Inertial effects in suspension and porous-media flows

The current understanding of the average flow properties of packed beds and particle suspensions, in which inertia plays a significant role on the par ticle length scale, is examined. The features of inertial suspensions posin g challenges to theoriticians include the nonlinear and unsteady nature of the governing equations, the inability to superimpose solutions, the preval ence of hydrodynamic instabilities, and the existence of particle-particle collisions. We discuss two special cases of inertial suspensions, for which detailed kinetic theories have been developed: (a) particles in a gas, and (b) spherical, high-Reynolds number bubbles in liquid. Subsequently, we re view recent applications of computational fluid dynamics to simulate the mo tion in particle suspensions with both inertia and vorticity in the continu eous phase. The synthesis of these analytical and numerical techniques is a promising approach to address the many challenges of modelling inertial su spensions.