Applied Nanophotonics, Liquid Crystals and Biomedical Optics

Within the kinetic theory of an ideal gas, the flux of particles having a number density n, and average velocity v̄ impinging on a plane from one side, is sometimes written in textbooks as nv̄/6 and sometimes as nv̄/4. The validity of each expression is worked out here with emphasis on their effect on the pre-factor for the expressions of the transport parameters such as viscosity, diffusion coefficient and heat conductivity. It is shown that nv̄/4 is valid in equilibrium while only when there are gradients, effectively the flux becomes nv̄/6. For the correct derivation of the transport parameters the introduction of a distribution function for the collision times or mean free paths is essential. A methodology is suggested on how to teach this subject to undergraduate and graduate students.