Chapter 7, Problem 7.10P

Interpretation Introduction

Interpretation: Flow of fluid through the internal pores is very small as compared to the flow between the particles is to be proved.

Concept introduction: Fluidization is a process where a very small particle from solid state is converted to the fluidized form. The minimum fluidization is the condition where the drag force on a particular particle is just equal to or balances the apparent weight of the body. In other words, it is the superficial velocity at which the bed of particle is just fluidized.

The equation for minimum fluidization for laminar flow is,

   ..... (1)

The notations used here are,

   = Minimum fluidization velocity

D_p = Particle diameter

g = Acceleration due to gravity

  ${\text{ρ}}_{\text{p}}$ = Particle density

  $\text{ρ}$ = Fluid density

  $\text{μ}$ = Fluid viscosity

  ${\varphi }_s$ = Sphericity of particle

  ${\text{ε}}_{\text{M}}$ = Porosity

The pressure drop across the particles is the ratio of the effective mass to the projected area.

For the spherical particle, the pressure drop is given as,

  $\text{ΔP}\text{=}\frac{{\text{2D}}_{\text{p}}{\text{(ρ}}_{\text{p}}\text{-}\text{ρ)g}}{\text{3}}$ ..... (2)

The notations used here are,

  $\text{ΔP}$ = Pressure drop

D_p = Particle diameter

g = Acceleration due to gravity

  ${\text{ρ}}_{\text{p}}$ = Particle density

  $\text{ρ}$ = Fluid density

The superficial velocity for the laminar flow of the particles is given by Hagen-Poiseuilleequation,

   ..... (3)

L = length of the pore

  $\text{μ}$ = Fluid viscosity

   = Pore velocity

D = Pore diameter