Transport Phenomena

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  • Relative number of gas molecules traversing the distance $s$ without collisions: $$ N/N_0 = e^{-s/\lambda},$$ where $\lambda$ is the mean free path.
  • Mean free path of a gas molecule: $$ \lambda = \frac{1}{\sqrt{2} \pi d^2 n},$$ where $d$ is the effective diameter of a molecule, and $n$ is the number of molecules per unit volume.
  • Coefficients of diffusion $D$, viscosity $\eta$, and heat conductivity $\varkappa$ of gases: $$D = \frac{1}{3}\langle v\rangle \lambda,\; \eta = \frac{1}{3}\langle v\rangle \lambda \rho,\; \varkappa = \frac{1}{3}\langle v\rangle \lambda \rho c_V,$$ where$\rho$ is the gas density, and $c_V$ is its specific heat capacity at constant volume.
  • Friction force acting on a unit area of plates during their motion parallel to each other in a highly rarefied gas: $$F = \frac{1}{6} \langle v \rangle \rho \left | u_1 - u_2 \right |,$$ where $u_1$ and $u_2$ are the velocities of the plates.
  • Density of a thermal flux transferred between two walls by highly rarefied gas: $$ q = \frac{1}{6} \langle v \rangle \rho c_V \left | T_1 - T_2 \right |,$$ where $T_1$ and $T_2$ are the temperatures of the walls.

 

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