Kinetic theory of polydisperse gas–solid flow: Navier–Stokes transport coefficients

The particulate phase stress and solid–solid drag force in the multifluid modeling of polydisperse gas–solid flows are usually closed using kinetic theory. This research aims to establish the hydrodynamic equations and constitutive relations of the multifluid model for polydisperse systems via species kinetic theory, in which the non-equipartition of energy and interphase slip velocity between different species are considered. Whereas previous studies have used approximations, such as Taylor series expansions, to simplify the calculation of collision integrals, the present study, for the first time, solves the collision integrals analytically without any approximations to obtain accurate constitutive relations. Explicit expressions for the constitutive laws are obtained, including the particle stress tensor, solid–solid drag force, heat flux, and energy dissipation rate up to the Navier–Stokes order. The present study offers more complete and mathematically rigorous constitutive laws for the multifluid modeling of polydisperse gas–solid flows.