A. Introduction, range of fluidization, bed expansion

Fluidization of solid particles by a streaming gas or liquid requires a fluid velocity u in the range

$$\label{eq1} u_{mf}\lt u \lt u_{t}\tag{1}$$

where u_mf is the so-called minimum fluidization velocity and u_t is the terminal velocity. The minimum fluidization velocity u_mf can be found from a force balance equating the pressure drop of a fixed bed to the weight of the particle (— buoyancy force) per cross-sectional area. Using Ergun's equation (Ergun, 1952 [1]) for the pressure drop of the fixed bed, one obtains the Reynolds number Re_mf ≡ p_f u_mf d /η_f as a function of Archimedes number Ar ≡ g d ³ρ_f (ρ_p – ρ_f) η_f² and void fraction at minimum fluidization ψ_mf (see Section 148):

$$\label{eq2} \mbox{Re}_{mf}=42.9(1-\psi_{mf})\left[ \sqrt{1+\dfrac{\psi_{mf}^{3}}{(1-\psi_{mf})^{2}}\,\dfrac{\mbox{Ar}}{3,214}}-1\right] \tag{2}$$