Based on a recent L-L framework, we establish the acoustic limit of the Boltzmann equation for general collision kernels. The scaling of the fluctuations with respect to Knudsen number is optimal. Our approach is based on a new analysis of the compressible Euler limit of the Boltzmann equation, as well as refined estimates of Euler and acoustic solutions.

In this work we show that moment methods devised to solve the Boltzmann kinetic equation for a simple gas exhibit some inconsistencies. This puzzle, which also appears for the Chapman-Enskog method, is solved resorting to a perturbative expansion in the Knudsen number, thus allowing for a clear way to arrive at a closure condition.

We present the results of deriving the Israel-Stewart equations of relativistic dissipative fluid dynamics from kinetic theory via Grad’s 14-moment expansion. Working consistently to second order in the Knudsen number, these equations contain several new terms which are absent in previous treatments.

When two surfaces at two different temperatures are separated by a distance comparable to a mean-free path of the molecules of the ambient medium, the surfaces experience Knudsen force. This mechanical force can be important in microelectromechanical systems and in atomic force microscopy. A theoretical discussion of the magnitude of the forces and the conditions where they can be encountered i...

Comparing the rates of molecular diffusion in porous materials under different regimes of measurement may provide valuable information about the underlying mechanisms. After quite generally explaining the benefit of such a procedure, we refer to a case which in the last few years has raised controversial discussion within the community, viz. the comparison of diffusion phenomena in pores of var...

A net gas flow can be induced in the gap between periodically structured surfaces held at fixed but different temperatures when the reflection symmetry along the channel axis is broken. Such a situation arises when one surface features a ratchet structure and can be augmented by altering the boundary conditions on different parts of this surface, with some regions reflecting specularly and othe...

Knudsen forces arise in microscale systems when there is a thermal gradient with a characteristic length scale comparable to the molecular mean free path of the ambient gas. These forces are sometimes referred as radiometric or thermo-molecular forces [1] and have been recently measured experimentally in a microscale configuration using heated atomic force microscopy (AFM) probes [2]. The Knuds...

A recently established version of the discrete-ordinates method is used to develop a solution to a class of problems in the theory of rarefied-gas dynamics. In particular, an accurate solution for the flow, described by the Bhatnagar, Gross and Krook model, of a rarefied gas between two parallel plates is developed for a wide range of the Knudsen number.