Thermodynamics of gases in nano cavities

In nanoscale, gas density is not really homogenous even in thermodynamic equilibrium especially in a region near to the domain boundaries due to the wave character of gas particles. This inhomogeneous region is called quantum boundary layer (QBL) since its thickness goes to zero when the Planck's constant goes to zero. QBL can be neglected and density is assumed to be homogenous as long as thermal de Broglie wavelength (λ_T) of particles is negligible in comparison with the domain sizes. In nanoscale, however, this condition breaks down and QBL changes the thermodynamic behaviour of gases considerably. In literature, density distribution of a Maxwellian gas has been examined for only a rectangular domain to obtain the analytical results. In this study, density distribution is examined for some regular and irregular domain geometries for which the analytical solution is not possible. It is shown that QBL covers the whole surface of the domain and both thickness and density profile of QBL are independent of the domain geometry. It is concluded that QBL has a universal thickness and density profile for a Maxwellian gas. Furthermore, an effective quantum potential is introduced to explain the inhomogeneous density distribution in thermodynamic equilibrium.