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

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

Existence and stability of regularized shock solutions, with applications to rimming flows

This paper is concerned with regularization of shock solutions of nonlinear hyperbolic equations, i.e., introduction of a smoothing term with a coefficient ε, then taking the limit ε → 0. In addition to the classical use of regularization for eliminating physically meaningless solutions which always occur in non-regularized equa tions (e.g. waves of depression in gas dynamics), we show that it is also helpful for stability analysis. The general approach is illustrated by applying it to rimming flows, i.e., flows of a thin film of viscous liquid on the inside of a horizontal rotating cylinder, with or without surface tension (which plays the role of the regularizing effect). In the latter case, the spectrum of available linear eigenmodes appears to be continuous, but in the former, it is discrete and, most importantly, remains discrete in the limit of infinitesimally weak surface tension. The regularized (discrete) spectrum is fully determined by the point where the velocity of small perturbations vanishes, with the rest of the domain, including the shock region, being unimportant.info:eu-repo/semantics/publishedVersio

Plasmas generated by ultra-violet light rather than electron impact

We analyze, in both plane and cylindrical geometries, a collisionless plasma consisting of an inner region where generation occurs by UV illumination, and an un-illuminated outer region with no generation. Ions generated in the inner region flow outwards through the outer region and into a wall. We solve for this system's steady state, first in the quasi-neutral regime (where the Debye length ${\lambda}_D$ vanishes and analytic solutions exist) and then in the general case, which we solve numerically. In the general case a double layer forms where the illuminated and un-illuminated regions meet, and an approximately quasi-neutral plasma connects the double layer to the wall sheath; in plane geometry the ions coast through the quasi-neutral section at slightly more than the Bohm speed $c_s$. The system, although simple, therefore has two novel features: a double layer that does not require counter-streaming ions and electrons, and a quasi-neutral plasma where ions travel in straight lines with at least the Bohm speed. We close with a pr\'{e}cis of our asymptotic solutions of this system, and suggest how our theoretical conclusions might be extended and tested in the laboratory.Comment: 10 pages, 3 figures, accepted by Physics of Plasma

Dynamics of large-amplitude geostrophic flows over bottom topography

International audienceWe examine the interaction of near-surface and near- bottom flows over bottom topography. A set of asymptotic equations for geostrophic currents in a three-layer fluid is derived. The depths of the active (top/bottom) layers are assumed small, the slope of the bottom is weak, the interfacial displacement is comparable to the depths of the thinner layers. Using the equations derived, we examine the stability of parallel flows and circular eddies. It is demonstrated that eddies with non-zero near-surface component are always unstable; eddies localized in the near-bottom layer may be stable subject to additional restrictions imposed on their horizontal profiles and bottom topography