Fluidization

Fluidization occurs when upward gas velocity is high enough that the bed pressure drop equals the bed weight per unit area; beyond the minimum fluidization velocity the pressure drop stays constant while the bed expands and behaves like a boiling liquid.

Key formulas & points

Skim these first — then read the full notes below.

  • At u_mf the bed is just suspended; pressure drop equals bed weight per area
  • Bubbling beds lose gas–solid contact efficiency through bubbles
  • Geldart groups A, B, C, D classify powders by size and density difference

Topic details

Introduction

This McCabe-Smith topic explains the fluidized state used in catalytic cracking, drying and combustion. You compute the minimum fluidization velocity from a force balance (Ergun pressure drop equal to bed weight), recognise the constant pressure drop signature of fluidization, and classify powders by the Geldart scheme to anticipate bubbling or channelling behaviour.

Key relations & formulas

ΔP=(ρpρf)(1εmf)Lmfg\Delta P = (\rho_{p} - \rho_{f})(1 - \varepsilon_{mf}) L_{mf} g
(bed pressure drop at fluidization)
umfdp2(ρpρf)g(1650μ)u_{mf} \approx d_{p}^{2} (\rho_{p} - \rho_{f}) \frac{g}{(1650 \mu)}
(minimum fluidization velocity, Re_p < 20)

Formulas (Indian textbook notation)

  • ΔPLacrossafluidizedbedbedweightperunitarea(constantoncefluidized)\frac{\Delta P}{L} across a fluidized bed \approx bed weight per unit area (constant once fluidized)

Notation and sign conventions

Relation 1 —
ΔP=\Delta P =
ΔP=(ρpρf)(1εmf)Lmfg\Delta P = (\rho_{p} - \rho_{f})(1 - \varepsilon_{mf}) L_{mf} g
(bed pressure drop at fluidization)
Write this relation with symbols exactly as in Unit Operations of Chemical Engineering — McCabe, Smith & Harriott before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 2 —
umfdp2u_{mf} \approx d_{p}^{2}
umfdp2(ρpρf)g(1650μ)u_{mf} \approx d_{p}^{2} (\rho_{p} - \rho_{f}) \frac{g}{(1650 \mu)}
(minimum fluidization velocity, Re_p < 20)
Write this relation with symbols exactly as in Unit Operations of Chemical Engineering — McCabe, Smith & Harriott before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 3 —
ΔPLacrossafluidizedbedbedweightperunitarea\frac{\Delta P}{L} across a fluidized bed \approx bed weight per unit area

Formulas (Indian textbook notation)

  • ΔPLacrossafluidizedbedbedweightperunitarea(constantoncefluidized)\frac{\Delta P}{L} across a fluidized bed \approx bed weight per unit area (constant once fluidized)
Write this relation with symbols exactly as in Unit Operations of Chemical Engineering — McCabe, Smith & Harriott before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Concept in depth

As gas flows up through a bed of solids, pressure drop rises with velocity (per Ergun) until it just supports the particles’ weight — that is minimum fluidization, and beyond it the pressure drop plateaus because the bed weight is fixed. The bed then behaves like a liquid: it has a level, exerts buoyancy, and flows. The excess gas above u_mf usually passes as bubbles that bypass the solids, reducing gas–solid contact efficiency, so real fluidized reactors trade excellent temperature uniformity against imperfect contacting. Geldart’s classification predicts whether a powder fluidizes smoothly (group A), bubbles readily (B), is cohesive and hard to fluidize (C), or spouts (D).

Assumptions and validity limits

State assumptions explicitly before using any relation for fluidization — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.
Wrong assumptions invalidate the entire solution even when the formula is correct. In Mechanical Operations viva and GATE descriptive questions, listing valid assumptions often earns separate marks.

Step-by-step problem approach

1. Read the question and list given data with SI units (common in Mechanical Operations papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to fluidization.
4. Use equation 1:
ΔP=\Delta P =
.
5. Use equation 2:
umfdp2u_{mf} \approx d_{p}^{2}
.
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.

Applications & exam relevance

Fluidization appears in solids processing industries. In Indian chemical curricula this topic is tested because it connects theory to size reduction, filtration, and fluidization.
GATE and semester exams often combine fluidization with earlier units — revise prerequisites before attempting mixed problems.
Industry interview panels sometimes ask: "Where did you use fluidization?" — answer with a lab, mini-project, or plant visit example if possible.

Common mistakes in exams

Students expect pressure drop to keep rising after fluidization (it becomes constant), use the Stokes regime formula for u_mf when Re_p is large, and forget the (1 − ε) voidage factor in the bed-weight term. Misassigning the Geldart group from particle size is common.

Quick revision checklist

Before attempting fluidization problems, confirm you can:
1. At u_mf the bed is just suspended; pressure drop equals bed weight per area
2. Bubbling beds lose gas–solid contact efficiency through bubbles
3. Geldart groups A, B, C, D classify powders by size and density difference
Revise the solved examples in Unit Operations of Chemical Engineering — McCabe, Smith & Harriott and one previous-year GATE or university paper for this unit.

Worked examples

Try the problem first — open the solution when you are ready to check.

Fluidized-bed pressure drop

Problem

A fluidized bed of solids (ρ_p = 1500 kg/m³) has voidage ε_mf = 0.45 and height 0.8 m. Estimate the pressure drop (neglect gas density).

Solution

ΔP = (ρ_p)(1 − ε_mf)L g = 1500×(1 − 0.45)×0.8×9.81 = 1500×0.55×0.8×9.81 ≈ 6475 Pa. This equals the bed weight per unit area and stays constant above u_mf.

Conceptual check — Fluidization

Problem

In a Mechanical Operations semester or GATE paper you are asked: "State the main assumption, the governing relation, and one practical consequence of fluidization." What should a complete answer include?

Exams & GATE

McCabe-Smith Ch. 32 — identify the Geldart group from d_p and Δρ.

📖 Standard books (India)

  • Unit Operations of Chemical EngineeringMcCabe, Smith & Harriott

    Read: Syllabus unit

    Momentum, heat, and mass transfer operations