Granular and gas–particle flows in a channel with a bidisperse particle mixture

Abstract

Steady state solutions of granular and gas–particle flows in a channel with a bimodal particle mixture have been computed using kinetic theory. For granular channel flows we find granular energy equipartition breaks down with an increase in the system inelasticity and the mass ratio of particles. The effect of the particle size ratio on breakdown of energy equipartition is very small if the two particle species have the same mass. The species segregation in the solid phase is enhanced with a decrease in the system inelasticity, an increase in the average solid fraction or an increase in the size ratio, due to the competition of three diffusion forces: the thermal diffusion force, the ordinary diffusion force, and the pressure diffusion force. In addition, we find a competition mechanism exists in the equal density case (particles with equal density but different sizes) since in the equal mass case (particles with equal mass but different sizes) small particles have a higher concentration in low granular energy regions, whereas in the equal size case (particles with equal size but different masses) heavy particles have a higher concentration in low granular energy regions. These findings are in agreement with the results for granular Couette flows. For equal density particles, the segregation of large particles has a transition from the walls to the center when the restitution coefficient ( e p ) decreases from 1 to 0.99. This sensitivity is reduced when the system becomes more inelastic. For a given monodisperse granular system, we show that if larger particles are mixed in the system the sensitivity of the total solid distribution to the restitution coefficient is suppressed, while if smaller particles are added in the system the situation reverses. Lastly, we extend our work to gas–particle flows in a channel where particles are fluidized by gas flowing upwards, and find that for the kinetic theory models used in the present study, the solid fraction, the species segregation and the granular energy profiles are quite similar between the granular flows and the gas–particle flows.