Velocity Distribution of a Dilute Chemically Reacting Gas

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Abstract
From the Wigner—Wilkins integral equation for the velocity distribution of a dilute chemically reacting gas which exchanges energy with a Maxwellian diluent gas, a simple integral equation for the high-energy region is derived. For a constant reaction cross section σr, the velocity distribution of the reactive molecules in the high-energy region is n(x)=xp exp(—x2), where p=2(1−λp)/(1−λ2)(1+σr/σs), σs is the scattering cross section, λ=(1—μ)/(1+μ), μ is the ratio of the reactive to diluent molecule mass, and x is the normalized velocity of the reactive molecule. A modified form of the Wigner—Wilkins equation is then used to extend these results into the thermal region. Small changes in the reaction cross section can produce significant changes in the velocity distribution; the perturbations of the Maxwellian distribution become even more pronounced when scattering is anisotropic in the forward direction.