Engineering & Science
Morton Number (Mo) & Grace Diagram Gas-Bubble Fluid Property Index
Calculate the dimensionless fluid-property Morton Number Mo = g * μ_L^4 * (ρ_L - ρ_G) / (ρ_L^2 * σ^3) and Grace diagram abscissa LOG10(Mo) spanning 14 orders of magnitude from clean water (-10.6) to viscous syrups (+1.1).
Why μ_L^4 makes Morton Number span 14 orders of magnitude across industrial liquids!
Unlike Reynolds and Eötvös numbers—which change with bubble diameter—the Morton Number Mo = g * μ_L^4 * (ρ_L - ρ_G) / (ρ_L^2 * σ^3) depends PURELY on fluid physical properties, locking each gas-liquid system onto a single contour line on John R. Grace’s (1973) universal bubble-shape regime map (Spherical, Wobbling/Ellipsoidal, Skirted, or Spherical-Cap)!
Because liquid viscosity μ_L enters to the FOURTH power, LOG10(Mo) spans an astonishing dynamic range: air bubbles in clean 20 °C water (μ_L = 0.001 Pa·s, ρ_L = 998 kg/m^3, ρ_G = 1.2 kg/m^3, σ = 0.0728 N/m) sit at LOG10(Mo) = -10.59 (Mo = 2.55 × 10^-11, producing wobbling ellipsoidal bubbles), whereas viscous glycerol/polymer broth (μ_L = 0.80 Pa·s, ρ_L = 1,260 kg/m^3, σ = 0.063 N/m) jumps nearly 12 orders of magnitude to LOG10(Mo) = +1.11 (Mo = 12.82, suppressing wobble into smooth dimpled/skirted caps)!
| Gas-Liquid Bioreactor / Column System | Viscosity μL (Pa·s) | Grace Parameter LOG10(Mo) | Characteristic Bubble Behavior |
|---|---|---|---|
| Air in Clean Water at 20 °C | 0.001 Pa·s | -10.59 (Mo = 2.55E-11) | Low-Mo Wobbling Ellipsoidal Regime |
| Mineral Oil Absorber | 0.050 Pa·s | -3.38 (Mo = 4.17E-4) | Intermediate Viscous Damping |
| Concentrated Glycerol / Polymer Melt | 0.800 Pa·s | +1.11 (Mo = 12.82) | High-Mo Laminar Dimpled / Skirted Cap |
Grace Diagram Logarithmic Morton Index LOG10(Mo)
Evaluates LOG10(9.80665 * μ_L^4 * (ρ_L - ρ_G) / (ρ_L^2 * σ^3)) directly onto Grace’s horizontal/contour axis.
=IF(OR(B2 <= 0, B3 <= B4, B4 < 0, B5 <= 0), "Invalid Fluid Properties", ROUND(LOG10((9.80665 * (B2 ^ 4) * (B3 - B4)) / ((B3 ^ 2) * (B5 ^ 3))), 2))Fluid Viscosity Regime Classification on Grace Bubble Map
Classifies LOG10(Mo) < -6 as Low-Morton Invicid/Water-Like (wobbling prone), -6 to -1 as Intermediate, and > -1 as High-Morton Viscous.
=IF(OR(B2 <= 0, B3 <= B4, B4 < 0, B5 <= 0), "Invalid Fluid Properties", IF(LOG10((9.80665 * (B2 ^ 4) * (B3 - B4)) / ((B3 ^ 2) * (B5 ^ 3))) < -6, "Low-Mo Water-Like Regime (Wobbling Ellipsoids)", IF(LOG10((9.80665 * (B2 ^ 4) * (B3 - B4)) / ((B3 ^ 2) * (B5 ^ 3))) <= -1, "Intermediate-Mo Regime", "High-Mo Viscous Regime (Smooth / Skirted Caps)")))Try the example
Use the original values or change them to test your understanding.