Fluid-particle drag and particle-particle drag in low-Reynolds-number bidisperse gas-solid suspensions

Particle-resolved direct numerical simulations (PR-DNSs) of dynamic bidisperse gas-solid suspensions are performed at low particle Reynolds numbers. Unlike the fixed-bed suspensions, the mobility of particles allows particles of different size types to develop different slip velocities relative to the fluid phase. The scaled slip velocity, defined as the ratio of the slip velocity of one particle type to the mean slip velocity of the mixture, varies profoundly depending on the specific properties of the bidisperse mixture. For large particles, the drag force, scaled by the mean drag force of the mixture, is reasonably predicted by the models obtained from fixed-bed suspensions, while for small particles, these models tend to underestimate the scaled drag force as the scaled slip velocity decreases. By introducing the scaled slip velocity, a new model for the fluid-particle drag on each particle type is proposed and agrees well with the PR-DNS data. For the situation where the monodisperse drag models are employed to predict the mixture mean drag force, a new mean diameter that is variant with the total solid volume fraction is suggested. This diameter increases as the total solid volume fraction decreases and approaches the Sauter mean diameter in the close-packed volume fraction. In dilute suspensions, due to the strong influence of surrounding fluids on the particle phase, the simulated particle-particle drag is significantly smaller than the predictions of models based on kinetic theory of granular flow. Based on the PR-DNS results, new relations for particle-particle drag are also proposed.