The evaporation of a liquid slab into vacuum is studied by numerical solutions of the Enskog–Vlasov equation for a fluid of spherical molecules interacting by Sutherland potential. The equation provides a simplified description of the microscopic behavior of the fluid but it has the capability of handling both the liquid and vapor phase, thus eliminating the necessity of postulating ad hoc models for boundary conditions at the vapor-liquid interface. This work focuses on obtaining the structure of the vapor-liquid interface in nonequilibrium conditions as well as the distribution function of evaporating molecules. The results show that the molecules crossing a properly defined vapor-liquid boundary have an almost Maxwellian distribution function and that the vapor phase is reasonably well described by the Boltzmann equation with diffusive boundary condition.

We study by direct numerical simulation the motion of incompressible fluid contained in an ellipsoid of revolution with ellipticity 0.1 or less which rotates about its axis of symmetry and whose rotation axis is executing precessional motion. A solution to this problem for an inviscid fluid given by Poincaré (1910) predicts motion of uniform vorticity. The simulations show how the orientation of the average vorticity of a real fluid is influenced by both pressure and viscous torques exerted by the boundaries. Axisymmetric shear layers appear which agree well with those observed experimentally by Malkus (1968). Shear caused by deviations from a velocity field with uniform vorticity triggers an instability consisting of waves propagating around the average rotation axis of the fluid. The Ekman layers at the boundaries may also become unstable.

Gas flow rates in microchannels have been rigorously evaluated by means of a variational technique which applies to the integrodifferential form of the Boltzmann equation based on the Bhatnagar, Gross, and Krook model. The Maxwell scattering kernel has been used to describe the gas-wall interactions in the most general case of two surfaces with different accommodation coefficients.

The objective of the present paper is to provide an analytic expression for the first- and second-order velocity slip coefficients. Therefore, gas flow rates in microchannels have been rigorously evaluated in the near-continuum limit by means of a variational technique which applies to the integrodifferential form of the Boltzmann equation based on the true linearized collision operator. The diffuse-specular reflection condition of Maxwell’s type has been considered in order to take into account the influence of the accommodation coefficient on the slip parameters. The polynomial form of the Knudsen number obtained for the Poiseuille mass flow rate and the values of the velocity slip coefficients, found on the basis of our variational solution of the linearized Boltzmann equation for hard-sphere molecules, are analyzed in the frame of potential applications of classical continuum numerical tools in simulations of microscale flows.

As a model for the precession-driven motion in the Earth's core, the flow of incompressible fluid inside a spheroidal shell with imposed rotation and precession is investigated by direct numerical simulation. In one set of simulations, free-slip boundary conditions are used in order to isolate inertial instabilities. These occur as triad resonances involving pairs of inertial modes which have the form of columnar vortices. The simulations reproduce the phenomenon of ‘resonant collapses’ in which the excited modes periodically grow and suddenly decay into turbulence. The experiments of Malkus (1968) are simulated using a hyperviscosity. A hysteretic transition towards developed turbulence observed in one of these experiments can be interpreted as a feature of the basic laminar flow rather than the instability itself. A similar transition can be excluded for Earth's parameters.