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Transport Phenomena

  • 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.

Keywords: 
mean free path, coefficient of diffusion, effective diameter, rarefied gas, thermal flux, viscosity, heat, conductivity
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