Fluid-mediated sources to granular temperature in homogeneous fluidization

The present study considers analytical solutions for hydrodynamic sources and sinks to granular temperature in homogeneous suspensions of elastic particles at finite Reynolds numbers and solids volume fraction. We model the neighbor-induced drag disturbances with an acceleration Langevin, which allows an exact solution for the joint fluctuating acceleration-velocity distribution function $P\left(v^{\prime},a^{\prime};t\right)$. The quadrant conditioned covariance integrals of $P\left(v^{\prime},a^{\prime};t\right)$ are derived, allowing direct computation of the hydrodynamic source and sink that dictate the evolution of granular temperature. Analytical predictions agree with benchmark data obtained from particle-resolved direct numerical simulations. Furthermore, the theory correctly predicts saturation of steady granular temperature at small particle-fluid density ratios $\rho_p/\rho_f \ll 1$, and thus, shows promise as a general theory from gas--solid to bubbly flows.