Engineering & Science
Lucas Corresponding-States Low-Pressure Gas Viscosity Formula (µPa·s)
Predict non-polar gas dynamic viscosity η (µPa·s) solely from critical temperature T_c, critical pressure P_c (bar), and molar mass M without Lennard-Jones collision integrals!
Predicting gas viscosity within 1%–3% when Lennard-Jones σ and ε/k_B aren’t tabulated!
Chapman-Enskog kinetic theory requires Lennard-Jones collision diameter σ and well depth ε/k_B—parameters unavailable for specialty process vapors and fluorocarbons! Klaus Lucas (1980; Poling, Prausnitz & O’Connell, Properties of Gases and Liquids) formulated an analytical corresponding-states viscosity correlation requiring only critical constants T_c (K), P_c (bar), and molar mass M (g/mol): inverse viscosity parameter ξ = 0.176 * (T_c / (M^3 * P_c^4))^(1/6) (µP^-1) and reduced viscosity η_0 * ξ = 0.807 * T_r^0.618 - 0.357 * EXP(-0.449 * T_r) + 0.340 * EXP(-4.058 * T_r) + 0.018 (divided by 10 to convert micropoise µP into SI µPa·s)!
Test nitrogen N_2 (T_c = 126.2 K, P_c = 33.98 bar, M = 28.013 g/mol): at 300 K (T_r = 2.377), Lucas gives η = 17.94 µPa·s (NIST: 17.89 µPa·s, +0.28% error!), and at 500 K Lucas gives 26.02 µPa·s (NIST: 26.06 µPa·s)!
| Nitrogen Temperature T (Tc = 126.2 K, Pc = 33.98 bar) | Reduced Temp T_r | Lucas Viscosity η (µPa·s) | NIST Reference η |
|---|---|---|---|
| 300 K Ambient Gas | 2.3772 | 17.94 µPa·s | 17.89 µPa·s (+0.28%) |
| 500 K Preheated Feed | 3.9620 | 26.02 µPa·s | 26.06 µPa·s (-0.15%) |
| Invalid T <= 0, Tc <= 0, Pc <= 0, or M <= 0 | Undefined | "Invalid Critical Constants" | Positivity Guard |
Lucas Low-Pressure Gas Dynamic Viscosity η (µPa·s)
Evaluates (f(T_r) / ξ) / 10 in SI µPa·s across operating temperature B2 (K), critical temperature B3 (K), critical pressure B4 (bar), and molar mass B5 (g/mol).
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B5 <= 0), "Invalid Critical Constants", ROUND((0.807 * ((B2 / B3) ^ 0.618) - 0.357 * EXP(-0.449 * (B2 / B3)) + 0.34 * EXP(-4.058 * (B2 / B3)) + 0.018) / (0.176 * ((B3 / ((B5 ^ 3) * (B4 ^ 4))) ^ (1 / 6))) / 10, 2))Lucas Inverse Reduced Viscosity Parameter ξ (µP^-1)
Computes 0.176 * (T_c / (M^3 * P_c^4))^(1/6).
=IF(OR(B3 <= 0, B4 <= 0, B5 <= 0), "Invalid Critical Constants", ROUND(0.176 * ((B3 / ((B5 ^ 3) * (B4 ^ 4))) ^ (1 / 6)), 5))Try the example
Use the original values or change them to test your understanding.