= Kinetic estimates of gas transport coefficients
{title2=$D\sim\overline v\lambda/3,\quad\eta\sim nm\overline v\lambda/3,\quad\kappa\sim nc_v\overline v\lambda/3$}
In a dilute <gas> whose <mean free path> $\lambda$ is short compared with macroscopic gradient lengths, <particles> carry properties from their previous <collisions> over distances of order $\lambda$. A first-gradient isotropic estimate gives a transported flux $-n\overline v\lambda\nabla a/3$ for a property $a$ carried per <particle>. Applying this reasoning to species abundance, directed <momentum> $mu_x$ and thermal <energy> with per-particle <heat capacity> $c_v$ gives <diffusivity> $D\sim\overline v\lambda/3$, <dynamic viscosity> $\eta\sim nm\overline v\lambda/3$ and <thermal conductivity> $\kappa\sim nc_v\overline v\lambda/3$. These numerical prefactors are estimates, not exact collision-integral results.
For a constant hard-sphere diameter $d$, $\lambda\propto1/(nd^2)$ and $\overline v\propto\sqrt{T/m}$. Consequently $\eta\propto\sqrt{mT}/d^2$, $\kappa\propto c_v\sqrt{T/m}/d^2$ and $D\propto\sqrt{T/m}/(nd^2)$. At fixed <pressure> the last scales as $T^{3/2}/p$. The near pressure-independence of <viscosity> and <thermal conductivity> applies only while gas-gas <collisions>, rather than apparatus walls, determine the <mean free path>. Temperature-dependent cross-sections and internal molecular excitations change the simple <power laws>.
Back to article page
