105 research outputs found
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
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
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
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 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 . 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
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