On the constitutive relations for dispersed particles in nonuniform flows. I: Dispersion in a simple shear flow

The work presented follows on from a previous study in which a kinetic approach was used to generate the continuum equations for a dilute dispersed phase of noncolliding particles in a nonuniform turbulent flow. Here this approach is used to derive forms for the Reynolds stresses and the fluctuating interphase momentum transfer for particles at equilibrium in a bounded simple shear flow; the combination of the two also gives the total stress and long-term particle diffusion coefficients. These forms are based on equilibrium solutions of a kinetic equation describing the transport of the particle phase space probability density