Fluid-Particle Drag in Low-Reynolds-Number Bidisperse Suspensions

A second-order immersed boundary-lattice Boltzmann method (IB-LBM) is used to study the drag force of freely evolving bidisperse suspensions at low Reynolds numbers. The total solid volume fraction of the suspension is varied between 0.1 and 0.4, and the particle size ratio from 1:1.2 to 1:4. The main characteristics of freely evolving suspensions, compared to fix beds that were well reported in the literature, is that the two dispersed phases have different slip velocities relative to the fluid phase. Hence, in freely evolving bidisperse systems, the drag force on each particle phase is normalized by the Stokes drag force based on their corresponding slip velocity. Surprisingly, it is found that the drag force in freely evolving bidisperse suspensions is significantly different from previous results based on computations of systems with static particles. The drag force on small particles increases as the particle size ratio decreases, which is utterly opposite to that obtained from stationary systems. This difference is believed to be caused by the inhomogeneous structures formed by the particles in freely evolving systems, even though the computational domains are very limited. It is also found that the difference between the drag force on each particle phase in dynamic systems and that in stationary systems correlates well with the relative velocity of the two particle phases. Therefore, based on the present simulation results, a new drag force relation is proposed for bidisperse suspensions by including the relative velocity of the two particle phases.