Engineering & Science
Chapman-Enskog Low-Pressure Gas Viscosity Formula (Lennard-Jones)
Calculate dilute gas dynamic viscosity μ = 2.6693 * SQRT(M * T) / (σ^2 * Ω_μ) (μPa·s) from molecular weight, absolute temperature, Lennard-Jones collision diameter σ (Å), and collision integral Ω_μ.
Why gas viscosity INCREASES with temperature—and is independent of pressure!
Unlike liquids whose viscosity plummets upon heating, dilute gases grow MORE viscous at higher temperatures because faster thermal molecules transport momentum across laminar shear layers at rate proportional to SQRT(T) / Ω_μ(T*)! Sydney Chapman and David Enskog solved the Boltzmann transport equation for Lennard-Jones (12-6) molecules to obtain the exact first-order kinetic viscosity law (Bird, Stewart & Lightfoot, Transport Phenomena): μ = 2.6693 * SQRT(M * T) / (σ^2 * Ω_μ) in micropascal-seconds (μPa·s, where 100 μPa·s = 0.1 cP)!
Evaluate nitrogen N_2 (M = 28.0134 g/mol, Lennard-Jones diameter σ = 3.798 Å): at T = 300 K (Neufeld collision integral Ω_μ = 1.074), μ = 15.80 μPa·s; heating the gas stream to T = 500 K (where higher kinetic energy weakens attractive deflection so Ω_μ drops to 0.955) raises N_2 viscosity by +45.2% to 22.93 μPa·s!
| Nitrogen N2 State (M = 28.0134, σ = 3.798 Å) | Collision Integral Ω_μ | Chapman-Enskog Viscosity μ (μPa·s) | Viscosity in Centipoise (cP) |
|---|---|---|---|
| 300 K Ambient Feed | 1.074 | 15.80 μPa·s | 0.01580 cP |
| 500 K Reactor Preheat | 0.955 | 22.93 μPa·s (+45.2%) | 0.02293 cP |
| Invalid σ <= 0 or T <= 0 | Undefined | "Invalid Kinetic Inputs" | Positivity Guard |
Chapman-Enskog Dynamic Gas Viscosity μ (μPa·s)
Computes 2.6693 * SQRT(M * T) / (σ^2 * Ω_μ) in μPa·s (= 10^-6 Pa·s) from molar mass B2 (g/mol), temperature B3 (K), Lennard-Jones diameter B4 (Å), and viscosity collision integral B5.
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B5 <= 0), "Invalid Kinetic Inputs", ROUND(2.6693 * SQRT(B2 * B3) / ((B4 ^ 2) * B5), 2))Gas Viscosity Converted to Centipoise (cP = mPa·s)
Divides μPa·s by 1,000 so values drop directly into standard chemical-engineering Reynolds number formulas.
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B5 <= 0), "Invalid Kinetic Inputs", ROUND(0.0026693 * SQRT(B2 * B3) / ((B4 ^ 2) * B5), 5))Try the example
Use the original values or change them to test your understanding.