Constitutive relations are derived for a gas-particle suspension in which the particles are subject to a fluid velocity field, and experience inter-particle collisions. The flow is driven by two types of energy sources, an imposed mean shear and fluid velocity fluctuations, in the limit where the time between collisions τ
is small compared to the viscous relaxation time τ
, so that the dissipation of energy between collisions is small compared to the energy of a particle. Constitutive relations from the kinetic theory of dense gases are used when the flow is driven by the mean shear. The effect of fluid velocity fluctuations is incorporated using an additional diffusive term in the Boltzmann equation for the particle velocity distribution, and this leads to an additional ‘diffusino’ stress.