Non-equilibrium Thermodynamic Approach Research Articles

Engineering ratchet-based particle separation via extended shortcuts to isothermality.

Microscopic particle separation plays a vital role in various scientific and industrial domains. Conventional separation methods relying on external forces or physical barriers inherently exhibit limitations in terms of efficiency, selectivity, and adaptability across diverse particle types. To overcome these limitations, researchers are constantly exploring new separation approaches, among which ratchet-based separation is a noteworthy method. However, in contrast to the extensive numerical studies and experimental investigations on ratchet separation, its theoretical exploration appears weak, particularly lacking in the analysis of energy consumption involved in the separation processes. The latter is of significant importance for achieving energetically efficient separation. In this paper, we propose a nonequilibrium thermodynamic approach, extending the concept of shortcuts to isothermality, to realize controllable separation of overdamped Brownian particles with low energy cost. By utilizing a designed ratchet potential with temporal period τ, we find in the slow-driving regime that the average particle velocity v[over ¯]_{s}∝(1-D/D^{*})τ^{-1}, indicating that particles with different diffusion coefficients D can be guided to move in distinct directions with a preset D^{*}. It is revealed that an inevitable portion of the energy cost in separation depends on the driving dynamics of the ratchet, with an achievable lower bound W_{ex}^{(min)}∝L^{2}|v[over ¯]_{s}|. Here, L is the thermodynamic length of the driving loop in the parametric space. With a sawtooth potential, we numerically test the theoretical findings and illustrate the optimal separation protocol associated with W_{ex}^{(min)}. Finally, for practical considerations, we compare our approach with the conventional ratchets in terms of separation velocity and energy consumption. The scalability of the current framework for separating various particles in two-dimensional space is also demonstrated. This paper bridges the gap between thermodynamic process control and particle separation, paving the way for further thermodynamic optimization in ratchet-based particle separation.

Principles of Molecular Evolution: Concepts from Non-equilibrium Thermodynamics for the Multilevel Theory of Learning.

We present a non-equilibrium thermodynamics approach to the multilevel theory of learning for the study of molecular evolution. This approach allows us to study the explicit time dependence of molecular evolutionary processes and their impact on entropy production. Interpreting the mathematical expressions, we can show that two main contributions affect entropy production of molecular evolution processes which can be identified as mutation and gene transfer effects. Accordingly, our results show that the optimal adaptation of organisms to external conditions in the context of evolutionary processes is driven by principles of minimum entropy production. Such results can also be interpreted as the basis of some previous postulates of the theory of learning. Although our macroscopic approach requires certain simplifications, it allows us to interpret molecular evolutionary processes using thermodynamic descriptions with reference to well-known biological processes.

РАЗРАБОТКА ТЕОРЕТИЧЕСКОЙ МОДЕЛИ ОТЖИГА ДЛЯ ДВУХКОМПОНЕНТНЫХ СИСТЕМ

The curve showing dependence of amount of silver in copper grains on the annealing temperature, compiled during the annealing process at different temperature has been theoretically analyzed. An attempt to develop a model based on the approach of nonequilibrium evolutionary thermodynamics to describe the annealing process was made. This model has been tested using computer simulation. Taking the previously developed model for megaplastic deformation within the framework of nonequilibrium evolutionary thermodynamics into account, the experiment was fully simulated, which consisted of annealing and further processing by plastic torsion deformation.

Theoretical approach to the scale effects of an OWC device

This research deals with the dynamic similarity problem for Oscillating Water Column (OWC) devices, for which air is the fluid that is subject to thermodynamic transformations in the inhalation/exhalation phases. Based on the differential problem, both linearized and full-nonlinear, the scale ratios satisfying similarity are calculated, with specific reference to the case where constraints are present on some of these scale ratios. The paper proceeds to identify the numerous processes of a turbulent interface that scales differently between model and prototype. With the aim of bringing to front the influence of the scale effects on featured aspects of the thermodynamic process involved, it is proposed that a non-equilibrium thermodynamics approach can be more comprehensive and representative not only of transformations, but also of scaling. The study reveals that in the case of OWC thermodynamics, non-equilibrium states which would be less evident in scaled model, would become more relevant as the scale is increased towards the size of the prototype, with consequences on performance.

Coupled Reactive Two-Phase Model Involving Dissolution and Dynamic Porosity for Deformable Porous Media Based on Mixture Coupling Theory

Carbon capture and storage (CCS) has attracted significant attention owing to its impact on mitigating climate change. Many countries with large oil reserves are adopting CCS technologies to reduce the impact of fossil fuels on the environment. However, because of the complex interactions between multi-phase fluids, planning for CCS is challenging. One of the challenges is the integration of chemical reactions with multi-phase hydro-mechanical relationships in deformable porous media. In this study, a multi-phase hydro-mechanical reactive model for deformable porous media is established by using mixture coupling theory approach. The non-equilibrium thermodynamic approach is extended to establish the basic framework and Maxwell’s relations to build multi-scale coupling. Chemical reaction coupling is achieved through the extent of the reaction and chemical affinity. The developed model can simulate CCS by considering the effect of calcite dissolution on porosity and permeability. It has been found from the simulation that the chemical reaction has a major influence on porosity and permeability change compared to both pressure and mechanical strain effect. Also, as the dissolution reaction takes place, the stress/strain decrease on the solid matrix. The results of this study successfully bridge the knowledge gap between chemical reactions and mechanical deformation. Furthermore, insights from this model hold substantial implications for refining CCS processes. By providing a more accurate prediction of pressure changes and porosity/permeability evolution over time, this research paves the way for improved CCS operation planning, potentially fostering safer, more efficient, and economically feasible climate change mitigation strategies.

A systematic non-equilibrium thermodynamics approach for assessing transport mechanisms in membrane distillation

Membrane distillation (MD) is a promising technique for purifying volatile liquids at temperatures below their boiling points. This study presents a systematic non-equilibrium thermodynamics (NET) approach for analysis of transport mechanisms in direct-contact membrane distillation (DCMD). By incorporating the transport properties of the membrane, membrane interfaces, and temperature polarization layers, a unified framework is established to assess mass and heat transfer, including coupling effects in the composite membrane system. Explicit expressions for the transport properties are derived, and a numerical solution procedure is used to obtain temperature and partial pressure profiles through the system. The NET approach reveals that the temperature difference across the membrane is the true driving force of mass transfer, which after suitable approximations is equivalent to the saturation pressure difference. The commonly employed formula for distillate flux in MD literature was found to agree with the comprehensive NET approach within 3% when predicting the water flux through a DuraPore GVHP membrane. Incorporating a correction factor that accounts for kinetic heat-mass coupling effects improves the agreement to 0.5%. The simplified model disregards interfacial transport phenomena and mass-heat coupling. These effects are shown to be insignificant for the DuraPore GVHP membrane. However, it is crucial to account for temperature polarization to obtain agreement with experimental results. The resistance of the vapor-liquid interface is shown to be more important if the membrane has a Cassie-Baxter wetting state than a Wenzel wetting state, and this can enhance the water flux. When the pore-sizes approach the nanometer scale, we show that direct interactions between the molecules and the pore walls must be accounted for due to sorption effects. In applications where nanometer scale pores are important, such as in systems where the membrane must maintain a large pressure difference, it may be important to take such corrections into consideration. The presented NET approach provides a comprehensive toolkit for assessing and analyzing transport properties in membrane systems, which can be used to better understand how the properties of MD systems can be tailored to enhance performance.

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.

Constitutive and numerical modeling for the coupled thermal-hydro-mechanical processes in dual-porosity geothermal reservoir

Enhanced geothermal system (EGS) is viewed as one of the most practical methods to explore geothermal energy in hot dry rock (HDR), which can contribute to zero carbon emissions and provide reliable and renewable energy. Modelling the performance and long-term environmental effects of the EGS remains a challenge as the rock is often fractured and experiences complicated multi-physics coupling behaviour. Despite studies on constitutive or numerical modelling of coupled behaviour in deformable dual-porosity media, those developed models often ignore the fully coupled processes in heat transfer and are highly empirical. Based on a non-equilibrium thermodynamics approach, the Mixture-Coupling Theory, this research derives the fully coupled Thermo-Hydro-Mechanical (THM) governing equations for dual-porosity geothermal reservoirs, addressing the interaction between strain, pore/fracture pressure and temperature. The constitutive model is obtained by the analysis of Helmholtz free energy evolution in dual-porosity reservoirs. The proposed model determines the fully coupled evolution of solid stress, both pore and fracture porosity, and solid entropy density. The governing equations can predict the fully coupled THM effect in dual-porosity geothermal reservoirs. Numerical modelling is then performed to study the production performance and coupled THM response in an EGS. The modelling results show that the production temperature is determined by the coupled THM effects. Porosity change is mainly determined by temperature change (accounting for over 87% of the total porosity change) during the extraction. The porosity change accounts for 1.03% and 1.23% of the initial porosity for pore and fracture, separately.

Coupled thermo-hydro-mechanical-chemical processes with reactive dissolution by non-equilibrium thermodynamics

The Clausius-Duhem Inequality has been widely adopted to model the coupled Thermo-Hydro-Mechanical-Chemical processes. However, this paper points out that when modelling a reacting system, the Clausius-Duhem Inequality may hide the reaction mechanism and reaction type if the reaction changes the solid, and it may generate imprecise constitutive result if the reaction occurs within the fluid without changing the solid. To overcome these challenges, this paper proposed a novel non-equilibrium thermodynamics approach to model the multiphysics coupling processes with reactive dissolution. The new approach focuses on the Helmholtz free energy change in a dissolution process by quantifying the entropy production with the knowledge from non-equilibrium thermodynamics. A new concept, solid affinity, is introduced to give a better description of Helmholtz free energy change due to reactive dissolution. The coupled Thermo-Hydro-Mechanical-Chemical equations with reactive dissolution are derived by this approach. A numerical simulation is presented to show the role of quartz dissolution.

Statistical Mechanic and Phenomenological Approaches to Isomeric Effects in Thermodiffusion.

We present a model that explains variance in the thermodiffusion of hydrocarbon isomers in binary liquid mixtures. The model relies on material transport equations for binary nonisothermal liquid systems that were derived through a nonequilibrium thermodynamic approach in a previous work, coupled with one of two methods: (i) use of equilibrium chemical potentials for each component under conditions of constant pressure, derived using statistical mechanics or (ii) use of the temperature derivative of chemical potential expressed phenomenologically as molecular entropy. The model is evaluated using Soret coefficients (ST) measured in binary solutions of heptane isomers in benzene. The statistical mechanic approach yields moderately acceptable agreement with experimental data. The phenomenological approach, which relies on both measured and calculated values of molecular entropy from the literature, yields values of ST centered around the experimental data, with the scatter likely due to poor precision in the measured or calculated values of entropy. For the latter case, we identify several methods for calculating entropy that yield good agreement with experimental data.

Why does thermomagnetic resonance affect cancer growth? A non-equilibrium thermophysical approach

Recently, the low frequency thermomagnetic effects on cancer cells have been analysed, both theoretically and experimentally. They have been explained by introducing an equilibrium thermodynamic approach. But, in this context, two related open problems have been highlighted: (1) Does there exist a magnetic interaction or do there exist any other processes? (2) Do there exist also thermal effects? Here, we introduce a non-equilibrium thermodynamic approach in order to address an answer to these questions. The results obtained point out that: (a) the effect produced by the electromagnetic wave is just a consequence of the interaction of the magnetic component of the electromagnetic wave with the biological matter; (b) the interaction of the electromagnetic wave causes also thermal effects, but related to heat transfer, even if there have been applied low frequency electromagnetic waves; (c) the presence of the magnetic field generates a symmetry breaking in the Onsager’s coefficients, with a related perturbation of the cancer stationary state.

Nonequilibrium evolution thermodynamic of poly- and two-components alloys affected by severe plastic deformation

The nonequilibrium evolutionary thermodynamics approach is generalized to the case of alloys prone to structural martensitic and diffusion phase transitions in them. A system of kinetic equations is written out to describe the evolution of the density of structural defects, grain boundaries, dislocations and point defects, as well as for the order parameter in the processing of these alloys by the severe plastic deformation way. The approach is illustrated by the numerical experiments results on a specific example of two-component copper-based alloys. Kinetic curves of the evolution of the grain boundaries, dislocations and atoms dissolved in a copper matrix are obtained, qualitative phase diagrams are constructed.

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.

Thermal Physics and Glaucoma II: Preliminary Evidences for a Thermophysical Design of a Possible Visible-Light-Photons Therapy

Recently, a non-equilibrium thermodynamic approach has been developed in order to model the fundamental role of the membrane electric potential in the cell behaviour. A related new viewpoint is introduced, with a design of a photobiomodulation treatment in order to restore part of the visual field. Here, a first step in experimental evidence of the validity of the thermodynamic approach is developed. This result represents the starting point for future experimental improvements for light stimulation in order to improve the quality of life of the patients. The future possible therapy will be in addition to the pharmacological treatments.

Influence of thermal diffusion on the solvent absorption kinetics of highly cross-linked epoxy resins

The influence of heat transfer on the solvent absorption kinetics of an epoxy o-cresol novolac resin composite which is applied for the encapsulation of heat emitting devices is investigated theoretically. The fundament of the model is the PC-SAFT equation of state which is extended by a network term for including the arising elastic forces in the epoxy resin network. PC-SAFT supplies an expression for the chemical potential which is the driving force in a non-equilibrium thermodynamic approach to account for the coupled heat and mass transfer. With this model, it is investigated how the influences of the solvent absorption kinetics due to thermal diffusion depend on factors such as the temperature gradient, the polarity and state of the solvent. It was found that in heat induced polymer matrices, the coupling of mass and heat transfer cannot be neglected. For the first time, it could be shown by the application of PC-SAFT in a non-equilibrium thermodynamic framework, that there is a large influence of the solvent polarity on the thermodiffusion.

Unified Extended Irreversible Thermodynamics and the Stability of Relativistic Theories for Dissipation

In a relativistic context, the main purpose of Extended Irreversible Thermodynamics (EIT) is to generalize the principles of non-equilibrium thermodynamics to the domain of fluid dynamics. In particular, the theory aims at modeling any diffusion-type process (like heat as diffusion of energy, viscosity as diffusion of momentum, charge-conductivity as diffusion of particles) directly from thermodynamic laws. Although in Newtonian physics this task can be achieved with a first-order approach to dissipation (i.e. Navier–Stokes–Fourier like equations), in a relativistic framework the relativity of simultaneity poses serious challenges to the first-order methodology, originating instabilities which are, instead, naturally eliminated within EIT. The first part of this work is dedicated to reviewing the most recent progress made in understanding the mathematical origin of this instability problem. In the second part, we present the formalism that arises by promoting non-equilibrium thermodynamics to a classical effective field theory. We call this approach Unified Extended Irreversible Thermodynamics (UEIT), because it contains, as particular cases, EIT itself, in particular the Israel-Stewart theory and the divergence-type theories, plus Carter’s approach and most branches of non-equilibrium thermodynamics, such as relativistic chemistry and radiation hydrodynamics. We use this formalism to explain why all these theories are stable by construction (provided that the microscopic input is correct), showing that their (Lyapunov) stability is a direct consequence of the second law of thermodynamics.

Phase field analysis of binary mixtures with partially miscible components

Understanding the flow dynamics of two-phase systems with partially-miscible components is of great importance to the extraction and purification of chemicals. Based on the generalized bracket approach of nonequilibrium thermodynamics, we propose a phase-field model to describe binary systems with different degrees of miscibility. By formulating the concentration equation associated with one of the two components in terms of the corresponding phase velocity, we can avoid excessive numerical diffusion as the diffusive components are all hidden in the advective part of this equation. We validate our numerical strategy by solving the rising bubble problem and comparing our results with benchmark data from the literature. Further, we successfully validate the implementation of our new phase-field model under real flow conditions, i.e., with experimental observations made inside a Y-shaped microchannel. We accurately predict the position of the interface and reproduce the mixing behavior of miscible and partially miscible components. In the future, we will extend our investigation to ternary systems.

A non-equilibrium thermodynamic approach to symmetry breaking in cancer

This paper develops a non-equilibrium thermodynamics approach to oncogenesis, with a particular focus on ‘symmetry breaking’. The Onsager phenomenological coefficients are introduced to show the biophysical and thermophysical properties of cellular systems with differences between normal and cancerous cells. Seebeck- and Peltier-like effects are introduced to simplify the description of heat exchange and ion fluxes, in an effort to characterize the distinct role of the cellular electric membrane potential. Our result indicate that oncogenesis leads to changes in: (i) the thermophysical properties of the cell cytoplasm, caused by differences in density and heat capacity, (ii) the interactions with the micro-environment, (iii) geometrical characteristics, both in fractal dimensions and in shape symmetry, and (iv) the constitutive properties of membrane fluxes. This presents a unifying biophysics concept for such diverse characteristics, and it may yield new diagnostic and therapeutic opportunities.

Seebeck–Peltier Transition Approach to Oncogenesis

In this paper, a non-equilibrium thermodynamic approach to cancer is developed. The thermo-electric effects in the cell membrane are analysed, in relation to the Seebeck-like and the Peltier-like effects. The role of the cell membrane electric potential is studied from a thermodynamic viewpoint, pointing out the relation between the proliferation rate and the membrane potential, the existence of a thermodynamic threshold for the mitotic activity, the relation between metastases and membrane potential and the comprehension of the role of ions fluxes in the cell behaviour.

Non-Equilibrium Thermodynamic Approach to Ca2+-Fluxes in Cancer

Living systems waste heat in their environment. This is the measurable effect of the irreversibility of the biophysical and biochemical processes fundamental to their life. Non-equilibrium thermodynamics allows us to analyse the ion fluxes through the cell membrane, and to relate them to the membrane electric potential, in order to link this to the biochemical and biophysical behaviour of the living cells. This is particularly interesting in relation to cancer, because it could represent a new viewpoint, in order to develop new possible anticancer therapies, based on the thermoelectric behaviour of cancer itself. Here, we use a new approach, recently introduced in thermodynamics, in order to develop the analysis of the ion fluxes, and to point out consequences related to the membrane electric potential, from a thermodynamic viewpoint. We show how any increase in the cell temperature could generate a decrease in the membrane electric potential, with a direct relation between cancer and inflammation. Moreover, a thermal threshold, for the cell membrane electric potential gradient, has been obtained, and related to the mitotic activity. Finally, we obtained the external surface growth of the cancer results related (i) to the Ca2+-fluxes, (ii) to the temperature difference between the the system and its environment, and (iii) to the chemical potential of the ion species.