Thermodynamics Of Fluids Research Articles

Structural and thermodynamic properties of a freely-jointed Yukawa hard-sphere chain fluid

Abstract We continue our long-term study of the application of the product-reactant Ornstein-Zernike approach (PROZA) to polymere-fluid models. The PROZA is a theory that yields monomer-monomer pair correlation functions, from which the thermodynamics of a model fluid of polymer molecules can be obtained. Here we extend our earlier work on hard-sphere chains by adding a van der Waals attraction, modelled by a Yukawa term, to the hard-sphere interaction between monomers.

Exact Moments of Curvature Measures in the Boolean Model

Curvature measures are important for the characterization of spatial structures since many physical phenomena depend essentially on the geometry of spatial configurations. Curvature-weighted correlation functions can be defined and calculated explicitly within the Boolean model. This standard model in statistical physics generates random geometries by overlapping grains (spheres, sticks) each with arbitrary location and orientation. A general decomposition relation for characteristic functions of submanifolds based on Chern's differential kinematic formula is used to obtain exact expressions for mean values and second order moments of curvature integrals, i.e., of Minkowski functionals. An exact relation for the canonical and grand-canonical second order moments of the morphological Minkowski measures can be derived based only on thermodynamic arguments. The results are applied on the morphological thermodynamics of complex fluids where specific heats are expressed in terms of curvature moments.

Hamilton’s action principle and thermodynamics of irreversible processes — a unifying procedure for reversible and irreversible processes

Thermodynamics of irreversible processes can be included into the framework of Lagrange formalism. This formalism presents a unified method for reversible and irreversible processes. As a remarkable fact the first and the second law of thermodynamics are derived in Lagrange formalism by means of straightforward procedures. The whole information on the dynamics of a system is included in one function only, namely in its Lagrangian. In this paper the theory is presented in two courses. The first one offers an almost qualitative insight into the structure of the theory; the second one is concerned with the associated mathematics in some detail. The theory is illustrated by three representative examples: the style of the paper is chosen as to stimulate the discussions at a workshop and a school on the state-of-art of non-equilibrium thermodynamics of complex fluids, Oxford, 2000.

Binary two-phase flow with phase change in porous media

Flow of multicomponent mixtures with interphase mass transfer through porous media has been analyzed by combining thermodynamics of real fluids, the use of immiscible Boltzmann code and reconstructed porous media. A general algorithm is detailed and applied for comparison with Poiseuille flow where a semi-analytical solution can be found. A series of structures and phenomena are then analysed; attention is mostly focused on liquid to gas transition (or vaporization) and retrograde condensation; phase distribution and macroscopic quantities such as composition, liquid saturation and pressure evolution are systematically plotted. The role of the location of nucleation sites is shortly investigated with a periodically constricted tube. The total mass flow rate influenced the phase distribution and circulation in a two-dimensional network. Finally, relative permeabilities of a reconstructed medium are discussed; an interesting feature is that they follow hysteresis cycles for retrograde condensation.

Absence of Phase Transitions in the Hydrogen Bond Subsystem of Associated Fluids

Phase transitions in the hydrogen bond subsystem of associating fluids are discussed in the framework of mean-field theory. It is shown that in the simplest case of independent (noncooperative) bonds the free energy of the subsystem as a function of the numbers of hydrogen bonds is convex. The consequences of this fact for thermodynamics of hydrogen-bonded fluids and the applications for the theory of associated liquids are discussed.

Structure and thermodynamics of a polar fluid at a discretely polarized wall

The structure and thermodynamics of a dipolar hard-sphere fluid at a discretely polarized hard wall are investigated using Monte Carlo computer simulation. In contrast to a continuously polarized wall, the discrete case exhibits significantly enhanced adsorption of the fluid at the surface relative to that observed for an unpolarized wall. Significant orientational ordering of the first liquid layer is observed plus correlation with the wall polarization that extends over several layers. The relative potential and free energy are calculated as a function of the polarization angle using thermodynamic integration.

Structure and thermodynamics of a polar fluid at a discretely polarized wall

Structure and thermodynamics of a polar fluid at a discretely polarized wall

A model dipolar ellipsoidal fluid

A theoretical method previously introduced in order to study the structure and thermodynamics of a charged ellipsoidal fluid is here applied to the study of a dipolar ellipsoidal fluid. To enable the strong-coupling (large dipole) form of the direct correlation function to be written analytically, the model employs ellipsoids with charges distributed over their surfaces. This implies that the electric field at a large distance from one molecule results from many multipoles although the dipole is the dominant one. A geometric ansatz for the direct correlation function containing a small number of parameters is then constructed and the parameters determined through the means of a variational principle based upon the mean spherical approximation. From the resultant direct correlation function it is possible to determine thermodynamic properties, including the relative permittivity of the fluid and the electrostatic energy. Within the model no ferroelectric transition is observed. Further the resultant direct correlation function is in a suitable analytic form for applications to the structure of an inhomogeneous fluid. The model is applied to fluids of ellipsoids with elongations ranging between 1/5 (oblate) and 5 (prolate). The range of dipole moments and densities allows relative permitivities up to approximately 80. The results are consistent with other studies of hard dipolar fluids although the model is not precisely the same except in the special case of hard spheres.

SCOZA critical exponents and scaling in three dimensions

The critical behavior of a self-consistent Ornstein–Zernike approach (SCOZA) that describes the pair correlation function and thermodynamics of a classical fluid, lattice gas, or Ising model is analyzed in three dimensions below the critical temperature, complementing our earlier analysis of the supercritical behavior. The SCOZA subcritical exponents describing the coexistence curve, susceptibility (compressibility), and specific heat are obtained analytically ( β=7/20, γ′=7/5, α′=−1/10 ). These are in remarkable agreement with the exact values ( β≈0.326, γ′≈1.24, α′≈0.11 ) considering that the SCOZA uses no renormalization group concepts. The scaling behavior that describes the singular parts of the thermodynamic functions as the critical point is approached is also analyzed. The subcritical scaling behavior in the SCOZA is somewhat less simple than that expected in an exact theory, involving two scaling functions rather than one.

Structure and thermodynamics of anisotropic polymer fluids

We investigate the structure and thermodynamics of anisotropic polymer fluids, focusing on the nematic phases of flexible polymers. The chains interact only through monomer–monomer excluded-volume interactions. As a function of an externally provided alignment along a fixed nematic director, we calculate the anisotropic pair correlation function, and demonstrate the existence of two density correlation lengths, ξ⊥ and ξz, controlling transverse and longitudinal density fluctuations, respectively. We allow the possibility that the chains align either along the director (nematic conformations), or are anti-aligned in a “discotic-like” configuration. The cohesive contribution to the free energy is established in a high-temperature approximation, and its sensitivity to the orientation of the chains is probed. Our approach is not limited to homogeneous liquid crystalline phases, but applies in any circumstance when the orientation of otherwise disordered polymers is the physically controlling effect, e.g., confinement in thin films or pores, shear-alignment of flexible polymers, or straining a cross-linked rubber network.

Nonlinear Extended Thermodynamics of a Non-Viscous Fluid in the Presence of Heat Flux

In this paper we build up, in a complete way, an Extended Thermodynamic theory of a nonviscous fluid in the presence of heat flux. The theory chooses as fundamental fields the density, the velocity, the energy density and the heat flux. The relations which constrain the constitutive quantities are deduced from the entropy principle, using the Liu method of Lagrange multipliers. These relations are exact, because no approximation has been used for their determination, and maintain their validity also for processes far from equilibrium. In the paper it is shown that the constitutive theory is determined by the choice of only four scalar functions of the intrinsic Lagrange multipliers. The complete nonequilibrium expressions of the chemical potential and of the entropy flux are determined: in these equations additional nonlinear terms appear, which are proportional to the Lagrange multiplier of a vector field related to the heat flux.

A self-consistent integral equation study of the structure and thermodynamics of the penetrable sphere fluid

The penetrable sphere fluid consists of a system of spherical particles interacting via a potential that remains finite and constant for distances smaller than the particle diameter and is zero otherwise. This system, which was proposed sometime ago as a model for micelles in a solvent, has represented so far a remarkable challenge for integral equation theories which proved unable to correctly model the behavior of the two-body correlations inside the particle overlap region. It is shown in this work that enforcing the fulfillment of zero separation theorems for the cavity distribution function y(r), and thermodynamic consistency conditions (fluctuation vs virial compressibility and Gibbs–Duhem relation), on a parametrized closure of the type proposed by Verlet, leads to an excellent agreement with simulation, both for the thermodynamics and the structure (inside and outside the particle core). Additionally, the behavior of the integral equation at high packing fractions is explored and the bridge functions extracted from simulation are compared with the predictions of the proposed integral equation.

Thermodynamics of structured fluids. Hard science for soft materials

Abstract At liquid-like densities, molecules of complex fluids can assume a variety of structures (or positions) in space; when the molecules contain many atoms as, for example, in polymers, that variety becomes very large. Further, when confined to a narrow space, it is possible to achieve structures that are not normally observed. Thanks to recent advances in statistical mechanics and molecular physics, and thanks to increasingly fast computers, it is now possible to calculate a fluid's structure, that is, the positions of molecules at equilibrium under given conditions. Calculation of fluid structure is useful because thermodynamic properties depend strongly on that structure, leading to possible applications for new materials. Three examples illustrate some recent developments; each example is presented only schematically (with a minimum of equations) to indicate the physical basis of the mathematical description. The first example considers the effect of branching on self-assembly (micellization) of copolymers (with possible long-range applications in medicine). The second and third examples consider the effect of confinement on fluid structure: first, crystallization in a narrow, confined space to produce a desired crystal structure (with possible applications for light-emitting diodes) and second, suppression of micellization of a diblock copolymer in a thin film (with possible application in lithography). Whenever possible, theoretical calculations are compared with experimental results.

Nonequilibrium relativistic thermodynamics in bulk viscous cosmology

Three different approaches to the relativistic thermodynamics of imperfect fluids are compared: the second-order causal theory of Israel and Stewart (IS), the phenomenological extension of the IS theory proposed by Maartens and M\'endez (MM), and the recently developed GENERIC formalism of Grmela and \"Ottinger. All theories are applied to the case of dissipative cosmology, with bulk viscosity as the only dissipative phenomenon. The MM theory as well as GENERIC give an upper bound on the bulk viscous stress, whereas there is none in the IS theory. In a flat Robertson-Walker universe, the relationship between the different approaches is illustrated for the special case of a relativistic Boltzmann gas. Far away from equilibrium we find qualitatively different behavior, indicating that care should be taken when using the IS theory in this regime.

Structure and thermodynamics of square-well and square-shoulder fluids

We have reinvestigated the structural and thermodynamic properties of the square-well and the square-shoulder system using two different theoretical frameworks, i.e., the optimized random-phase approximation and the Rogers-Young integral equation. We discuss the limits of applicability of the respective concepts and compare the results with `exact' Monte Carlo simulation results and with data obtained from a semi-analytic method proposed by Nezbeda for narrow wells. Using these correlation functions, we study in the framework of the modified-weighted-density approximation the isostructural solid-solid transition predicted for narrow wells and narrow shoulders.

Density-functional theory for soft interactions by dimensional crossover.

A density-functional theory for spherical particles interacting via an arbitrary soft pair potential is presented. The derivation is solely based on limits, where the behavior is exactly known, namely, a zero-dimensional cavity and the low-density virial expansion. The approach generalizes the fundamental-measure theory for hard bodies and yields the structure and thermodynamics of the homogeneous fluid as an output. We apply the theory to an ultrasoft logarithmic potential that mimics star polymers in a good solvent. The theory, when supplemented by a rescaling procedure, reproduces the peculiar features of the pair correlations in this system that we also find in computer simulations.

Thermodynamics and structural properties of the dipolar Yukawa fluid

We report computer simulations and a theoretical study of the thermodynamics and structure of a dipolar Yukawa system. A comparison between the analytical mean spherical approximation (MSA) solution, perturbation theory and Monte Carlo simulation data of pressure, internal energy and dielectric constant is given. In the perturbation theory, the MSA solution of hard core Yukawa fluid is used as a reference system. It was found that the MSA solution is reasonable only at lower dipole moments, while the perturbation theory gives good results at low and high values of dipole moment. Liquid–vapor coexistence data of dipolar Yukawa fluid are also obtained by Monte Carlo simulation and by both MSA and perturbation theory. It was found that at high dipole moments the liquid–vapor equilibrium disappears while chain-like structures appear in the low density fluid phase. The appearance of chain-like structures of dipolar Yukawa fluid is discussed in comparison with the Stockmayer fluid.

Temperature dependence of surface tension and capillary waves at liquid metal surfaces

The temperature dependence of the surface tension γ(T) is treated theoretically and experimentally. The theoretical model based on the Gibbs thermodynamics of a one-component fluid relates ∂γ/∂T to the surface excess entropy density −ΔS. All specific surface effects, namely ordering, capillary waves, and double layer influence the surface entropy, which in turn governs the sign and the magnitude of ∂γ/∂T. Experimental data collected at a free Hg surface in the temperature range from 0°C to 30°C show that ∂γ/∂T is negative.

Letter to the Editor: Comment on “Thermodynamics of viscoelastic fluids: The temperature equation” [J. Rheol. 42, 999–1019 (1998)

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Response to “Comment on: ‘Thermodynamics of viscoelastic fluids: The temperature equation’ ” [J. Rheol. 42, 1565–1567 (1998)

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