Question 8.7: Minimum Fluidizing Velocity A bed of perfectly spherical so......
Minimum Fluidizing Velocity
A bed of perfectly spherical solid particles with a diameter of 85 μm and density of 3500 kgm ^{–3} is fluidized using a gas of density 1.2 kgm ^{–3} and a viscosity of 1.9 × 10 ^{–5} Nsm ^{–2} . Determine the minimum fluidizing velocity if a representative sample of particles extracted from the bed occupying a volume of 0.001 m³ has a mass of 2 kg.
By assuming laminar flow occurs at onset of fluidization, the pressure drop across the entire bed, the laminar flow part of the Ergun equation
{\frac{\Delta p}{L}}=\left(1-e\right)\left(\rho_{p}-\rho\right)g={\frac{150 \mu { U}\left(1-e\right)^{2}}{d_{\mathrm{p}}^{2}e^{3}}} (8.31)
The bed voidage, e, is the space between the solid particles expressed as a percentage or fraction of the total volume. The voidage is used to indicate the available space for the flow of a gas or liquid. In terms of volume, the voidage is therefore
e=\frac{V_{b}-\sum V_{p}}{V_{p}}=1-\frac{\mathsf{\rho}}{\mathsf{\rho}_{p}}=1-\frac{2000}{3500}=0.428 (8.32)
The void fraction depends on the size and shape of the particles and also their particle size distribution. Light materials are regarded as having bulk densities below 600 kgm ^{–3} , while heavy materials have densities in excess of 2000 kgm ^{–3} .
Assuming that the gas density is considerably less than that of the particles, the fluidization velocity is
U={\frac{\mathsf{\rho}_{b}g d_{\mathsf{p}}{}^{2}e^{3}}{150\mathsf{\mu}(1-e)}}=\frac{3500\times9.81\times\left(8.5\times10^{-5}\right)^{2}\times0.428^{3}}{150\times1.9\times10^{-5}\times\left(1-0.428\right)}=0.0103\ \mathrm{ms}^{-1} (8.33)