Nanoscale Gas Transport

The Navier-Stokes (NS) description breaks down as characteristic flow lengthscales are on the order of, or smaller than, the molecular mean free path. Breakdown of the NS description is quantified by the Knudsen number (Kn), defined as the ratio of the molecular mean free path to the characteristic flow lengthscale. Asymptotic expansion of the Boltzmann equation in the Kn<<1 limit, shows that while the Navier-Stokes description is valid in the bulk, the inhomogeneity associated with the wall presence requires a kinetic correction, which introduces slip at the walls, as well as a kinetic boundary layer at the wall known as Knudsen layer. Slip conditions and coefficients can be rigorously and uniquely derived as matching conditions between this inner and outer solutions. While first order slip conditions have been generally determined, second order slip coefficients for the hard-sphere gas have not. We are currently working on determining a number of slip coefficients within this rigorous framework.