Thermodynamics of gases in nano cavities

It is evident that density of a gas confined in a macro domain is homogenous in thermodynamic equilibrium. Actually, density distribution losses its homogeneity in a small region near to the domain boundaries due to the wave character of gas particles. This inhomogeneous gas region is called quantum boundary layer (QBL) since its thickness is in the order of thermal de Broglie wavelength (λ_T) of gas particles. Inhomogeneous region can be neglected and density is assumed to be homogenous as long as λ_T is negligible in comparison with the domain sizes. In nano scale, however, this condition breaks down and the existence of QBL changes the thermodynamic behaviour of gases considerably. It causes some interesting results like anisotropic pressure, size dependent diffusion, thermosize effects. In literature, density distribution of a Maxwellian gas has been examined for only a rectangular domain to obtain the analytical expressions for both density distribution and the thickness of QBL. 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 whatever the domain geometry is. Also it is seen that the thickness and density profile of QBL are independent of the domain geometry. Therefore it can be concluded that QBL has a universal thickness and density profile for a Maxwellian gas. Furthermore, an effective quantum potential (EQP) is defined to represent the true interaction between gas particles and boundaries. EQP explains the inhomogeneous gas density in thermodynamic equilibrium.