Drag Law for Bidisperse Gas−Solid Suspensions Containing Equally Sized Spheres

In this study, we constructed from lattice-Boltzmann simulations a drag correlation for bidisperse gas−solid suspensions containing equally sized particles that are moving with different velocities relative to the interstitial fluid. Our analysis is limited to flows at low Reynolds numbers and high Stokes numbers, and the microstructure of the suspension is identical to that of a hard-sphere fluid. The Stokes drag forces acting on the two particle species are related to the fluid−particle relative velocities by a friction coefficient matrix, the off-diagonal components of which represent the particle−particle drag due to hydrodynamic interactions and were found to give important contributions to the net drag force. The off-diagonals exhibit a logarithmic dependence on the lubrication cutoff distance, a length scale on which the lubrication force between approaching particles begins to level off. In our simulations, the total particle volume fraction ϕ ranges from 0.1 to 0.4, and the volume fraction ratio ϕ 1 /ϕ 2 ranges from 1:1 to 1:7. The results from these simulations are captured in explicit constitutive models, which can be readily generalized to multicomponent mixtures.