Engineering & Science
Tyn-Calus Liquid Diffusivity Correlation (Molar Volume & Surface Tension)
Estimate dilute liquid molecular diffusivity D_AB = 0.00893 * (V_B^0.267 / V_A^0.433) * (T / μ_B) * (σ_B / σ_A)^0.15 (× 10^-5 cm^2/s) without empirical association factors!
Replacing Wilke-Chang’s guessed association factor φ with measurable parachor / surface tension!
Wilke-Chang requires guessing an empirical solvent association parameter φ—which is uncalibrated for mixed, fluorinated, or specialty organic solvents! Myint Tyn and William F. Calus (Journal of Chemical & Engineering Data, 1975; recommended in Poling, Prausnitz & O’Connell, Properties of Gases and Liquids) eliminated empirical association factors altogether using boiling-point molar volumes V_A, V_B (cm^3/mol) and surface tensions σ_A, σ_B (dyn/cm = mN/m): D_AB = 8.93 × 10^-8 * (V_B^0.267 / V_A^0.433) * (T / μ_B) * (σ_B / σ_A)^0.15 cm^2/s (or 0.00893 * ... in units of 10^-5 cm^2/s)!
Evaluate dilute acetone (V_A = 77.5 cm^3/mol, σ_A = 23.7 mN/m) diffusing in water (V_B = 18.7 cm^3/mol, σ_B = 72.0 mN/m, μ_B = 0.890 cP) at 25 °C (T = 298.15 K): Tyn-Calus predicts D_AB = 1.174 × 10^-5 cm^2/s—matching experimental diaphragm-cell measurements (1.16 × 10^-5 cm^2/s) within 1.2%!
| Acetone in Water Condition (VA=77.5, VB=18.7, σB/σA=72/23.7) | Water Viscosity μB | Tyn-Calus D_AB (× 10^-5 cm^2/s) | Experimental Comparison |
|---|---|---|---|
| 25 °C Ambient (298.15 K) | 0.890 cP | 1.174 × 10^-5 cm^2/s | 1.16 × 10^-5 cm^2/s (+1.2% Error) |
| 50 °C Extraction Column (323.15 K) | 0.547 cP | 2.071 × 10^-5 cm^2/s | +76.4% Faster Stripping |
| Invalid μB <= 0 or σ <= 0 | Undefined | "Invalid Tyn-Calus Inputs" | Positivity Guard |
Tyn-Calus Dilute Liquid Diffusivity D_AB (in units of 10^-5 cm^2/s)
Evaluates 0.00893 * (V_B^0.267 / V_A^0.433) * (T / μ_B) * (σ_B / σ_A)^0.15 across solute/solvent molar volumes B2:B3, temperature B4 (K), solvent viscosity B5 (cP), and surface tensions B6:B7 (mN/m).
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B5 <= 0, B6 <= 0, B7 <= 0), "Invalid Tyn-Calus Inputs", ROUND(0.00893 * ((B3 ^ 0.267) / (B2 ^ 0.433)) * (B4 / B5) * ((B7 / B6) ^ 0.15), 3))Surface-Tension Parachor Correction Factor (σ_B / σ_A)^0.15
Isolates the interfacial-tension correction factor (equals 1.0000 when solute and solvent have similar parachor/surface tension).
=IF(OR(B6 <= 0, B7 <= 0), "Invalid Tyn-Calus Inputs", ROUND((B7 / B6) ^ 0.15, 4))Try the example
Use the original values or change them to test your understanding.