D pg Ap M2

This result can also be applied directly to coarse particle ''swarms.'' For fine particle systems, the suspending fluid properties are assumed to be modified by the fines in suspension, which necessitates modifying the fluid properties in the definitions of the Reynolds and Archimedes numbers accordingly. Furthermore, because the particle drag is a direct function of the local relative velocity between the fluid and the solid (the interstitial relative velocity, Vr), it is this velocity that must be used in the drag equations (e.g., the modified Dallavalle equation). Since Vr = Vs/(1 — ')= Vs/e, the appropriate definitions for the Reynolds number and drag coefficient for the suspension (e.g., the particle "swarm") are (after Barnea and Mizrahi, 1973):

dVrP

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