Hong Life CalculatorsUnderstanding the minimum fluidisation velocity calculator — concept and principle
When gas flows upward through a bed of particles, there is a velocity at which the drag on the particles balances their weight and the bed starts to behave like a fluid. This minimum fluidisation velocity, U_mf, is the starting point for designing fluidised-bed reactors, dryers, combustors and coaters. The calculator uses the Wen–Yu correlation with particle diameter, particle density, gas density and gas viscosity.
How it is calculated
- Archimedes number Ar = d_p³ ρ_g (ρ_p − ρ_g) g ÷ μ², with d_p in metres and g = 9.81 m/s².
- Wen–Yu: Re_mf = √(33.7² + 0.0408 Ar) − 33.7
- U_mf = Re_mf × μ ÷ (ρ_g d_p), shown in cm/s.
Densities are in kg/m³ and viscosity in Pa·s; the particle diameter is entered in µm.
The principle
At minimum fluidisation the pressure drop across the bed equals the bed's buoyant weight per unit area. The pressure drop of gas flowing through a packed bed is given by the Ergun equation, which has a viscous term (dominant for fine particles) and an inertial term (dominant for coarse ones). Equating the two expressions gives a quadratic in Re_mf with Ar on the other side. Wen and Yu found that, for many materials, the bed voidage and particle shape at minimum fluidisation combine into nearly constant coefficients, 33.7 and 0.0408, so the quadratic can be solved directly. Ar compares gravity-driven buoyant weight with viscous forces.
Worked example
- Inputs: d_p = 300 µm, ρ_p = 2,500 kg/m³, ρ_g = 1.2 kg/m³, μ = 1.8 × 10⁻⁵ Pa·s.
- Ar = (3 × 10⁻⁴)³ × 1.2 × 2,498.8 × 9.81 ÷ (1.8 × 10⁻⁵)² = 2,451.3.
- Re_mf = √(1,135.69 + 0.0408 × 2,451.3) − 33.7 = √1,235.70 − 33.7 = 1.453.
- U_mf = 1.453 × 1.8 × 10⁻⁵ ÷ (1.2 × 3 × 10⁻⁴) = 0.0726 m/s = 7.26 cm/s.
| Particle diameter (µm) | U_mf (cm/s) |
|---|---|
| 75 | 0.4635552156 |
| 150 | 1.849781803 |
| 225 | 4.135372339 |
| 300 | 7.262906371 |
| 375 | 11.13312362 |
| 450 | 15.6092384 |
| 600 | 25.74436809 |
How to read the result
A 300 µm sand-like powder in air fluidises at about 7 cm/s. Fine particles have Re_mf well below 20, where U_mf scales roughly with d_p²; very coarse particles fall into the inertial regime, where it scales roughly with √d_p. Beds are usually operated at several times U_mf, but below the terminal velocity of the particles to avoid carrying them out of the bed.
Common mistakes
- Entering the particle diameter in metres or millimetres instead of µm.
- Using the true solid density for porous particles instead of the particle (envelope) density.
- Applying a single diameter to a wide size distribution; use a surface–volume mean diameter.
Frequently asked questions
Does temperature change U_mf?
Yes. Gas viscosity rises and density falls with temperature, which usually lowers U_mf for fine particles.
What is the Geldart classification?
A map of particle size and density difference that predicts fluidisation behaviour; this example falls in group B, which bubbles almost as soon as it fluidises.
Does the bed height matter?
Not for U_mf itself, since both weight and pressure drop scale with height.
Sources: C. Y. Wen and Y. H. Yu, AIChE Journal 12 (1966) 610 · D. Kunii and O. Levenspiel, Fluidization Engineering, 2nd edition, Butterworth-Heinemann · D. Geldart, Powder Technology 7 (1973) 285