This review touches on some of the fundamental problems in this subject and some practical solutions, viz: (i) the force on a small rigid particle, solid or gaseous; a general heuristic expression is presented for a spherical particle based on combining the limiting cases of inviscid non-uniform flow and simple viscous flow; (ii) how the lift and acceleration forces produce non-uniform distributions of bubbles in non-uniform turbulent pipe flows inclined at different angles to the horizontal; computer simulations are presented using the results of (i); (iii) the relative contributions of the spatial and temporal fluctuations to the difference between the diffusivities of solid and fluid particles; an idealised model of small inertial particles in turbulent motion gives useful insight; (iv) the differences in the spectra of their velocities; hypotheses based on (iii) tested by computing the trajectories of particles in velocity fields that simulate turbulence (Kinematic Simulation); (v) how low concentrations of particles interact between each other and affect the average flow field.

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