Engineering & Science
Fuller-Schettler-Giddings Binary Gas Diffusivity Formula (D_AB)
Calculate binary gas-phase diffusion coefficients D_AB = 0.00143 * T^1.75 / (P * SQRT(M_AB) * (v_A^(1/3) + v_B^(1/3))^2) (cm^2/s) from atomic diffusion volumes.
Predicting binary vapor diffusivity without Lennard-Jones collision tables!
When sizing VOC solvent condensers, catalytic monoliths, or drying ovens, Lennard-Jones force constants ε/k and σ are often unavailable for polar organic vapors—whereas atomic diffusion volumes Σv (C = 15.9, H = 2.31, O = 6.11, Air = 19.7) sum directly from the molecular formula! Edward N. Fuller, Paul D. Schettler, and J. Calvin Giddings (Ind. Eng. Chem., 1966) regressed 340 gas pairs to obtain D_AB = 0.00143 * T^1.75 / (P_bar * SQRT(M_AB) * (Σv_A^(1/3) + Σv_B^(1/3))^2) cm^2/s, where harmonic molecular weight M_AB = 2 / (1/M_A + 1/M_B)!
For ethanol vapor (C_2H_5OH: M_A = 46.07 g/mol, Σv_A = 2*15.9 + 6*2.31 + 6.11 = 51.77) diffusing through air (M_B = 28.97 g/mol, Σv_B = 19.70) at 40 °C (T = 313.15 K) and P = 1.01325 bar, M_AB = 35.572 g/mol and D_AB = 0.1335 cm^2/s; pressurizing to P = 2.00 bar at 100 °C (373.15 K) yields D_AB = 0.0919 cm^2/s via the inverse pressure / T^1.75 scaling!
| Ethanol–Air Condition (vA=51.77, vB=19.70) | Harmonic Mass M_AB | FSG Gas Diffusivity D_AB (cm^2/s) | P–T Scaling Law |
|---|---|---|---|
| 40 °C Atmospheric Dryer (313.15 K, 1.01325 bar) | 35.572 g/mol | 0.1335 cm^2/s | Baseline VOC Vapor Film |
| 100 °C Pressurized Column (373.15 K, 2.00 bar) | 35.572 g/mol | 0.0919 cm^2/s | T^1.75 / P Competition |
| Zero Pressure P <= 0 | Undefined | "Invalid Gas State" | Division-by-Zero Guard |
Fuller-Schettler-Giddings Binary Gas Diffusivity D_AB (cm^2/s)
Evaluates D_AB (cm^2/s) from temperature B2 (K), total pressure B3 (bar), molecular weights B4 & B5 (g/mol), and atomic diffusion volumes B6 & B7.
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B5 <= 0, B6 <= 0, B7 <= 0), "Invalid Gas State", ROUND((0.00143 * (B2 ^ 1.75)) / (B3 * SQRT(2 / ((1 / B4) + (1 / B5))) * (((B6 ^ (1 / 3)) + (B7 ^ (1 / 3))) ^ 2)), 4))Harmonic Mean Molecular Weight M_AB = 2 / (1/M_A + 1/M_B)
Computes twice the reduced molar mass M_AB (g/mol) appearing in kinetic binary collision frequency.
=IF(OR(B4 <= 0, B5 <= 0), "Invalid Gas State", ROUND(2 / ((1 / B4) + (1 / B5)), 3))Try the example
Use the original values or change them to test your understanding.