudsen number and large particle Stokes numbers in which interparticle collisions and/or particle trajectory crossing (PTC) can be significant. The probability density function (PDF) of the particle velocity space is discretized with a two-point quadrature, the minimum resolution required to capture PTC which is common to these flows. Both two-dimensional (2D) test cases (designed to assess numerical procedures) and a three-dimensional (3D) fully developed particle-laden turbulent channel flow were implemented for collisionless particles. The driving gas-phase carrier flow is computed using direct numerical simulation of the incompressible Navier–Stokes (N–S) equations and one-way coupled to the particle phase via the drag force. Visualizations and statistical descriptors demonstrate that CQMOM predicts physical features such as PTC, particle accumulation near the channel walls, and more uniform particle velocity profiles relative to the carrier flow. The improvements in modeling compared to monokinetic representations are highlighted.