arXiv subjects

E. S. Benilov

Publications and source records attributed to E. S. Benilov.

17 recordsLinked to original sources

arXiv2026

Supercooling of liquids, as described by the Enskog-Vlasov kinetic equation

A model combining Enskog's collision integral for dense fluids with a Vlasov-style description of the van der Waals force is applied to supercooling. First, the spinodal temperature $T_{s}$ is calculated, at which a liquid becomes unstable to small perturbations and transitions to solid. In particular, it turns out that isochoric cooling allows one to reach a lower temperature than isobaric cooling. Second, the surface tension of a supercooled liquid-vapor interface is shown to diverge at $T_{s}$. The singularity is caused by an oscillatory region emerging on the liquid side of the interface as $T\rightarrow T_{s}$; it develops because the liquid approaches instability, and the interface starts radiating (so far, evanescent) waves. At $T=T_{s}$, the waves cease to be evanescent and the oscillatory region extends to infinity -- hence, the singularity of the surface tension. Since this effect has a clear physical interpretation, it should occur regardless of the model and approximations under which it was obtained. This and the other results of the paper are illustrated using argon and several other fluids.

cond-mat.stat-mech↗

arXiv2026

Multispecies Bhatnagar-Gross-Krook models and the Onsager reciprocal relations

It is shown that most of the existing versions of the Bhatnagar$-$Gross$-$Krook model $-$ those whose coefficient are independent of the molecular velocity $-$ do not satisfy the Onsager relations. This circumstance poses a problem when calibrating these models, making their transport properties match those of a specific fluid.

cond-mat.stat-mech↗

arXiv2024

Does the van der Waals force play a part in evaporation?

It is argued that the van der Waals force exerted by the liquid and vapor/air on the molecules escaping from one phase into the other strongly affects the characteristics of evaporation. This is shown using two distinct descriptions of the van der Waals force: the Vlasov and diffuse-interface models, each of which is applied to two distinct settings: a liquid evaporating into its vapor and a liquid evaporating into air (in all cases, the vapor-to-liquid density ratio is small). For the former setting, the results are consistent with the Hertz--Knudsen Law (HKL), but the evaporation/condensation probability is very small (in the classical HKL, it is order one). For the latter setting, the dependence of the evaporation rate on the difference between the saturated vapor pressure and its actual value is shown to be nonlinear (whereas the classical HKL predicts a linear dependence). The difference between the two settings indicates that the van der Waals force exerted by the air strongly affects evaporation (contrary to the general assumption that the ambient gas is unimportant). Finally, the diffuse interface model is shown to be inapplicable in a narrow region at the outskirts of the interface -- as a result, it noticeably underestimates the evaporative flux by comparison with the (more accurate) Vlasov model.

cond-mat.soft↗

arXiv2023

Nonisothermal evaporation

Evaporation of a liquid layer on a substrate is examined without the often-used isothermality assumption -- i.e., temperature variations are accounted for. Qualitative estimates show that nonisothermality makes the evaporation rate depend on the conditions the substrate is maintained at. If it is thermally insulated, evaporative cooling dramatically slows evaporation down; the evaporation rate tends to zero with time and cannot be determined by measuring the external parameters only. If, however, the substrate is maintained at a fixed temperature, the heat flux coming from below sustains evaporation at a finite rate -- deducible from the fluid's characteristics, relative humidity, and the layer's depth (whose importance has not been recognized before). The qualitative predictions are quantified using the diffuse-interface model applied to a liquid evaporating into its own vapor.

cond-mat.soft↗

arXiv2022

The multicomponent diffuse-interface model and its application to water/air interfaces

Fundamental properties of the multicomponent diffuse-interface model (DIM), such as the maximum entropy principle and conservation laws, are used to explore the basic interfacial dynamics and phase transitions in fluids. Flat interfaces with monotonically-changing densities of the components are proved to be stable. A liquid layer in contact with oversaturated but stable vapour is shown to either fully evaporate or eternally expand (depending on the initial perturbation), whereas a liquid in contact with saturated vapour always evaporates. If vapour is bounded by a solid wall with a sufficiently large contact angle, spontaneous condensation occurs in the vapour. The external parameters of the multicomponent DIM -- e.g., the Korteweg matrix describing the long-range intermolecular forces -- are determined for the water-air combination. The Soret and Dufour effects are shown to be negligible in this case, and the interfacial flow, close to isothermal.

physics.flu-dyn↗

arXiv2022

Capillary condensation of saturated vapor in a corner formed by two intersecting walls

The dynamics of saturated vapor between two intersecting walls is examined. It is shown that, if the angle $ϕ$ between the walls is sufficiently small, the vapor becomes unstable, and spontaneous condensation occurs in the corner, similar to the so-called capillary condensation of vapor into a porous medium. As a result, an ever-growing liquid meniscus develops near the corner. The diffuse-interface model and the lubrication approximation are used to demonstrate that the meniscus grows if and only if $ϕ+2θ<π$, where $θ$ is the contact angle corresponding to the fluid/solid combination under consideration. This criterion has a simple physical explanation: if it holds, the meniscus surface is concave -- hence, the Kelvin effect causes condensation. Once the thickness of the condensate exceeds by an order of magnitude the characteristic interfacial thickness, the volume of the meniscus starts to grow linearly with time. If the near-vertex region of the corner is smoothed, the instability can be triggered off only by finite-size perturbations, such that include enough liquid to cover the smoothed aria by a microscopically-thin liquid film.

cond-mat.soft↗

arXiv2022

Dynamics of a drop floating in vapor of the same fluid

Evaporation of a liquid drop surrounded by either vapor of the same fluid, or vapor and air, is usually attributed to vapor diffusion -- which, however, does not apply to the former setting, as pure fluids do not diffuse. The present paper puts forward an additional mechanism, one that applies to both settings. It is shown that disparities between the drop and vapor in terms of their pressure and chemical potential give rise to a flow. Its direction depends on the vapor density and the drop's size. In undersaturated or saturated vapor, all drops evaporate -- but in oversaturated (yet thermodynamically stable) vapor, there exists a critical radius: smaller drops evaporate, larger drops act as centers of condensation and grow. The developed model is used to estimate the evaporation time of a drop floating in saturated vapor. It is shown that, if the vapor-to-liquid density ratio is small, so is the evaporative flux -- as a result, millimeter-sized water drops at temperatures lower than $70^{\circ}\mathrm{C}$ survive for days. If, however, the temperature is comparable (but not necessarily close) to its critical value, such drops evaporate within minutes. Micron-sized drops, in turn, evaporate within seconds for all temperatures between the triple and critical points.

physics.flu-dyn↗

arXiv2021

The dynamics of liquid films, as described by the diffuse-interface model

The dynamics of a thin layer of liquid, between a flat solid substrate and an infinitely-thick layer of saturated vapor, is examined. The liquid and vapor are two phases of the same fluid, governed by the diffuse-interface model. The substrate is maintained at a fixed temperature, but in the bulk of the fluid the temperature is allowed to vary. The slope $\varepsilon$ of the liquid/vapor interface is assumed to be small, as is the ratio of its thickness to that of the film. Three asymptotic regimes are identified, depending on the vapor-to-liquid density ratio $ρ_{v}/ρ_{l}$. If $ρ_{v}/ρ_{l}\sim1$ (which implies that the temperature is comparable, but not necessarily close, to the critical value), the evolution of the interface is driven by the vertical flow due to liquid/vapor phase transition, with the horizontal flow being negligible. In the limit $ρ_{v}/ρ_{l}\rightarrow0$, it is the other way around, and there exists an intermediate regime, $ρ_{v}/ρ_{l}\sim\varepsilon^{4/3}$, where the two effects are of the same order. Only the $ρ_{v}/ρ_{l}\rightarrow0$ limit is mathematically similar to the case of incompressible (Navier--Stokes) liquids, whereas the asymptotic equations governing the other two regimes are of different types.

cond-mat.stat-mech↗

arXiv2021

Dependence of the surface tension and contact angle on the temperature, as described by the diffuse-interface model

Four results associated with the diffuse-interface model (DIM) for contact lines are reported in this paper. First, a boundary condition is derived, which states that the fluid near a solid wall must have a certain density $ρ_{0}$ depending on the solid's properties. Unlike previous derivations, the one presented here is based on the same physics as the DIM itself and does not require additional assumptions. Second, asymptotic estimates are used to check a conjecture lying at the foundation of the DIM, as well as all other models of contact lines: that liquid-vapor interfaces are nearly isothermal. It turns out that, for water, they are not -- although, for a more viscous fluid, they can be. The non-isothermaility occurs locally, near the interface, but can still affect the contact-line dynamics. Third, the DIM coupled with a realistic equation of state for water is used to compute the dependence of the surface tension $σ$ on the temperature $T$, which agrees well with the empiric $σ(T)$. Fourth, the same framework is used to compute the static contact angle of a water-vapor interface. It is shown that, with increasing temperature, the contact angle becomes either $180^{\circ}$ (perfect hydrophobicity) or $0^{\circ}$ (perfect hydrophilicity), depending on whether $ρ_{0}$ matches the density of saturated vapor or liquid, respectively. Such behavior presumably occurs in all fluids, not just water, and for all sufficiently strong variations of parameters, not just that of the temperature -- as corroborated by existing observations of drops under variable electric field.

physics.flu-dyn↗

arXiv2021

Nonexistence of two-dimensional sessile drops in the diffuse-interface model

The diffuse-interface model (DIM) is a widely used tool for modeling fluid phenomena involving interfaces -- such as, for example, sessile drops (liquid drops on a solid substrate, surrounded by saturated vapor) and liquid ridges (two-dimensional sessile drops). In this work, it is proved that, surprisingly, the DIM does not admit solutions describing static liquid ridges. If, however, the vapor-to-liquid density ratio is small -- as, for example, for water at room temperature -- the ridges can still be observed as quasi-static states, as their evolution is too slow to be distinguishable from evaporation. Interestingly, the nonexistence theorem cannot be extended to axisymmetric sessile drops and ridges near a vertical wall, which are not ruled out.

physics.flu-dyn↗

arXiv2021

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.

cond-mat.stat-mech↗

arXiv2021

Can a liquid drop on a substrate be in equilibrium with saturated vapor?

It is well-known that liquid and saturated vapor, separated by a flat interface in an unbounded space, are in equilibrium. One would similarly expect a liquid drop, sitting on a flat substrate, to be in equilibrium with the vapor surrounding it. Yet, it is not: as shown in this work, the drop evaporates. Mathematically, this conclusion is deduced using the diffuse-interface model, but it can also be reformulated in terms of the maximum-entropy principle, suggesting model independence. Physically, evaporation of drops is due to the so-called Kelvin effect, which gives rise to a liquid-to-vapor mass flux in all cases where the boundary of the liquid phase is convex.

cond-mat.soft↗

arXiv2021

Paradoxical predictions of liquid curtains with surface tension

This paper examines two-dimensional liquid curtains ejected at an angle to the horizontal and affected by gravity and surface tension. The flow is, to leading order, shearless and viscosity, negligible. The Froude number is large, so that the radius of the curtain's curvature exceeds its thickness. The Weber number is close to unity, so that the forces of inertia and surface tension are almost perfectly balanced. An asymptotic equation is derived under these assumptions, and its steady solutions are explored. It is shown that, for a given pair of ejection velocity/angle, infinitely many solutions exist, each representing a steady curtain with a stationary capillary wave superposed on it. These solutions describe a rich variety of behaviours: in addition to arching downwards, curtains can zigzag downwards, self-intersect, and even rise until the initial supply of the liquid's kinetic energy is used up. The last type of solutions corresponds to a separatrix between upward- and downward-bending curtains -- in both cases, self-intersecting (such solutions are meaningful only until the first intersection, after which the liquid just splashes down). Finally, suggestions are made as to how the existence of upward-bending curtains can be tested experimentally.

physics.flu-dyn↗

arXiv2021

Asymptotic reductions of the diffuse-interface model, with applications to contact lines in fluids

The diffuse-interface model (DIM) is a tool for studying interfacial dynamics. In particular, it is used for modeling contact lines, i.e., curves where a liquid, gas, and solid are in simultaneous contact. As well as all other models of contact lines, the DIM implies an additional assumption: that the flow near the liquid/gas interface is isothermal. In this work, this assumption is checked for the four fluids for which all common models of contact lines fail. It is shown that, for two of these fluids (including water), the assumption of isothermality does not hold.

cond-mat.soft↗

arXiv2019

Peculiar property of noble gases and its explanation through the Enskog--Vlasov model

A new observation is presented that the densities and temperatures at the critical and triple points ($n_{cr}$, $n_{tp}$, $T_{cr}$, and $T_{tp}$) of neon, argon, krypton, and xenon are such that $T_{cr}/T_{tp}=1.803\pm 0.5\%$ and $n_{cr}/n_{tp}=$ $0.3782\pm 1.7\%$ (of the two remaining noble gases, helium does not have a triple point and, for radon, $n_{tp}$ is unknown). None other group of substances seem to have these parameters within such narrow ranges. We explain this peculiar property of noble gases by sphericity of their molecules, as a result of which they satisfy the Enskog--Vlasov (EV) kinetic model. The EV model has also allowed us to identify two more parameter combinations which are virtually the same for all noble gases.

cond-mat.stat-mech↗

arXiv2013

Stability of frozen waves in the Modified Cahn--Hilliard model

We examine the existence and stability of frozen waves in diblock copolymers with local conservation of the order parameter, which are described by the modified Cahn--Hilliard model. It is shown that a range of stable waves exists and each can emerge from a `general' initial condition (not only the one with the lowest density of free energy). We discuss the implications of these results for the use of block copolymers in templating nanostructures.

cond-mat.mes-hall↗

arXiv2012

Why do bubbles in Guinness sink?

Stout beers show the counter-intuitive phenomena of sinking bubbles while the beer is settling. Previous research suggests that this phenomena is due the small size of the bubbles in these beers and the presence of a circulatory current, directed downwards near the side of the wall and upwards in the interior of the glass. The mechanism by which such a circulation is established and the conditions under which it will occur has not been clarified. In this paper, we demonstrate using simulations and experiment that the flow in a glass of stout depends on the shape of the glass. If it narrows downwards (as the traditional stout glass, the pint, does), the flow is directed downwards near the wall and upwards in the interior and sinking bubbles will be observed. If the container widens downwards, the flow is opposite to that described above and only rising bubbles will be seen.

physics.flu-dyn↗