Engineering & Science
Wilke-Chang Liquid Diffusivity Correlation (Dissolved Gas & Solute D_AB)
Estimate dilute liquid-phase molecular diffusivity D_AB (in 10^-5 cm^2/s) using Charles Wilke and Pin Chang’s 1955 Stokes-Einstein association correlation.
Why dissolved oxygen diffuses 10,000× slower in water than in air—and how bioreactors size for it!
Designing gas-liquid sparged bioreactors, packed absorption towers, or liquid-liquid extractors requires the dilute liquid diffusivity D_AB when experimental data at operating temperature T are unavailable. Charles R. Wilke and Pin Chang (AIChE Journal, 1955) modified Stokes-Einstein hydrodynamic drag with a solvent hydrogen-bonding association factor φ (2.6 for water, 1.9 for methanol, 1.5 for ethanol, 1.0 for unassociated organics): D_AB = 7.4 × 10^-8 * SQRT(φ * M_B) * T / (μ_B * V_A^0.6) cm^2/s—or directly in standard handbook units of 10^-5 cm^2/s, D_AB,1e-5 = 0.0074 * SQRT(φ * M_B) * T / (μ_B * V_A^0.6)!
Check dissolved O_2 (molar volume at normal boiling point V_A = 25.6 cm^3/mol) in water (φ = 2.6, M_B = 18.015 g/mol): at 25 °C (T = 298.15 K, μ_B = 0.890 cP), D_AB = 2.425 × 10^-5 cm^2/s; warming to mammalian cell-culture temperature 37 °C (T = 310.15 K, where water viscosity drops to 0.692 cP) boosts oxygen diffusivity by +33.8% to 3.244 × 10^-5 cm^2/s!
| Dissolved O2 in Water (φ=2.6, MB=18.015, VA=25.6) | Solvent Viscosity μB (cP) | D_AB (× 10^-5 cm^2/s) | Schmidt Number Sc = ν / D_AB |
|---|---|---|---|
| 25 °C Benchtop (298.15 K) | 0.890 cP | 2.425 × 10^-5 cm^2/s | ~368 (Thin Mass-Transfer Film) |
| 37 °C Mammalian Bioreactor (310.15 K) | 0.692 cP | 3.244 × 10^-5 cm^2/s (+33.8%) | ~215 (Faster k_L*a Oxygenation) |
| Non-Positive μB or VA <= 0 | Invalid | "Invalid Wilke-Chang Inputs" | Physical Guard |
Wilke-Chang Liquid Diffusivity D_AB (in units of 10^-5 cm^2/s)
Computes 0.0074 * SQRT(φ * M_B) * T / (μ_B * V_A^0.6) from association factor B2, solvent molecular weight B3 (g/mol), temperature B4 (K), solvent viscosity B5 (cP = mPa·s), and solute boiling molar volume B6 (cm^3/mol).
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B5 <= 0, B6 <= 0), "Invalid Wilke-Chang Inputs", ROUND(0.0074 * SQRT(B2 * B3) * B4 / (B5 * (B6 ^ 0.6)), 3))SI Diffusivity D_AB in 10^-9 m^2/s
Since 10^-5 cm^2/s equals 1.0 × 10^-9 m^2/s exactly, converts to raw cm^2/s scientific value rounded to 8 decimals.
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B5 <= 0, B6 <= 0), "Invalid Wilke-Chang Inputs", ROUND(0.000000074 * SQRT(B2 * B3) * B4 / (B5 * (B6 ^ 0.6)), 8))Try the example
Use the original values or change them to test your understanding.