Global Thermodynamics for Heat Conduction Systems

We propose the concept of global temperature for spatially non-uniform heat conduction systems. With this novel quantity, we present an extended framework of thermodynamics for the whole system such that the fundamental relation of thermodynamics holds, which we call "global thermodynamics" for heat conduction systems. Associated with this global thermodynamics, we formulate a variational principle for determining thermodynamic properties of the liquid-gas phase coexistence in heat conduction, which corresponds to the natural extension of the Maxwell construction for equilibrium systems. We quantitatively predict that the temperature of the liquid-gas interface deviates from the equilibrium transition temperature. This result indicates that a super-cooled gas stably appears near the interface.Comment: 59 pages, 20 figure

Thermodynamics of gas–liquid colloidal equilibrium states: hetero-phase fluctuations

Following on from two previous JETC (Joint European Thermodynamics Conference) presentations, we present a preliminary report of further advances towards the thermodynamic description of critical behavior and a supercritical gas-liquid coexistence with a supercritical fluid mesophase defined by percolation loci. The experimental data along supercritical constant temperature isotherms (T >= T-c) are consistent with the existence of a two-state mesophase, with constant change in pressure with density, rigidity, (dp/d rho) (T), and linear thermodynamic state-functions of density. The supercritical mesophase is bounded by 3rd-order phase transitions at percolation thresholds. Here we present the evidence that these percolation transitions of both gaseous and liquid states along any isotherm are preceded by pre-percolation hetero-phase fluctuations that can explain the thermodynamic properties in the mesophase and its vicinity. Hetero-phase fluctuations give rise to one-component colloidal-dispersion states; a single Gibbs phase retaining 2 degrees of freedom in which both gas and liquid states with different densities percolate the phase volume. In order to describe the thermodynamic properties of two-state critical and supercritical coexistence, we introduce the concept of a hypothetical homo-phase of both gas and liquid, defined as extrapolated equilibrium states in the pre-percolation vicinity, with the hetero-phase fractions subtracted. We observe that there can be no difference in chemical potential between homo-phase liquid and gaseous states along the critical isotherm in mid-critical isochoric experiments when the meniscus disappears at T = T-c. For T > T-c, thermodynamic states comprise equal mole fractions of the homo-phase gas and liquid, both percolating the total phase volume, at the same temperature, pressure, and with a uniform chemical potential, stabilised by a positive finite interfacial surface tension.info:eu-repo/semantics/publishedVersio

Layering Transitions and Solvation Forces in an Asymmetrically Confined Fluid

We consider a simple fluid confined between two parallel walls (substrates), separated by a distance L. The walls exert competing surface fields so that one wall is attractive and may be completely wet by liquid (it is solvophilic) while the other is solvophobic. Such asymmetric confinement is sometimes termed a `Janus Interface'. The second wall is: (i) purely repulsive and therefore completely dry (contact angle 180 degrees) or (ii) weakly attractive and partially dry (the contact angle is typically in the range 160-170 degrees). At low temperatures, but above the bulk triple point, we find using classical density functional theory (DFT) that the fluid is highly structured in the liquid part of the density profile. In case (i) a sequence of layering transitions occurs: as L is increased at fixed chemical potential (mu) close to bulk gas--liquid coexistence, new layers of liquid-like density develop discontinuously. In contrast to confinement between identical walls, the solvation force is repulsive for all wall separations and jumps discontinuously at each layering transition and the excess grand potential exhibits many metastable minima as a function of the adsorption. For a fixed temperature T=0.56Tc, where Tc is the bulk critical temperature, we determine the transition lines in the L, mu plane. In case (ii) we do not find layering transitions and the solvation force oscillates about zero. We discuss how our mean-field DFT results might be altered by including effects of fluctuations and comment on how the phenomenology we have revealed might be relevant for experimental and simulation studies of water confined between hydrophilic and hydrophobic substrates, emphasizing it is important to distinguish between cases (i) and (ii).Comment: 16 pages, 13 figure

Liquid-liquid equilibrium for monodisperse spherical particles

A system of identical particles interacting through an isotropic potential that allows for two preferred interparticle distances is numerically studied. When the parameters of the interaction potential are adequately chosen, the system exhibits coexistence between two different liquid phases (in addition to the usual liquid-gas coexistence). It is shown that this coexistence can occur at equilibrium, namely, in the region where the liquid is thermodynamically stable.Comment: 6 pages, 8 figures. Published versio

Phase transitions of fluids in heterogeneous pores

We study phase behaviour of a model fluid confined between two unlike parallel walls in the presence of long range (dispersion) forces. Predictions obtained from macroscopic (geometric) and mesoscopic arguments are compared with numerical solutions of a non-local density functional theory. Two capillary models are considered. For a capillary comprising of two (differently) adsorbing walls we show that simple geometric arguments lead to the generalized Kelvin equation locating capillary condensation very accurately, provided both walls are only partially wet. If at least one of the walls is in complete wetting regime, the Kelvin equation should be modified by capturing the effect of thick wetting films by including Derjaguin's correction. Within the second model, we consider a capillary formed of two competing walls, so that one tends to be wet and the other dry. In this case, an interface localized-delocalized transition occurs at bulk two-phase coexistence and a temperature $T^*(L)$ depending on the pore width $L$. A mean-field analysis shows that for walls exhibiting first-order wetting transition at a temperature $T_{w}$, $T_{s}>T^*(L)>T_{w}$, where the spinodal temperature $T_{s}$ can be associated with the prewetting critical point, which also determines a critical pore width below which the interface localized-delocalized transition does not occur. If the walls exhibit critical wetting, the transition is shifted below $T_{w}$ and for a model with the binding potential $W(\ell)=A(T)\ell^{-2}+B(T)\ell^{-3}+\cdots$, where $\ell$ is the location of the liquid-gas interface, the transition can be characterized by a dimensionless parameter $\kappa=B/(AL)$, so that the fluid configuration with delocalized interface is stable in the interval between $\kappa=-2/3$ and $\kappa\approx-0.23$.Comment: 18 pages, 12 figure

Dynamic Phase Transitions in PVT Systems

The main objective of this article are two-fold. First, we introduce some general principles on phase transition dynamics, including a new dynamic transition classification scheme, and a Ginzburg-Landau theory for modeling equilibrium phase transitions. Second, apply the general principles and the recently developed dynamic transition theory to study dynamic phase transitions of PVT systems. In particular, we establish a new time-dependent Ginzburg-Landau model, whose dynamic transition analysis is carried out. It is worth pointing out that the new dynamic transition theory, along with the dynamic classification scheme and new time-dependent Ginzburg Landau models for equilibrium phase transitions can be used in other phase transition problems, including e.g. the ferromagnetism and superfluidity, which will be reported elsewhere. In addition, the analysis for the PVT system in this article leads to a few physical predications, which are otherwise unclear from the physical point of view

Roles of energy dissipation in a liquid-solid transition of out-of-equilibrium systems

Self-organization of active matter as well as driven granular matter in non-equilibrium dynamical states has attracted considerable attention not only from the fundamental and application viewpoints but also as a model to understand the occurrence of such phenomena in nature. These systems share common features originating from their intrinsically out-of-equilibrium nature. It remains elusive how energy dissipation affects the state selection in such non-equilibrium states. As a simple model system, we consider a non-equilibrium stationary state maintained by continuous energy input, relevant to industrial processing of granular materials by vibration and/or flow. More specifically, we experimentally study roles of dissipation in self-organization of a driven granular particle monolayer. We find that the introduction of strong inelasticity entirely changes the nature of the liquid-solid transition from two-step (nearly) continuous transitions (liquid-hexatic-solid) to a strongly discontinuous first-order-like one (liquid-solid), where the two phases with different effective temperatures can coexist, unlike thermal systems, under a balance between energy input and dissipation. Our finding indicates a pivotal role of energy dissipation and suggests a novel principle in the self-organization of systems far from equilibrium. A similar principle may apply to active matter, which is another important class of out-of-equilibrium systems. On noting that interaction forces in active matter, and particularly in living systems, are often non-conservative and dissipative, our finding may also shed new light on the state selection in these systems.Comment: 17 pages, 11 figure

Study of theoretical models for the liquid-vapor and metal-nonmetal transitions of alkali fluids

Theoretical models for the liquid-vapor and metal-nonmetal transitions of alkali fluids are investigated. Mean-field models are considered first but shown to be inadequate. An alternate approach is then studied in which each statistical configuration of the material is treated as inhomogeneous, with the energy of each ion being determined by its local environment. Nonadditive interactions, due to valence electron delocalization, are a crucial feature of the model. This alternate approach is implemented within a lattice-gas approximation which takes into account the observed mode of expansion in the materials of interest and which is able to treat the equilibrium density fluctuations. We have carried out grand canonical Monte Carlo simulations, for this model, which allow a unified, self-consistent, study of the structural, thermodynamic, and electronic properties of alkali fluids. Applications to Cs, Rb, K, and Na yield results in good agreement with observations.Comment: 13 pages, REVTEX, 10 ps figures available by e-mail