Linear Nonequilibrium Thermodynamics Research Articles

A Non-Equilibrium Thermodynamic Approach for Analysis of Power Conversion Efficiency in the Wind Energy System

This article proposes an approach and develops an appropriate method of applying linear non-equilibrium thermodynamics to analyze energy processes, in particular using the example of the wind energy conversion system (WECS) with a directly connected vertical axis wind turbine (VAWT) and vector-controlled permanent magnet synchronous generator (PMSG). The main steps of the proposed approach are the description of the component subsystems as universal linear or linearized energy converters (ECs), which are characterized by several dimensionless parameters, the main one of which is the degree of coupling between their input and output. According to their value, as well as justified efficiency criteria, the optimal operating points of each ECs can be easily found. Such an approach makes it possible to abstract from physical laws of a different nature and equally assess the work of each of the subsystems. The next step is a connection of the received ECs. As shown in the paper, for the most common cascade connection of ECs, there are the best conditions for their connection, under which the newly formed equivalent EC can have maximum efficiency. This opens up an opportunity to analyze the influence of already real parameters of cascaded interconnected subsystems on the quality of their connection and justify specific solutions that would not have been seen without this approach. For example, in this study, from all parameters of the PMSG, only the selection of the optimal rated inductance of the armature winding made it possible to improve the quality of the connection of the PMSG with a specific VAWT and approximate the efficiency of the entire WECS to the maximum possible, especially in medium and high winds.

Heterogeneous consecutive reaction kinetics of direct oxidation of H2 to H2O2: Effect and regulation of confined mass transfer

Porous catalysts in heterogeneous reactions have played an important role in the modern chemical industry, but it is still challenging to quantitatively describe mass transfer and surface reaction behaviors of reactants in nano-confined space. Direct synthesis of hydrogen peroxide (H2O2) is considered as an attractive alternative to anthraquinone oxidation process, while the confined mass transfer of H2O2 in porous catalysts limits the reactivity. In this work, taking the consecutive reaction of H2O2 synthesis as an example, a quantitative method in modeling the effects of confined mass transfer on the reactivity was studied. More specifically, calorimetry was developed to characterize the confined structures of porous carbon experimentally, the linear nonequilibrium thermodynamics and the statistical mechanics method were further combined. Then, the heterogeneous consecutive reaction kinetics and the Thiele modulus influenced by confined mass transfer were modeled. Consequently, regulation strategies were proposed with the help of theoretical models. The optimized catalyst with biological skeleton carbon support and 0.5 wt% palladium loading shows an excellent catalytic performance. Lastly, for the mesoscience in heterogeneous reaction, the resistance was explored as a quantitative descriptor to compromise in the competition between mass transfer and surface reaction. The mesoscale structures were considered as the dynamic spatiotemporal distribution of substance concentrations, and the resistance minimization multi-scale (RMMS) model was proposed.

Приближенная модель многокомпонентного двухфазного течения с частичным смешением

A new approximated model of multi-component two-phase flow is proposed. This model is based on the thermodynamically consisitent model of multi-component two-phase diffuse interface flow and additional assumption that the interface thickness is much smaller than all other length scales. The thermodynamically consisitent model of multi-component two-phase diffuse interface flow in its turn is based on the components’ mole amounts and momentum conservation laws, the linear non-equilibrium thermodynamics relationships and «square gradient» Helmholtz free energy form.

Pattern formation revisited within nonequilibrium thermodynamics: Burgers'-type equation.

We revisit the description of reaction-diffusion phenomena within nonequilibrium thermodynamics and investigate the role of a nonstandard splitting of the entropy balance into the entropy production and the divergence of entropy flux. As previously reported by Pavelka et al. (Int J Eng Sci 78:192-217, 2014), a new term is identified following from the kinetic energy of diffusion. This newly appearing term acts as a thermodynamic force driving the reaction kinetics. Using the standard constitutive relations within the linear nonequilibrium thermodynamics, the governing equations for a reaction-diffusion problem in a two-species system are derived. They turn out to be linked to Burgers' equation. It is shown that the onset of stability is not altered, but a non-periodic pattern can emerge. The latter follows from the relation of the governing equation to Burger's equation with a source term. Hence, transients formed by glued and merging parabolic profiles are expected to appear at least in certain parameter regimes. We explore the significance of this effect and observe that for a comparable magnitude of the diffusion and of the new term stemming from the kinetic energy of diffusion, the solution is expected to be linked to the saw-tooth like solution to Burger's equation rather than to the eigenmodes of the Laplacian. We conclude that the reaction-diffusion model proposed by Turing is robust to the addition of this effect of the kinetic energy of diffusion, at least when this new term is sufficiently small. As the governing equations can be rewritten into the classical reaction-diffusion problem but with reaction kinetics outside of the classical law of mass action, the analysis presented in this study suggests that a yet richer behaviour of the classical reaction-diffusion problems can be expected, if nonstandard reaction kinetics are considered.

On the construction of a family of anomalous-diffusion Fokker–Planck−Kolmogorov’s equations based on the Sharma–Taneja–Mittal entropy functional

A logical scheme for constructing thermodynamics of anomalous stochastic systems based on the nonextensive two-parameter (κ, ς) -entropy of Sharma–Taneja–Mittal (SHTM) is considered. Thermodynamics within the framework (2 - q) -statistics of Tsallis was constructed, which belongs to the STM family of statistics. The approach of linear nonequilibrium thermodynamics to the construction of a family of nonlinear equations of Fokker−Planck−Kolmogorov (FPK), is used, correlated with the entropy of the STM, in which the stationary solution of the diffusion equation coincides with the corresponding generalized Gibbs distribution obtained from the extremality (κ, ς) - entropy condition of a non-additive stochastic system. Taking into account the convexity property of the Bregman divergence, it was shown that the principle of maximum equilibrium entropy is valid for (κ, ς) - systems, and also was proved the H - theorem determining the direction of the time evolution of the non-equilibrium state of the system. This result is extended also to non-equilibrium systems that evolve to a stationary state in accordance with the nonlinear FPK equation. The method of the ansatz- approach for solving non-stationary FPK equations is considered, which allows us to find the time dependence of the probability density distribution function for non-equilibrium anomalous systems. Received diffusive equations FPК can be used, in particular, at the analysis of diffusion of every possible epidemics and pandemics. The obtained diffusion equations of the FPK can be used, in particular, in the analysis of the spread of various epidemics and pandemics.

Fluid and Osmotic Pressure Balance and Volume Stabilization in Cells

A fundamental problem for cells with their fragile membranes is the control of their volume. The primordial solution to this problem is the active transport of ions across the cell membrane to modulate the intracellular osmotic pressure. In this work, a theoretical model of the cellular pump-leak mechanism is proposed within the general framework of linear nonequilibrium thermodynamics. The model is expressed with phenomenological equations that describe passive and active ionic transport across cell membranes, supplemented by an equation for the membrane potential that accounts for the electrogenicity of the ionic pumps. For active ionic transport, the model predicts that the intracellular fluid pressure will be balanced by the osmotic pressure and a new pressure component that arises from the active ionic fluxes. A model for the pump-leak mechanism in an idealized human cell is introduced to demonstrate the applicability of the proposed theory.

Thermodynamics of Animal Locomotion.

Muscles are biological actuators extensively studied in the frame of Hill's classic empirical model as isolated biomechanical entities, which hardly applies to a living organism subjected to physiological and environmental constraints. Here we elucidate the overarching principle of a living muscle action for locomotion, considering it from the thermodynamic viewpoint as an assembly of actuators (muscle units) connected in parallel, operating via chemical-to-mechanical energy conversion under mixed (potential and flux) boundary conditions. Introducing the energy cost of effort as the generalization of the well-known oxygen cost of transport in the frame of our compact locally linear nonequilibrium thermodynamics model, we analyze oxygen consumption measurement data from a documented experiment on energy cost management and optimization by horses moving at three different gaits. Horses adapt to a particular gait by mobilizing a nearly constant number of muscle units minimizing waste production per unit distance covered; this number significantly changes during transition between gaits. The mechanical function of the animal is therefore determined both by its own thermodynamic characteristics and by the metabolic operating point of the locomotor system.

Mesoscience in supported nano-metal catalysts based on molecular thermodynamic modeling: A mini review and perspective

Supported nano-metal catalysts are widely used in industrial processes. There is a trade-off between the activity and stability from mesoscale, which can be effectively tackled with the principle of compromise in competition (mechanisms A and B). To apply mesoscience methodology in this specific area, this work summarized research progress, where direct H2O2 synthesis was chosen as a typical case to identify and represent mechanism A (activity) and mechanism B (stability). It was found that mechanism A has been widely studied, while mechanism B still cannot reflect explosion. Subsequently, reaction heat and fusion enthalpy were proposed to represent mechanism B in this work, and the molecular thermodynamic model was identified as an effective tool for the study. A corresponding framework for mechanism B was constructed and the progress in developing the model for this particular purpose was provided. Finally, perspectives were discussed based on the linear non-equilibrium thermodynamics.

Electro-Osmotic Behavior of Polymeric Cation-Exchange Membranes in Ethanol-Water Solutions.

The aim of this work is to apply linear non-equilibrium thermodynamics to study the electrokinetic properties of three cation-exchange membranes of different structures in ethanol-water electrolyte solutions. To this end, liquid uptake and electro-osmotic permeability were estimated with potassium chloride ethanol-water solutions with different ethanol proportions as solvent. Current–voltage curves were also measured for each membrane system to estimate the energy dissipation due to the Joule effect. Considering the Onsager reciprocity relations, the streaming potential coefficient was discussed in terms of ethanol content of the solutions and the membrane structure. The results showed that more porous heterogeneous membrane presented lower values of liquid uptake and streaming potential coefficient with increasing ethanol content. Denser homogeneous membrane showed higher values for both, solvent uptake and streaming coefficient for intermediate content of ethanol.

Anion exchanger functionality and thermodynamic characterization of chicken erythrocytes

Abstract After a remark on linear response theory and non-equilibrium thermodynamics with internal variables foundation, this paper focuses on chicken blood characterization. Using a model for low frequencies, a new expression of the conductivity, is introduced. This new definition allows to the separation of the dielectric part from the conductivity part in complex dielectric functions. These thermodynamic elaborations supported by biochemical kinetic studies allowed to highlight some chicken RBC peculiarities. In this context, displacement conductivity value is well associated with the anion flux through band 3 protein exchanger and the value of complex entropy related to the complex conductivity, reflects the peculiar structure of nucleated chicken RBC. The study aims to open new perspectives of thermodynamic investigations that, if well supported by biochemical observations, can provide new research ideas for metabolic and eventually therapeutic investigations.

Non-equilibrium thermodynamics approach for the coupled heat and mass transfer of wet mineral porous media in dielectric and magnetic drying

A linear non-equilibrium thermodynamics (LNT) microwave-multiphase transport model was developed in order to describe the microwave drying behavior of lignite and hematite thin layer. The moisture ratio profiles and temperature distribution derived in terms of dielectric and coupled dielectric and magnetic loss mechanisms fitted the experimental results well with reasonable deviations. The electric and magnetic field intensities of the corner and edge in the samples were higher than that of the center regions, which met with the experimental temperature distribution. No pumping phenomenon was detected during the whole drying process. The heat flux driven by the polarization relaxation at the higher electric and magnetic field intensities (103–5 × 103 V m−1, 4–7 A m−1) regions was higher than that at the lower ones (2 × 102–2 × 103 V m−1, 1–4 A m−1), and the electric-thermal effects also decreased with the increasing of the sample temperature and the decreasing of the moisture content in the sample.

Molecular Simulation of Pervaporation of a Lennard-Jones Mixture Using a Crystalline Membrane

Numeric simulation of the pervaporation process is carried out using molecular dynamics. Various conditions of the separation of an ideal binary Lennard-Jones mixture using a crystalline membrane are considered. Components of separated mixtures differ in regards to the energy of interaction with molecules of the membrane. As a result of simulation, fields of concentrations and densities along the cell, as well as flux values of components, are obtained. In addition, coefficients of the diffusion of components in the membrane are computed. It is shown that the correspondence of numeric simulation data to macroscopic mass transfer equations are observed in all cases. It can be concluded that the behavior of molecules in a nonequilibrium system with a scale of several dozens of molecule diameters corresponds to transfer equations of linear nonequilibrium thermodynamics. Results of numeric simulation show the selectivity of a membrane in regard to the component with a larger interaction energy. It is shown that molecular simulation is able to predict the main characteristics of membrane separation (fluxes, selectivity, adsorption, and diffusion coefficients).

Common mathematical-physical essence involved from chromatographic separation to intelligent medicine: irreversibility

The chromatographic separation processes for many molecules in solute bands by stationary phase-mobile phase separation can be compared to ordering disease severity. The common features of chromatographic processes and machine-disease diagnosis-doctor's advice is the separation (classification) of components (individual disease states), both of which show irreversibility of time evolution; however, the former is caused by linear non-equilibrium thermodynamics and latter by nonlinear non-equilibrium thermodynamics (dissipative structure). When the scientific view is extended from drug detection and preparation to evidence-based medicine (EBM), discrete mathematics (axiomatic set theory and probability measure), and artificial intelligence (AI) cloud computing, the convection-diffusion equation and irreversibility in non-equilibrium thermodynamics form a common and core essence of mathematical physics that crosses fields of chromatographic separation and intelligent medicine. It is of profound scientific and practical significance to construct and develop a unified and all-encompassing mathematical framework by incorporating the generality and characteristics of the two subjects.

Beyond Onsager-Casimir Relations: Shared Dependence of Phenomenological Coefficients on State Variables.

Phenomenological coefficients in linear nonequilibrium thermodynamics have been considered to be independent, apart from restrictions due to the Onsager-Casimir reciprocal relations and the requirement to have non-negative entropy production. Recently, it has been shown that functional constraints between these coefficients may hold, restricting their dependence on state variables, especially in the case of coupled phenomena. Here we demonstrate that such restrictions require only mild assumptions on the system of interest and are, in fact, much more constraining than previously reported. Such constraints vastly reduce the set of plausible models for constitutive relations and allow for simpler experimental determinations of dependencies in coupled systems. These results may also clarify inconsistencies in the literature regarding constitutive models used that do not obey these thermodynamic constraints.

SOME PROBLEMS OF PHYSICS OF THE THERMOELECTRIC PHENOMENA

This paper shows inadequacy of contemporary conceptions of physics on nature of thermoelectric phenomena (Sebeck, Peltie and Thomson effects), based on linear nonequilibrium thermodynamics, to experimental data having in wide range of temperature and for various materials (pure metals, Si, Ge, intermetallic and oxide compounds, borides, silicides). Shape extrema of thermopower (increasing up to 100−1000 times) and change of its sign are observed experimentally. Reasons for use of methods of nonlinear nonequilibrium thermodynamics and structure conceptions of thermoelectric materials are motivated.

Flow injection analysis: An approach via linear non-equilibrium thermodynamics

A novel approach to flow injection analysis (FIA) was proposed based on the main principles of linear non-equilibrium thermodynamics (LNET). The basic principles of I. Prigogine theory for dissipative structures, internal entropy production rates, thermodynamic forces and fluxes arising in flow systems were shown to be applicable to FIA. The practical application of this novel FIA approach allowed the use of the extent of analytical reaction and the entropy production rates for flow system optimization, and in-depth understanding of the steady state. The FIA approach was also found to be a suitable technique for and characterizes its quality, explaining the peculiarities of short-term and long-term steady states in a FIA system and their role for reproducibility of practical measurements. The practical application o the FIA approach was found to support its theoretical principles and allow formulating an original manner to derive a basic equation in FIA theory.

Modeling solvent evaporation during thin film formation in phase separating polymer mixtures

Preparation of thin films by dissolving polymers in a common solvent followed by evaporation of the solvent has become a routine processing procedure. However, modeling of thin film formation in an evaporating solvent has been challenging due to a need to simulate processes at multiple length and time scales. In this work, we present a methodology based on the principles of linear non-equilibrium thermodynamics, which allows systematic study of various effects such as the changes in the solvent properties due to phase transformation from liquid to vapor and polymer thermodynamics resulting from such solvent transformations. The methodology allows for the derivation of evaporative flux and boundary conditions near each surface for simulations of systems close to the equilibrium. We apply it to study thin film microstructural evolution in phase segregating polymer blends dissolved in a common volatile solvent and deposited on a planar substrate. Effects of the evaporation rates, interactions of the polymers with the underlying substrate and concentration dependent mobilities on the kinetics of thin film formation are studied.

New Non-Stationary Gradient Model of Heat-Mass-Electric Charge Transfer in Thin Porous Media

The well-known complicated system of non-equilibrium balance equations for a continuous fluid (f) medium needs the new non-Gibbsian model of f-phase to be applicable for description of the heterogeneous porous media (PMs). It should be supplemented by the respective coupled thermal and caloric equations of state (EOS) developed specially for PMs to become adequate and solvable for the irreversible transport f-processes. The set of standard assumptions adopted by the linear (or quasi-linear) non-equilibrium thermodynamics are based on the empirical gradient-caused correlations between flows and forces. It leads, in particular, to the oversimplified stationary solutions for PMs. The most questionable but typical modeling suppositions of the stationary gradient (SG) theory are: 1) the assumption of incompressibility accepted, as a rule, for f-flows; 2) the ignorance of distinctions between the hydrophilic and hydrophobic influence of a porous matrix on the properties; 3) the omission of effects arising due to the concomitant phase intra-porous transitions between the neighboring f-fragments with the sharp differences in densities; 4) the use of exclusively Gibbsian (i.e. homogeneous and everywhere differentiable) description of any f-phase in PM; 5) the very restrictive reduction of the mechanical velocity field to its specific potential form in the balance equation of f-motion as well as of the heat velocity field in the balance equation of internal energy; 6) the neglect of the new specific peculiarities arising due to the study of any non-equilibrium PM in the meso- and nano-scales of a finite-size macroscopic (N,V)-system of discrete particles. This work is an attempt to develop the alternative non-stationary gradient (NSG) model of real irreversible processes in PM. Another aim is to apply it without the above restrictions 1)-6) to the description of f-flows through the obviously non-Gibbsian thin porous medium (TPM). We will suppose that it is composed by two inter-penetrable fractal sf-structures of f-phase (formed by the “mixture” of g- and l-phases termed, in total, interphase) and solid (s) porous matrix termed below s-phase. The permanent influence of humidity and the respective increase of the moisture content in TPM including the unavoidable phenomenon of capillary condensation are the main factors to occur the non-stationary transport f-flows through its texture.

Information geometrical characterization of the Onsager-Machlup process

The Onsager-Machlup (OM) relaxation process, which provides a prototypical example of linear nonequilibrium thermodynamics, is characterized in terms of information geometry over the two-dimensional temperature-time parameter space. After deriving the probability distribution function for the OM process under the harmonic potential within a theoretical framework based on a transformation into imaginary-time quantum mechanics, the Fisher information metric is explicitly obtained. Differential geometry in the temperature-time space then gives the scalar curvature R=-1, thus specifying the OM process in a topological manner.

Cell growth, division, and death in cohesive tissues: A thermodynamic approach.

Cell growth, division, and death are defining features of biological tissues that contribute to morphogenesis. In hydrodynamic descriptions of cohesive tissues, their occurrence implies a nonzero rate of variation of cell density. We show how linear nonequilibrium thermodynamics allows us to express this rate as a combination of relevant thermodynamic forces: chemical potential, velocity divergence, and activity. We illustrate the resulting effects of the nonconservation of cell density on simple examples inspired by recent experiments on cell monolayers, considering first the velocity of a spreading front, and second an instability leading to mechanical waves.