The Enskog--Vlasov equaton: a kinetic model describing gas, liquid, and solid

The Enskog--Vlasov (EV) equation is a semi-empiric kinetic model describing gas-liquid phase transitions. In the framework of the EV equation, these correspond to an instability with respect to infinitely long perturbations, developing in a gas state when the temperature drops below (or density rises above) a certain threshold. In this paper, we show that the EV equation describes one more instability, with respect to perturbations with a finite wavelength and occurring at a higher density. This instability corresponds to fluid-solid phase transition and the perturbations' wavelength is essentially the characteristic scale of the emerging crystal structure. Thus, even though the EV model does not describe the fundamental physics of the solid state, it can `mimic' it -- and, thus, be used in applications involving both evaporation and solidification of liquids. Our results also predict to which extent a pure fluid can be overcooled before it definitely turns into a solid

Steady rimming flows with surface tension

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

Kinetic approach to condensation: diatomic gases with dipolar molecules

We derive a kinetic equation for rarefied diatomic gases whose molecules have a permanent dipole moment. Estimating typical parameters of such gases, we show that quantum effects cannot be neglected when describing the rotation of molecules, which we thus approximate by quantum rotators. The intermolecular potential is assumed to involve an unspecified short-range repulsive component and a long-range dipole-dipole Coulomb interaction. In the kinetic equation derived, the former and the latter give rise, respectively, to the collision integral and a self-consistent electric field generated collectively by the dipoles (as in the Vlasov model of plasma). It turns out that the characteristic period of the molecules’ rotation is much shorter than the time scale of the collective electric force and the latter is much shorter than the time scale of the collision integral, which allows us to average the kinetic equation over rotation. In the averaged model, collisions and interaction with the collective field affect only those rotational levels of the molecules that satisfy certain conditions of synchronism. It is then shown that the derived model does not describe condensation; i.e., permanent dipoles of molecules cannot exert the level of intermolecular attraction necessary for condensation. It is argued that an adequate model of condensation must include the temporary dipoles that molecules induce on each other during interaction, and that this model must be quantum, not classical.info:eu-repo/semantics/publishedVersio

Energy conservation and H theorem for the Enskog-Vlasov equation

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.info:eu-repo/semantics/publishedVersio

On the approach to the critical solution in leading order thin-film coating and rimming flow

The approach to the critical solution in leading order coating and rimming flow of a thin fluid film on a uniformly rotating horizontal cylinder is investigated. In particular, it is shown that the weight of the leading order 'full film' solution approaches its critical maximum value with logarithmically infinite slope as the volume flux approaches its critical value

Modeling the physics of interaction of high-pressure arcs with their electrodes: advances and challenges

Incorporation of realistic models of plasma-electrode interaction remains a bottleneck in the development of predictive models of devices with high-pressure arcs. The most important aspects of the underlying physics have already been understood, so no fundamentally new physical mechanisms have been described in the recent publications (which are many); the aim was rather to develop practicable numerical models that adequately describe known mechanisms. Unfortunately, no universally accepted numerical models have emerged: the developed models are in many cases incompatible with each other and it is not easy to identify the place of each model in the global picture. The aim of this contribution is to summarize physically justified descriptions of the interaction of high-pressure arcs with their electrodes and to survey from this point of view the recent works, thus bringing them into a kind of system as possible. The relevant aspects of the conventional LTE arc models are discussed. Outstanding challenges for future work are identified.info:eu-repo/semantics/publishedVersio

Understanding and modelling plasma–electrode interaction in high-pressure arc discharges: a review

Considerable advances have been attained during the last decade in the theoretical and experimental investigation of electrode phenomena in high-pressure arc discharges, in particular, in low-current arcs that occur in high-intensity discharge lamps. The aim of this paper is to deliver a concise review of the understanding achieved and modelling methods developed.info:eu-repo/semantics/publishedVersio

Bifurcations of current transfer through a collisional sheath with ionization and self-organization on glow cathodes

A bifurcation analysis is performed of a dc glow discharge between parallel electrodes and of a dc near cathode space-charge sheath bordering a uniform plasma column. A model of plasma is considered with a single ion species and motion of the charged particles dominated by drift. Bifurcation points are found at which steady-state modes with spots on the cathode branch off from the abnormal mode or from the mode corre sponding to the falling section of the current-density–voltage characteristic. In both discharge configurations, bifurcations in the abnormal mode have been detected; an unexpected result given that loss of stability and pattern appearance in dc gas discharges are usually associated with a negative differential resistance of the discharge. The conclusion is drawn that the two most important mechanisms governing appearance of patterns on glow cathodes, which are electrostatic mechanism and diffusion, produce competing effects: the former favors appearance of modes with multiple spots, while the latter favors appearance of a mode with one spot. This may explain the appearance in experiments of a normal spot or, alternatively, of patterns with multiple spots.info:eu-repo/semantics/publishedVersio