scholarly journals Macroscopic Entropy of Non-Equilibrium Systems and Postulates of Extended Thermodynamics: Application to Transport Phenomena and Chemical Reactions in Nanoparticles

Entropy ◽  
2018 ◽  
Vol 20 (10) ◽  
pp. 802 ◽  
Author(s):  
Sergey Serdyukov
Keyword(s):  
Chemical Reactions ◽  
Constitutive Equations ◽  
Linear Equations ◽  
Reaction Diffusion ◽  
Irreversible Thermodynamics ◽  
Entropy Density ◽  
Higher Order ◽  
Reaction Diffusion Systems ◽  
Reaction Rate Constants ◽  
Thermodynamic Variables

In this work, we consider extended irreversible thermodynamics in assuming that the entropy density is a function of both common thermodynamic variables and their higher-order time derivatives. An expression for entropy production, and the linear phenomenological equations describing diffusion and chemical reactions, are found in the context of this approach. Solutions of the sets of linear equations with respect to fluxes and their higher-order time derivatives allow the coefficients of diffusion and reaction rate constants to be established as functions of size of the nanosystems in which these reactions occur. The Maxwell-Cattaneo and Jeffreys constitutive equations, as well as the higher-order constitutive equations, which describe the processes in reaction-diffusion systems, are obtained.

Thermodynamic Structure of Nonlinear Macrokinetics in Reaction-Diffusion Systems

2004 ◽  
Vol 11 (02) ◽  
pp. 185-202 ◽  
Author(s):  
Stanisław Sieniutycz
Keyword(s):  
Chemical Reactions ◽  
Reaction Diffusion ◽  
Transport Processes ◽  
Mass Action ◽  
Nonlinear Kinetics ◽  
Reaction Diffusion Systems ◽  
Thermodynamic Structure ◽  
Far From Equilibrium ◽  
Physical Consequences ◽  
Kinetics Of

Affinity picture — new for transport phenomena — and the traditional Onsagerian picture are shown to constitute two equivalent representations for kinetics of chemical reactions and transfer processes. Two competing directions in elementary chemical or transport steps are analyzed. Nonequilibrium systems are described by equations of nonlinear kinetics of Marcelin-Kohnstamm-de Donder type that contain terms exponential with respect to the Planck potentials and temperature reciprocal. Simultaneously these equations are analytical expressions characterizing the transport of the substance or energy through the energy barrier. We regard kinetics of this sort as potential representations of a generalized law of mass action that includes the effect of transfer phenomena and external fields. We also consider physical consequences of these kinetics closely and far from equilibrium, and show how diverse processes can be described. In these developments we point out the significance of nonlinear symmetries and generalized affinity. Correspondence with the Onsager's theory is shown in the vicinity of thermodynamic equilibrium. Yet, the theory shows that far from equilibrium the rates of transport processes and chemical reactions cannot be determined uniquely in terms of their affinities because these rates depend on all state coordinates of the system.

A Fully Coupled Chemomechanical Formulation With Chemical Reaction Implemented by Finite Element Method

2019 ◽  
Vol 86 (4) ◽  
Author(s):  
Jianyong Chen ◽  
Hailong Wang ◽  
K. M. Liew ◽  
Shengping Shen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Chemical Reactions ◽  
Chemical Reaction ◽  
Reaction Diffusion ◽  
Irreversible Thermodynamics ◽  
Free Energy Function ◽  
Stress Dependent ◽  
Fully Coupled ◽  
Element Method

Based on the irreversible thermodynamics, a fully coupled chemomechanical model, i.e., the reaction–diffusion–stress model, is proposed and implemented numerically into the finite element method (FEM) with user-defined element (UEL) subroutines in abaqus. Compositional stress and growth stress are induced by the diffusion and chemical reactions in the solid, and in turn, both the diffusion and chemical reactions are stress-dependent. By providing specialization of the chemical reaction and free energy function, the specialized constitutive equations are introduced, which are highly coupled and nonlinear. The FE formulations are derived from the standard Galerkin approach and implemented via UEL subroutines in abaqus. Several illustrative numerical simulation examples are shown. The results demonstrate the validity and capability of the UEL subroutines, and show the interactions among mechanical deformation, diffusion, and chemical reaction.

Instability and pattern formation in reaction-diffusion systems: A higher order analysis

2007 ◽  
Vol 127 (6) ◽  
pp. 064503 ◽  
Author(s):  
Syed Shahed Riaz ◽  
Rahul Sharma ◽  
S. P. Bhattacharyya ◽  
D. S. Ray
Keyword(s):  
Pattern Formation ◽  
Reaction Diffusion ◽  
Higher Order ◽  
Reaction Diffusion Systems ◽  
Order Analysis ◽  
Diffusion Systems

scholarly journals Stationary reaction–diffusion systems in L1

2018 ◽  
Vol 28 (11) ◽  
pp. 2161-2190 ◽  
Author(s):  
El Haj Laamri ◽  
Michel Pierre
Keyword(s):  
Chemical Reactions ◽  
Existence Of Solutions ◽  
Reaction Diffusion ◽  
Systems Modeling ◽  
Main Difficulty ◽  
Accretive Operators ◽  
Abstract Result ◽  
Reaction Diffusion Systems ◽  
Cross Diffusion ◽  
Diffusion Systems

We prove existence of solutions to stationary [Formula: see text] reaction–diffusion systems where the data are in [Formula: see text] or in [Formula: see text]. We first give an abstract result where the “diffusions” are nonlinear [Formula: see text]-accretive operators in [Formula: see text] and the reactive terms are assumed to satisfy [Formula: see text] structural inequalities. It implies that the situation is controlled by an associated cross-diffusion system and provides [Formula: see text]-estimates on the reactive terms. Next we prove existence for specific systems modeling chemical reactions and which naturally satisfy less than [Formula: see text] structural (in)equalities. The main difficulty is also to obtain [Formula: see text]-estimates on the nonlinear reactive terms.

Role of new resonance states on fluctuations and correlations of conserved charges in hadron resonance gas model

2018 ◽  
Vol 27 (10) ◽  
pp. 1850080
Author(s):  
Subhasis Samanta ◽  
Susil Kumar Panda ◽  
Bedangadas Mohanty
Keyword(s):  
Experimental Data ◽  
Lattice Qcd ◽  
Entropy Density ◽  
Higher Order ◽  
Thermodynamic Quantities ◽  
Net Charge ◽  
Resonance States ◽  
Conserved Charges ◽  
Thermodynamic Variables

We investigate the role of suspected resonance states, that are yet to be confirmed experimentally, on different thermodynamic quantities as well as the higher-order fluctuations and the correlation between conserved charges using ideal hadron resonance gas (HRG) model. We have discussed the temperature dependence of the various thermodynamic quantities and compared them with the lattice QCD result. We observe that the values of the bulk thermodynamic variables such as pressure, energy density, entropy density and second-order susceptibilities are increased by the inclusion of the additional resonances. Further, we find that the hadronic phase of lattice QCD result of [Formula: see text] and [Formula: see text] can be described well in ideal HRG model with the additional resonances. We have also studied the [Formula: see text] dependence of the fluctuation observables of net-proton, net-kaon and net-charge. Proper experimental acceptance cuts have been used in the model to compare with the data from experimental measurements. It has been observed that the experimental data of lower-order fluctuation observable can be described well by the ideal HRG model. However, higher-order fluctuation observables cannot be described by ideal HRG model for all [Formula: see text] studied here, which indicates the possibility of presence of critical or nonequilibrium physics for those energies. The effect of additional resonances on fluctuation observables of net-charge at different [Formula: see text] has also been studied. Finally, the chemical freeze-out parameters have been extracted from the experimental data of [Formula: see text] of net-proton and net-charge using two different sets of hadronic spectra. We find that for both the sets, the extracted temperature is slightly lower than those obtained from the hadronic yields. Moreover, it is observed that the extracted temperature of the system gets further reduced with addition of more resonances.

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