Effect of mesoscopic conservative phenomena in the dynamics of chemical reactions at the macroscopic scale

Zárate-Navarro, Marco A.; García-Sandoval, J.P.; Dochain, Denis; Hudon, Nicolas

doi:10.1016/j.physa.2017.05.029

Cited by 10 publications

(5 citation statements)

References 19 publications

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“…For the diffusion process, the linear relationship between diffusion flux and concentration gradient is given by Fick's diffusion laws and appears to be valid for a wide range of concentrations. On the contrary, in the field of chemical reactions, the linear proportionality between chemical flows and forces seems strictly valid only near the equilibrium [54][55][56]. This question constitutes an advantage for our formalism, where this relation of proportionality emerges naturally for linear systems.…”

Section: Discussionmentioning

confidence: 98%

Energy and entropy on irreversible chemical reaction-diffusion systems with asymptotic stability

Ledesma-Durán,

Santamaría-Holek

2021

Preprint

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Section: Discussionmentioning

confidence: 98%

Energy and entropy on irreversible chemical reaction-diffusion systems with asymptotic stability

Ledesma-Durán,

Santamaría-Holek

2021

Preprint

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“…For simplicity, it is assumed that all chemical species behave ideally, i.e. incompressible liquids and diluted nonionic chemical species, such that no excess functions are required and the activities are equal to the mole fraction.These assumptions lead to a mass action rate obtained from mesoscopic non-equilibrium thermodynamics [37] is…”

Section: A First Law Balancesmentioning

confidence: 99%

“…is the only term in the DSOI that causes this sign shift in the entropy production dynamics [14], [37].…”

Section: B Entropy Entropy Production and Stabilitymentioning

confidence: 99%

Dissipative Boundary Control for an Adiabatic Plug Flow Reactor With Mass Recycle

et al. 2022

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In this contribution the stability properties and regulation of a class of convective systems described by first order hyperbolic partial differential equations are studied. The systems' setting is consistent with the first and second laws of thermodynamics, allowing to use the entropy functional as a storage function and the internal entropy production as the dissipation in an analogue context to Hamiltonian systems. It is found that the difference of the entropy evaluated at the boundaries is directly proportional to the supply rate, fulfilling the dissipation inequality. Furthermore, the dynamics of the entropy balance allows to define a saturated Proportional-Integral controller with variable parameters, whose design is achieved through a cascade structure. The inner loop tracks an entropy reference, while the outer loop tracks a process variable. The main advantage of the regulation design is that only a lumped actuator is needed with continuous measurements at the boundaries. The controller is designed for an adiabatic plug flow reactor with a recycle of the output stream into the input stream, where the recycle rate is used as the control variable. Finally, the controller is tested to track a set point under several disturbances.

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“…The stoichiometric coefficients for the k reactants and l products are given by the sparse vectors A = col{ α 1 , …, α k , 0 n − k } and B = col{0 k , β 1 , …, β l , 0 n − k − l }, respectively. This thermodynamically consistent reaction rate has the following structure

r = D_{r} \exp ((), - \frac{((), 1 - ε_{0}) A_{d}^{o} + ε_{0} A_{r}^{o}}{RT}) ([], \exp ((), \frac{A_{d}}{italicRT}) - \exp ((), \frac{A_{r}}{italicRT}))

where T is the temperature, R is the ideal gas constant, D r is a reaction diffusion coefficient, ε 0 ∈ [0, 1] is a constant related to the point where the transition state occurs in the mesoscopic reaction path (for further detail, see),

A_{d} = \sum_{normali = 1}^{k} a_{i} μ_{i}

and

A_{r} = \sum_{normalj = 1}^{l} b_{i} μ_{normalk + normalj}

are the direct and reverse affinities, and

A_{d}^{o} = \sum_{normali = 1}^{k} a_{i} μ_{i}^{o}

and

A_{r}^{o} = \sum_{normalj = 1}^{l} b_{i} μ_{normalk + normalj}^{o}

are the standard direct and reverse affinities that do not depend on the extend of the reaction. Here

μ_{i} = μ_{i}^{o} + italicRT \ln a_{i}

is the chemical potential of species i = 1,2,…, n , and a i is the activity.…”

Section: Constitutive Equationsmentioning

confidence: 99%

A simple kinetic model for complex rheological fluids based on irreversible thermodynamics

et al. 2019

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In this work, we analyze the kinetics of the entanglement-disentanglement process of complex fluids coupled to a rheological constitutive equation of state within an irreversible thermodynamics framework. In the context of the coupling between the kinetics and the mechanical phenomena, we assume that the rate constants are functions of the affinities that contain the chemical potentials, which are themselves functions of the extended Gibbs free energy containing the irreversible dissipation terms. Although the derived model has a simple mathematical structure, it is able to predict complex flow behaviors, including shear-thickening, shear-thinning, and more complex flow histories such as shear-banding. As special case, we derive the constitutive equations of the Bautista-Manero-Puig (BMP) model in which the material constants have a thermodynamic basis and have been successfully used for the last two decades to predict the behavior of complex fluids such as the ones examined here.

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Effect of mesoscopic conservative phenomena in the dynamics of chemical reactions at the macroscopic scale

Cited by 10 publications

References 19 publications

Energy and entropy on irreversible chemical reaction-diffusion systems with asymptotic stability

Energy and entropy on irreversible chemical reaction-diffusion systems with asymptotic stability

Dissipative Boundary Control for an Adiabatic Plug Flow Reactor With Mass Recycle

A simple kinetic model for complex rheological fluids based on irreversible thermodynamics

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