Brokaw Gas Mixture Viscosity Formula: Polar & Nonpolar Binary Interaction

Why linear mole-fraction averaging fails badly for polar–nonpolar gas mixtures like NH3–N2 or H2O–Air!

Richard S. Brokaw (1965, NASA Lewis Research Center) extended the Wassiljewa kinetic-theory mixture equation μ_m = Σ [y_i * μ_i / Σ (y_j * φ_ij)] to polar vapor mixtures (steam, ammonia, SO2, HCl) where permanent dipole attraction distorts binary collision cross-sections! Instead of assuming φ_12 = φ_21 = 1 (linear mixing), Brokaw incorporates molecular-weight asymmetry S_12 * A_12 so asymmetric light/polar molecules exhibit a pronounced nonlinear viscosity curve!

For a 40% NH3 (μ_1 = 108.5 μP) + 60% N2 (μ_2 = 182.4 μP) synthesis loop gas with Brokaw interaction factors φ_12 = 1.184 and φ_21 = 0.812, mixture viscosity evaluates to μ_m = 157.42 μP—shifting to 134.99 μP when ammonia mole fraction rises to y_1 = 0.70 (y_2 = 0.30)!

Brokaw Binary Polar Gas Mixture Viscosity μ_m (Micropoise, μP)

Evaluates Wassiljewa-Brokaw mixture viscosity from mole fractions B2, B3 (summing to 1), pure gas viscosities B4, B5 (μP), and Brokaw interaction parameters φ_12 (B6) and φ_21 (B7).

=IF(OR(B2 < 0, B3 < 0, ABS(B2 + B3 - 1) > 0.0001, B4 <= 0, B5 <= 0, B6 <= 0, B7 <= 0), "Invalid Mixture Inputs", ROUND((B2 * B4) / (B2 + B3 * B6) + (B3 * B5) / (B3 + B2 * B7), 2))

Nonlinear Deviation from Naive Mole-Fraction Weighted Average (μP)

Quantifies μ_Brokaw minus (y_1*μ_1 + y_2*μ_2) to expose dipole/mass collision nonlinearity.

=IF(OR(B2 < 0, B3 < 0, ABS(B2 + B3 - 1) > 0.0001, B4 <= 0, B5 <= 0, B6 <= 0, B7 <= 0), "Invalid Mixture Inputs", ROUND(((B2 * B4) / (B2 + B3 * B6) + (B3 * B5) / (B3 + B2 * B7)) - (B2 * B4 + B3 * B5), 2))

Further reading

• Microsoft Support — ABS function