In this work we address the effect of particle inertia in particulate density currents. First we introduce a novel two-fluid model based on the equilibrium Eulerian approach . The resulting model captures very important physics of two-phase flows, such as preferential concentration and migration of particles down turbulence gradients (turbophoresis), which modify substantially the structure and dynamics of the flow.We solve the mathematical model with a highly accurate spectral code, capturing all the length and time scales of the flow. We present two-dimensional simulations in planar configuration for Grashof Gr = 1.5 × 106. In the simulation results we observe the particles to migrate from the core of Kelvin-Helmholtz vortices shed from the front of the current and to accumulate in the current head, which affects the propagation speed of the front.