A bed of coal particles, $2 \mathrm{ft}$ in diameter and $6 \mathrm{ft}$ deep, is fluidized using a hydrocarbon liquid with a viscosity $15 \mathrm{cP}$ and a density of $0.9 \mathrm{~g} / \mathrm{cm}^{3}$. The coal particles have a density of $1.4 \mathrm{~g} / \mathrm{cm}^{3}$ and an equivalent spherical diameter of $1 / 8$ in. If the bed porosity is 0.4 ,

(a) Determine the range of liquid superficial velocities over which the bed is fluidized.

(b) Repeat the problem using the "particle swarm" (Barnea and Mizrahi) "swarm terminal velocity" approach, assuming (1) $\varphi=1-\varepsilon$; (2) $\varphi=1-\varepsilon_{\mathrm{mf}}$.