Lateral diffusive migration of massive particles in high-velocity vertical pipe flow of moderately dense gas-solid suspensions

Abstract

Transport processes involved in a gas-particle flow, comprised of spherical particles with a narrow size distribution suspended in a turbulent gas, are investigated theoretically on the basis of the recently developed Enskog theory for multicomponent dense mixtures of slightly smooth inelastic spherical particles [P. Zamankhan, Phys. Rev. E 52, 4877 (1995)]. The generalized Boltzmann equation of the previous work is modified to incorporate the relevant forces exerted upon individual particles including the drag force by the relative gas motion. Extending the method of moments of Grad [Commun. Pure Appl. Math. 2, 331 (1949)], the modified Boltzmann equation is solved to obtain the nonequilibrium velocity distribution function for particles of each size. By taking the monodisperse limit, a basic equation is derived for the treatment of the problem of lateral diffusive migration of solids in an assembly composed of separate equisized spherical particles traveling in a fully developed, turbulent upward flow of a gas within a vertical pipe. At moderately high solid concentrations, where the random component of the particle velocity is generated mainly by particle-particle collisions, the particle diffusivity and the thermal diffusion coefficient are found to increase with the square root of the granular temperature, a term that measures the energy of the random motion of the particles.