Formulation Of Nonequilibrium Thermodynamics Research Articles

Hydroelectric energy conversion of waste flows through hydroelectronic drag

Hydraulic energy is a key component of the global energy mix, yet there exists no practical way of harvesting it at small scales, from flows with low Reynolds number. This has triggered a search for alternative hydroelectric conversion methodologies, leading to unconventional proposals based on droplet triboelectricity, water evaporation, osmotic energy, or flow-induced ionic Coulomb drag. Yet, these approaches systematically rely on ions as intermediate charge carriers, limiting the achievable power density. Here, we predict that the kinetic energy of small-scale "waste" flows can be directly and efficiently converted into electricity thanks to the hydroelectronic drag effect, by which an ion-free liquid induces an electronic current in the solid wall along which it flows. This effect originates in the fluctuation-induced coupling between fluid motion and electron transport. We develop a nonequilibrium thermodynamic formalism to assess the efficiency of such hydroelectric energy conversion, dubbed hydronic energy. We find that hydronic energy conversion is analogous to thermoelectricity, with the efficiency being controlled by a dimensionless figure of merit. However, in contrast to its thermoelectric analogue, this figure of merit combines independently tunable parameters of the solid and the liquid, and can thus significantly exceed unity. Our findings suggest strategies for blue energy harvesting without electrochemistry, and for waste flow mitigation in membrane-based filtration processes.

Inconsistency between the micropolar theory and non-equilibrium thermodynamics in the case of polar fluids

Abstract The balance equation of angular momentum in anisotropic fluids includes a couple stress contribution, also responsible for an antisymmetric contribution to the force stress tensor. We herein derive all balance equations for the simplest anisotropic fluid, i.e., a polar fluid, using the GENERIC formalism of non-equilibrium thermodynamics. In doing so, we find that there is an inconsistency between the internal energy density evolution equation derived using non-equilibrium thermodynamics and the one usually considered in micropolar theory.

Introducing the concept of generalized thermal diffusivity to understand coupled heat–charge transport in ionic solutions

A theoretical framework addressing the coupled thermal and charge transport phenomena in ionic solutions is here developed. Starting from the microscopic definitions of thermal and charge currents from Onsager formulation of non-equilibrium thermodynamics, a unique, very general and compact form of the governing differential equation for the evolution of a temperature profile is derived. In particular, the concept of generalized thermal diffusivity is introduced to capture the overall effect of the coupling between heat and charge transport in a single phenomenological coefficient as well as to shed light on the non-equivalent situations of concurrent or discordant heat and charge currents. To validate our theoretical framework, an ionic salt solution of NaCl in water is investigated.

Relativistic hydrodynamics from the single-generator bracket formalism of nonequilibrium thermodynamics

Abstract We employ the generalized bracket formalism of nonequilibrium thermodynamics by Beris and Edwards to derive Lorentz-covariant time-evolution equations for an imperfect fluid with viscosity, dilatational viscosity, and thermal conductivity. Following closely the analysis presented by Öttinger (Physica A, 259, 1998, 24–42; Physica A, 254, 1998, 433–450) to the same problem but for the GENERIC formalism, we include in the set of hydrodynamic variables a covariant vector playing the role of a generalized thermal force and a covariant tensor closely related to the velocity gradient tensor. In our work here, we derive first the nonrelativistic equations and then we proceed to obtain the relativistic ones by elevating the thermal variable to a four-vector, the mechanical force variable to a four-by-four tensor, and by representing the Hamiltonian of the system with the time component of the energy-momentum tensor. For the Poisson and dissipation brackets we assume the same general structure as in the nonrelativistic case, but with the phenomenological coefficients in the dissipation bracket describing friction to heat and viscous effects being properly constrained for the resulting dynamic equations to be manifest Lorentz-covariant. The final relativistic equations are identical to those derived by Öttinger but the present approach seems to be more general in the sense that one could think of alternative forms of the phenomenological coefficients describing friction that could ensure Lorentz-covariance.

Predicting High-Density Polyethylene Melt Rheology Using a Multimode Tube Model Derived Using Non-Equilibrium Thermodynamics.

Based on the Generalized bracket, or Beris-Edwards, formalism of non-equilibrium thermodynamics, we recently proposed a new differential constitutive model for the rheological study of entangled polymer melts and solutions. It amended the shortcomings of a previous model that was too strict regarding the values of the convective constraint release parameter for the model not to violate the second law of thermodynamics, and it has been shown capable of predicting a transient stress undershoot (following the overshoot) at high shear rates. In this study, we wish to further examine this model's capability to predict the rheological response of industrial polymer systems by extending it to its multiple-mode version. The comparison with industrial rheological data (High-Density Polyethylene resins), which was based on comparison with experimental data available in (a) Small Amplitude Oscillatory shear, (b) start-up shear, and (c) start-up uniaxial elongation, was noted to be good.

Some aspects of the development of formalism of nonequilibrium thermodynamics for systems based on polyelectrolyte hydrogels

Показано, что формализм неравновесной термодинамики, основанныйна использовании функционалов, выражающих определенный принцип максимума илиминимума, для ряда частных задач может быть развит вне зависимости от адекватноститрактовки понятия "энтропия" в применении к системам, далеким от состояния равновесия.В частности, показано, что для неравновесных систем, поведение которых преимущественноопределяется движением низкомолекулярных ионов, функционалы, выполняющие ту жефункцию, что и термодинамические, могут быть получены как первые интегралыуравнений движения данных частиц. Преимуществом такого подхода является исключениенеобходимости обоснования адекватности использования понятия "энтропия". Получен явныйвид таких функционалов. Обсуждаются возможности их использования в прикладных целях

Modeling the rheological behavior of crude oil–water emulsions

During crude oil extraction, crude oil is often mixed with water, leading to the formation of water-in-oil emulsions. Since these emulsions pose severe flow resistance, such as higher pressure drops, due to their complex fluid rheology, it is important to have in our arsenal a rheological constitutive model that accurately predicts their rheological response. In the present work, we propose such a model wherein the emulsions are modeled as deformable volume-preserving droplets via the use of a determinant-preserving contravariant second-rank tensor. We use the generalized bracket formalism of non-equilibrium thermodynamics to make sure that the derived model is by construction thermodynamically admissible. An additional scalar structural variable is considered to allow the prediction of a yielding point, following previous work. The predictions of the new model are shown to be in very good agreement with available experimental measurements.

Continuum mechanics modeling of complex fluid systems following Oldroyd's seminal 1950 work

A review of some key developments in the continuum mechanics – based macroscopic modelling of complex fluid flows, following the pioneering work of Oldroyd in the 1950s will be presented. We start by reviewing the major developments achieved by Oldroyd, namely how his work established rules for consistency in developing continuum stress constitutive models extending the material into objective time derivatives for tensor quantities, with first application the stress tensor in viscoelastic constitutive relationships. We then show how the impact of his work to viscoelastic fluid flows has been amplified from the kinetic theory work of Bird and others who established a firm macromolecular structural connection. The use of objective time derivatives was then extended to include second order conformation tensors and through them the connection was made to internal deformation energy by Marrucci. We then further demonstrate the impact of this work by analysing the models through the microstructural descriptions offered within the non-equilibrium thermodynamics formalism. We then conclude with a brief mentioning of direct applications of the original Oldroyd-B model (through stability analyses, etc.) towards bettering our understanding of the rheological behaviour of complex fluid systems.

Hamiltonian variational formulation for nonequilibrium thermodynamics of simple closed systems

In this paper, we develop a Hamiltonian variational formulation for the nonequilibrium thermodynamics of simple adiabatically closed systems that is an extension of Hamilton's phase space principle in mechanics. We introduce the Hamilton-d'Alembert principle for thermodynamic systems by considering nonlinear nonholonomic constraints of thermodynamic type. In particular, for the case in which the given Lagrangian is degenerate, we construct the Hamiltonian by incorporating the primary constraints via Dirac's theory of constraints. We illustrate our Hamiltonian variational formulation with some examples of systems with friction, with internal matter transfer as well as with chemical reactions.

Covariant formulation of non-equilibrium thermodynamics in General Relativity

We construct a generally-covariant formulation of non-equilibrium thermodynamics in General Relativity. We find covariant entropic forces arising from gradients of the entropy density, and a corresponding non-conservation of the energy momentum tensor in terms of these forces. We also provide a Hamiltonian formulation of General Relativity in the context of non-equilibrium phenomena and write the Raychaudhuri equations for a congruence of geodesics. We find that a fluid satisfying the strong energy condition could avoid collapse for a positive and sufficiently large entropic-force contribution. We then study the forces arising from gradients of the bulk entropy of hydrodynamical matter, as well as the entropy of boundary terms in the action, like those of black hole horizons. Finally, we apply the covariant formulation of non-equilibrium thermodynamics to the expanding universe and obtain the modified Friedmann equations, with an extra term corresponding to an entropic force satisfying the second law of thermodynamics.

Continuum mechanics modeling of complex fluid systems following Oldroyd's seminal 1950 work

We present a review of some key developments in the continuum mechanics – based macroscopic modeling of complex fluid flows, following the pioneering work of Oldroyd in the 1950s. We start by reviewing the major developments achieved by Oldroyd, namely how his work established rules for consistency in developing continuum stress constitutive models extending the material into objective time derivatives for tensor quantities, with first application the stress tensor in viscoelastic constitutive relationships. We then show how the impact of his work to viscoelastic fluid flows has been amplified from the kinetic theory work of Bird and others who established a firm macromolecular structural connection. The use of objective time derivatives was then extended to include second order conformation tensors and through them the connection was made to internal deformation energy by Marrucci. We then further demonstrate the impact of this work by analyzing the models through the microstructural descriptions offered within the non-equilibrium thermodynamics formalism. We then conclude with a brief mentioning of direct applications of the original Oldroyd-B model (through stability analyses, etc.) towards bettering our understanding of the rheological behaviour of complex fluid systems.

Nonequilibrium thermodynamics of light-induced reactions

Current formulations of nonequilibrium thermodynamics of open chemical reaction networks only consider chemostats as free-energy sources sustaining nonequilibrium behaviors. Here, we extend the theory to include incoherent light as a source of free energy. We do so by relying on a local equilibrium assumption to derive the chemical potential of photons relative to the system they interact with. This allows us to identify the thermodynamic potential and the thermodynamic forces driving light-reacting chemical systems out-of-equilibrium. We use this framework to treat two paradigmatic photochemical mechanisms describing light-induced unimolecular reactions-namely, the adiabatic and diabatic mechanisms-and highlight the different thermodynamics they lead to. Furthermore, using a thermodynamic coarse-graining procedure, we express our findings in terms of commonly measured experimental quantities, such as quantum yields.

The Role of pH and Ionic Strength in the Attraction-Repulsion Balance of Fibrinogen Interactions.

Fibrinogen (Fg) self-assembly is sensitive to the physicochemical properties of an environment like pH and ionic strength. These parameters tune the direction and strength of noncovalent physical driving forces determining protein intermolecular interactions. The attraction-repulsion balance in intermolecular interactions of the multidomain protein Fg at pH values 3.5, 7.4, and 9.5 and varying ionic strengths of the water medium has been analyzed by the complex diffusive approach, proposed by us previously. The concentration dependence of protein collective diffusion was analyzed within the phenomenological approach, based on the frictional formalism of nonequilibrium thermodynamics proposed by H. Vink. The analysis of protein diffusion data has shown the fundamental difference in the physical nature and direction of interaction forces between protein molecules at different conditions. The paired interaction potential of protein molecules was characterized in terms of second virial coefficients and Hamaker constants within the Deryaguin-Landau-Verwey-Overbeek theory and the "porous" colloid particle model. Our results indicated the maximum Hamaker constant and dominance of the van der Waals attraction between Fg molecules at pH 7.4. The increase in pH up to 9.5 results in the zero values of the second virial coefficient and Hamaker constant, corresponding to the full reciprocal compensation for electrostatic repulsion and van der Waals attraction. In the acidic medium (pH 3.5), the strong electrostatic repulsion substantially exceeds the van der Waals attraction. A high ionic strength is characterized by a significant decrease of all intermolecular interactions, which is expressed in almost zero values of virial coefficients and the Hamaker constant. Thus, it is experimentally shown that the physiological conditions of the Fg environment (pH 7.4 and slight ionic strength) provide a high probability for peak physical attraction between fibrinogen molecules, which is used in nature to facilitate blood clotting.

Landscape-Flux Framework for Nonequilibrium Dynamics and Thermodynamics of Open Hamiltonian Systems Coupled to Multiple Heat Baths.

We establish a nonequilibrium dynamic and thermodynamic formalism in the landscape-flux framework for open Hamiltonian systems in contact with multiple heat baths governed by stochastic dynamics. To systematically characterize nonequilibrium steady states, the nonequilibrium trinity construct is developed, which consists of detailed balance breaking, nonequilibrium potential landscape, and irreversible probability flux. We demonstrate that the temperature difference of the heat baths is the physical origin of detailed balance breaking, which generates the nonequilibrium potential landscape characterizing the nonequilibrium statistics and creates the irreversible probability flux signifying time irreversibility, with the latter two aspects closely connected. It is shown that the stochastic dynamics of the system can be formulated in the landscape-flux form, where the reversible force drives the conservative Hamiltonian dynamics, the irreversible force consisting of a landscape gradient force and an irreversible flux force drives the dissipative dynamics, and the stochastic force adds random fluctuations to the dynamics. The possible connection of the nonequilibrium trinity construct to nonequilibrium phase transitions is also suggested. A set of nonequilibrium thermodynamic equations, applicable to both nonequilibrium steady states and transient relaxation processes, is constructed. We find that an additional thermodynamic quantity, named the mixing entropy production rate, enters the nonequilibrium thermodynamic equations. It arises from the interplay between detailed balance breaking and transient relaxation, and it also relies on the conservative dynamics. At the nonequilibrium steady state, the heat flow, entropy flow, and entropy production are demonstrated to be thermodynamic manifestations of the nonequilibrium trinity construct. The general nonequilibrium formalism is applied to a class of solvable systems consisting of coupled harmonic oscillators. A more specific example of two harmonic oscillators coupled to two heat baths is worked out in detail. The example may facilitate connection with experiments.

A numerical method for the simulation of viscoelastic fluid surfaces

Viscoelastic surface rheology plays an important role in multiphase systems. A typical example is the actin cortex which surrounds most animal cells. It shows elastic properties for short time scales and behaves viscous for longer time scales. Hence, realistic simulations of cell shape dynamics require a model capturing the entire elastic to viscous spectrum. However, currently there are no numerical methods to simulate deforming viscoelastic surfaces. Thus models for the cell cortex, or other viscoelastic surfaces, are usually based on assumptions or simplifications which limit their applicability. In this paper we develop a first numerical approach for simulation of deforming viscoelastic surfaces. To this end, we derive the surface equivalent of the upper convected Maxwell model using the GENERIC formulation of nonequilibrium thermodynamics. The model distinguishes between shear dynamics and dilatational surface dynamics. The viscoelastic surface is embedded in a viscous fluid modelled by the Navier-Stokes equation. Both systems are solved using Finite Elements. The fluid and surface are combined using an Arbitrary Lagrange-Eulerian (ALE) Method that conserves the surface grid spacing during rotations and translations of the surface. We verify this numerical implementation against analytic solutions and find good agreement. To demonstrate its potential we simulate the experimentally observed tumbling and tank-treading of vesicles in shear flow. We also supply a phase-diagram to demonstrate the influence of the viscoelastic parameters on the behaviour of a vesicle in shear flow. Finally, we explore cytokinesis as a future application of the numerical method by simulating the start of cytokinesis using a spatially dependent function for the surface tension.

Potentials of continuous Markov processes and random perturbations

With a scalar potential and a bivector potential, the vector field associated with the drift of a diffusion is decomposed into a generalized gradient field, a field perpendicular to the gradient, and a divergence-free field. We give such decomposition a probabilistic interpretation by introducing cycle velocity from a bivectorial formalism of nonequilibrium thermodynamics. New understandings on the mean rates of thermodynamic quantities are presented. Deterministic dynamical system is further proven to admit a generalized gradient form with the emerged potential as the Lyapunov function by the method of random perturbations.

Nonequilibrium thermodynamics of non-ideal chemical reaction networks.

All current formulations of nonequilibrium thermodynamics of open chemical reaction networks rely on the assumption of non-interacting species. We develop a general theory that accounts for interactions between chemical species within a mean-field approach using activity coefficients. Thermodynamic consistency requires that rate equations do not obey standard mass-action kinetics but account for the interactions with concentration dependent kinetic constants. Many features of the ideal formulations are recovered. Crucially, the thermodynamic potential and the forces driving non-ideal chemical systems out of equilibrium are identified. Our theory is general and holds for any mean-field expression of the interactions leading to lower bounded free energies.

A variational perspective on the thermodynamics of non-isothermal reacting open systems

We make a review of the variational formulation of nonequilibrium thermodynamics as an extension of the Hamilton principle and the Lagrange-d’Alembert principle of classical mechanics. We then focus on the case of open systems that include the power exchange due to heat and matter transfer, with special emphasis on reacting systems which are very important in biological science.

Impact of intermolecular attraction and repulsion on molecular diffusion and virial coefficients of spheroidal and rod-shaped proteins

Recognition of protein intermolecular interactions is a key factor for the study and manipulation of protein activity in living systems and biotechnology formulations. Experimental parameter that is sensitive to intermolecular interactions is molecular diffusion. This work presents an extension of an earlier work where we proposed the complementary use of pulsed field gradient nuclear magnetic resonance (PFG NMR) and dynamic light scattering (DLS) to study the specific features of intermolecular interactions via protein translational diffusion. PFG NMR methodology characterizes the thermal motion of protein by means of the self-diffusion coefficient and friction formalism. DLS experiments provide the protein collective (or mutual) diffusion coefficient, which evaluates the direct, non-specific intermolecular interactions of proteins by means of virial coefficients. Theoretical analysis of obtained experimental diffusion data is based on the combination of the friction formalism of nonequilibrium thermodynamics (Vink approach) with the Deryaguin-Landau-Verwey-Overbeek (DLVO) theory. To evaluate the electrostatic potential of proteins with different shape - spheroidal alfa-chymotrypsin (ChTr) and the rod-shaped fibrinogen (Fg) we applied the model of “porous” colloid particles. Our analysis has shown that the atypical local decrease of collective diffusion relative to self-diffusion is a consequence of the dominance of van der Waals attraction over electrostatic repulsion for the rod-shaped Fg.

From variational to bracket formulations in nonequilibrium thermodynamics of simple systems

A variational formulation for nonequilibrium thermodynamics was recently proposed in Gay-Balmaz and Yoshimura (2017a, 2017b) for both discrete and continuum systems. This formulation extends the Hamilton principle of classical mechanics to include irreversible processes. In this paper, we show that this variational formulation yields a constructive and systematic way to derive, from a unified perspective, several bracket formulations for nonequilibrium thermodynamics proposed earlier in the literature, such as the single generator bracket and the double generator bracket. In the case of a linear relation between the thermodynamic fluxes and the thermodynamic forces, the metriplectic or GENERIC bracket is recovered. We also show how the processes of reduction by symmetry can be applied to these brackets. In the reduced setting, we also consider the case in which the coadjoint orbits are preserved and explain the link with double bracket dissipation. A similar development has been presented for continuum systems in Eldred and Gay-Balmaz (2020) and applied to multicomponent fluids.