The Enskog-Vlasov (EV) equation is a widely used semiphenomenological model of gas-liquid phase transitions. We show that it does not generally conserve energy, although there exists a restriction on its coefficients for which it does. Furthermore, if an energy-preserving version of the EV equation satisfies an $H$ theorem as well, it can be used to rigorously derive the so-called Maxwell construction which determines the parameters of liquid-vapor equilibria. Finally, we show that the EV model provides an accurate description of the thermodynamics of noble fluids, and there exists a version simple enough for use in applications.

We examine the dynamics of a thin film of viscous fluid on the inside surface of a cylinder with horizontal axis, rotating around this axis. An asymptotic equation is derived, which takes into account two orders of the so-called lubrication approximation. The equation admits a solution describing a steady-state distribution of film around the cylinder, and we examine the stability of this solution. It is demonstrated that the linearized problem admits infinitely many harmonic solutions, all of which have real frequencies (are neutrally stable). On the other hand, there are non-harmonic solutions that ‘explode’ (develop singularities) in a finite time. Systems having solutions of both types simultaneously have never been described in the literature. An example of this phenomenon is the main result of this paper.

We examine steady flows of a thin film of viscous fluid on the inside of a cylinder with horizontal axis, rotating about this axis. If the amount of fluid in the cylinder is sufficiently small, all of it is entrained by rotation and the film is distributed more or less evenly. For medium amounts, the fluid accumulates on the ‘rising’ side of the cylinder and, for large ones, pools at the cylinder's bottom. The paper examines rimming flows with a pool affected by weak surface tension. Using the lubrication approximation and the method of matched asymptotics, we find a solution describing the pool, the ‘outer’ region, and two transitional regions, one of which includes a variable (depending on the small parameter) number of asymptotic zones.

We examine the dynamics of a thin film of viscous fluid on the inside surface of a cylinder with horizontal axis, rotating about this axis. The stability of the film has been previously explored using the leading-order lubrication approximation, under which it was found to be neutrally stable. In the present paper, we examine how the stability of the film is affected by higher-order corrections, such as inertia (described by the material derivatives in the Navier–Stokes equations), surface tension, and the hydrostatic pressure gradient. Assuming that these effects are weak, we derive an asymptotic equation which takes them into account as perturbations. The equation is used to examine the stability of the steady-state distribution of film around the cylinder (rimming flow) with respect to linear disturbances with harmonic dependence on time (normal modes). It is shown that hydrostatic pressure gradient does not affect those at all, and the effect of surface tension is weak—whereas inertia always causes instability. The inertial instability, however, can be inhibited by viscosity, which can make the characteristic time of growth so large that the film would be effectively stable.