Engineering & Science
Mears Criterion: External Boundary-Layer Mass Transfer Check (< 0.15)
Test whether external fluid-film mass transfer limits heterogeneous catalytic reaction rates (< 5% error) via David Mears’ observable criterion Ω_Mears = (-r_A')_obs * ρ_b * R * n / (k_c * C_Ab) < 0.15.
Crushing catalyst pellets tests INTERNAL pores—boosting velocity tests EXTERNAL Mears film!
Before fitting kinetic rate laws in a packed-bed microreactor, reaction engineers check two distinct transport resistances: Weisz-Prater tests diffusion INSIDE catalyst pores, whereas David E. Mears (Industrial & Engineering Chemistry Process Design and Development, 1971) derived the universal diagnostic for stagnant boundary-layer film resistance OUTSIDE the pellet: Ω_Mears = (-r_A')_obs * ρ_b * R * n / (k_c * C_Ab)!
When Ω_Mears < 0.15 (for positive reaction order n > 0), surface concentration C_As stays within a few percent of bulk gas concentration C_Ab so external film resistance drops below < 5% error! Watch a packed bed (measured rate (-r_A')_obs = 3.0 × 10^-5 mol/(g_cat·s), bulk bed density ρ_b = 0.85 g/cm^3, pellet radius R = 0.25 cm, order n = 1, bulk concentration C_Ab = 5.0 × 10^-4 mol/cm^3): at sluggish superficial velocity (k_c = 0.05 cm/s), Ω_Mears = 0.2550 (>= 0.15, Film-Limited!), whereas raising gas velocity so k_c = 0.40 cm/s slashes Ω_Mears to 0.0319 (< 0.15, Clean Kinetic Data)!
| Superficial Gas Velocity Regime | External Film kc (cm/s) | Mears Number Ω_Mears | Packed-Bed Diagnostic Status |
|---|---|---|---|
| Low Recycle Flow (Sluggish Film) | 0.05 cm/s | 0.2550 (>= 0.15) | External Film Mass-Transfer Limited! |
| Borderline Flow Cutoff | 0.085 cm/s | 0.1500 (= 0.15) | 5% Rate Deviation Boundary |
| High Recycle Flow (Thin Boundary Layer) | 0.40 cm/s | 0.0319 (< 0.15) | Negligible External Film Resistance |
Mears External Mass-Transfer Criterion Ω_Mears
Evaluates (r_obs * ρ_b * R * n) / (k_c * C_Ab) in consistent CGS molar units.
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B5 <= 0, B6 <= 0, B7 <= 0), "Invalid Mears Inputs", ROUND((B2 * B3 * B4 * B5) / (B6 * B7), 4))Mears < 0.15 External Film Resistance Pass/Fail Decision
Flags whether bulk gas velocity / recycle rate is sufficient to eliminate external boundary-layer disguises.
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B5 <= 0, B6 <= 0, B7 <= 0), "Invalid Mears Inputs", IF((B2 * B3 * B4 * B5) / (B6 * B7) < 0.15, "Negligible External Film Resistance (<0.15)", "External Film Limited (>=0.15: Increase Flow Velocity)"))Try the example
Use the original values or change them to test your understanding.