Fluctuation-Dissipation Theorems for Multiphase Flow in Porous Media

A thermodynamic description of porous media must handle the size- and shape-dependence of media properties, in particular on the nano-scale. Such dependencies are typically due to the presence of immiscible phases, contact areas and contact lines. We propose a way to obtain average densities suitable for integration on the course-grained scale, by applying Hill’s thermodynamics of small systems to the subsystems of the medium. We argue that the average densities of the porous medium, when defined in a proper way, obey the Gibbs equation. All contributions are additive or weakly coupled. From the Gibbs equation and the balance equations, we then derive the entropy production in the standard way, for transport of multi-phase fluids in a non-deformable, porous medium exposed to differences in boundary pressures, temperatures, and chemical potentials. Linear relations between thermodynamic fluxes and forces follow for the control volume. Fluctuation-dissipation theorems are formulated for the first time, for the fluctuating contributions to fluxes in the porous medium. These give an added possibility for determination of the Onsager conductivity matrix for transport through porous media. Practical possibilities are discussed.

Fluctuation-Dissipation Theorems for Flow in Porous Media

A thermodynamic description of nano-porous media must handle the size- and shape-dependence of the media properties. Such dependencies are typically due to the presence of immiscible phases, contact areas and contact lines. We propose a way to obtain average densities suitable for integration on the course grained scale, applying Hill's thermodynamics for small systems to the subsystems. we argue that the average densities of the porous medium, when defined in a proper way, obey the Gibbs equation. All contributions are additive or weakly coupled. From the Gibbs equation and the balance equations, we derive the entropy production in the standard way, for transport of multi-phase fluids in a non-deformable, porous medium exposed to di¤erences in boundary pressures, temperatures, and chemical potentials. Linear relations between thermodynamic fluxes and forces follow for the control volume. Fluctuation- dissipation theorems are formulated for the first time, for the fluctuating contributions to fluxes in the porous medium. These give an added possibility for determination of porous media permeabilities. Practical possibilities are further discussed.

Viscosity of evolving magmas: a case study of the Glass House Mountains, Australia

The viscosity of the remelted rock compositions of the Glass House Mountains, SE Queensland, Australia, has been determined via micro-penetration in the high-viscosity regime (108–1013 Pa s). The heat capacity of these melts has also been determined from room temperature to above the glass transition. The combination of these two data sets allows the fitting of the viscosity data by the Adam-Gibbs equation using the configurational heat capacity Cpconf(Tg12) and configurational entropy Sconf(Tg12). The resulting fit parameters allow the robust extrapolation of the viscosity data to higher temperature and viscosities of 10–4 Pa s. This data can now be used in the discussion of the emplacement of the magmas of the plugs, laccoliths, sills and dykes that form the Glass House Mountains complex and the plate motion and the plume responsible for the volcano plugs. The large increase in viscosity of the evolving magma and the resulting decrease in discharge rate of the volcanic vents suggest that very little magma appeared as extrusive lavas or pyroclastic material and that the Glass House Mountains are mainly remnants of intrusive bodies exposed by erosion.

Studies on the Interactions of Paracetamol in Water and Binary Solvent Mixtures at T = (298.15–313.15) K: Viscometric and Surface Tension Approach

Temperature, concentration, and solvent conditions have consequences on the formation and dissolution of the drug. Viscometric measurements of paracetamol solutions of different concentrations in 5, 10, and 15% methanol have been made at 298.15, 303.15, 308.15, and 313.15K. Surface tension values (γ) of the solutions were obtained experimentally by using a stalagmometer as well as were derived from the ultrasonic velocity (U) and density (d) values at 298.15 K. The surface tension data have been analyzed using the Gibbs equation to evaluate surface excess (Γ_2). The surface tension and surface excess data obtained by the two different methods are well in accordance. The viscosity (ɳ) data were used to calculate relative viscosity (ɳ_(r ) ), Falkenhagen coefficients (A_(F )), Jone-Dole’s coefficients (B_(J ) ) and chemical potential (μ). The obtained data have been analyzed based on the Jones-Dole equation to know the molecular interactions.

Thermodynamics of phase equilibrium in solid-liquid and solid-gas systems

The thermodynamic equilibrium of a two-phase system is described by the Gibbs equation, which includes state parameters. On the basis of the Gibbs equation and the combined equation of the first and second laws of thermodynamics, thermodynamic potentials are written: internal energy, enthalpy and Gibbs free energy. If the two phases are in equilibrium, then the temperatures, pressures and chemical potentials of these phases are equal to each other. Equalities express the conditions of thermal and mechanical equilibrium, as well as the condition for the absence of a driving force for the transfer of a component across the interface. For a two-phase system, the Gibbs-Duhem equation connects the volume and entropy of 1 mole of the mixture, the content of any component, expressed in mole fractions. Extraction from lupine particles with cheese whey (solid-liquid system) is considered. The driving force of the extraction process in the solid-liquid system is the difference between the concentration of the solvent at the surface of the solid C and its average concentration C0 in the bulk of the solution. The concentration at the interface is usually taken to be equal to the concentration of a saturated solution of Cn, since equilibrium is established rather quickly near the surface of a solid. Then the driving force of the process is expressed as Cn – C0. A curve for the extraction of extractives from lupine with cheese whey was plotted by superimposing low-frequency mechanical vibrations.

Time-Independent Plasticity Formulated by Inelastic Differential of Free Energy Function

The authors presented a time-independent plasticity approach, where a typical plastic-loading process is viewed as an infinitesimal state change of two neighboring equilibrium states, and the yield and consistency conditions are formulated based on the conjugate forces of the internal variables. In this paper, a stability condition is proposed, and the yield, consistency, and stability conditions are reformatted by the inelastic differential form of the Gibbs free energy. The Gibbs equation in thermodynamics with internal variables is a representation to the differential form of the Gibbs free energy by a single Gibbs free energy function. In this paper, we propose the so-called extended Gibbs equation, where the differential form may be represented by multiple potential functions. Various associated and nonassociated plasticity with a single or multiple yield functions can be derived from various representations based on the reformulated approach, where yield and plastic potential functions are in the form of inelastic differentials of the potential functions. The generalized Drucker inequality can only be derived from the one-potential representation as a stability condition. For a multiple-potential representation, the stability condition can be ensured if the multiple potentials are concave functions and possess the same stationary point.

Gas Formation Reactions in the Raw Mixture Based on TPP Ash

The article discusses the physicochemical mechanisms of the effect of chemical reagents on the processes of swelling of the raw mixture based on the ash of thermal power plants. The process of structure formation in such mixtures occurs as a result of physicochemical transformations of its constituent components. To intensify gas evolution and obtain materials of a porous structure, the presence of a gas former is necessary. The author has analysed the possibility of creating a porous structure in a raw mixture based on ash with the introduction of various gas formers or their formation as a result of exchange reactions. The main chemical compounds contributing to pore formation have been determined. To form a given structure, it is proposed to control chemical transformations at the stage of swelling. To study the processes of intensification of gas evolution, the author proposes to investigate the mechanisms of the influence of mineral fillers and chemical reagents on swelling processes based on the analysis of the Gibbs equation. The parameters of the Gibbs equation are obtained, by which it is possible to determine the probability of the occurrence of chemical reactions with the proposed chemical agents for the formation of gas bubbles with (pores) in the raw material.

Relativistic Theory of Irreversible Thermodynamics for Multi-Component Fluids and Its Post-Newtonian Limit in Relation to Classical Extended Thermodynamics

First, the special-relativistic Theory of Irreversible Processes for a multi-component fluid is formulated. It is based on (i) the balance equations of the particle number and the energy-momentum for the total system (i. e., the mixture of the components) as well as the sub-systems (i. e., the components) and (ii) the dissipation inequality and the Gibbs equation for the mixture. In order to allow for reactions between the single components, in contrast to the total system, the sub-systems are assumed to be open, which means that their particle number and energy-momentum are not constrained by conservation laws. Without making any assumptions on the thermodynamic behavior of the interacting components, one arrives at a thermodynamic description of the mixture showing now heat conduction and viscosity. In particular, this makes it possible to calculate the entropy production and, thus, to identify thermodynamic currents and forces. In a second part, the post-Newtonian limit of this theory is calculated to show that for the mixture there result relations known from classical Extended Thermodynamics that partly are corrected by entrainment terms. The mathematical origin and physical consequences of these terms are discussed.