Non-isothermal reaction-diffusion systems with thermodynamically coupled heat and mass transfer

Demi̇rel, Yaşar

doi:10.1016/j.ces.2005.11.063

Cited by 30 publications

(39 citation statements)

References 21 publications

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“…͑46͒. For the same reason, our present results may also be applicable to some kinds of open systems 36 for which the stationary solution can still be represented by Eqs. ͑45a͒ and ͑45b͒ with v = 0, but with a nonvanishing diffusion flux J at the boundaries.…”

Section: B Nonequilibrium Structure Factormentioning

confidence: 59%

“…Hence, Eq. ͑47͒ displays corrections to the penetration length due to the Soret and Dufour effects, similarly to recent work of Demirel 36 for the nonlinear regime. For a so-called "diffusion-controlled" process, is very large, so that the ratio d / L becomes very small.…”

Section: A the Stationary Solutionmentioning

confidence: 80%

“…͑45a͒ and ͑45b͒ have often been considered in the context of reacting gases inside pores of a solid catalyst pellet. [34][35][36][37] In those studies, the temperature dependence of the rate constant L r is not neglected, and an Arrhenius dependence, 36 or other more complicated nonlinear kinetic expressions 34,35,37 are assumed for L r ͑T͒. These approaches lead to a system of nonlinear coupled differential equations for the temperature and activity profiles that can be solved only numerically.…”

Section: A the Stationary Solutionmentioning

confidence: 99%

“…9 The dimensionless parameter in Eq. ͑47͒ has been used by Demirel 36 when solving the nonlinear ͑Arrhen-ius͒ version of Eq. ͑45a͒ and ͑45b͒.…”

Section: A the Stationary Solutionmentioning

confidence: 99%

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Concentration fluctuations in nonisothermal reaction-diffusion systems

Zárate

Sengers

Bedeaux

et al. 2007

The Journal of Chemical Physics

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In this paper a simple reaction-diffusion system, namely a binary fluid mixture with an association-dissociation reaction between the two components, is considered. Fluctuations at hydrodynamic spatiotemporal scales when a temperature gradient is present in this chemically reacting system are studied. First, fluctuating hydrodynamics when the system is in global equilibrium ͑isothermal͒ is reviewed. Comparing the two cases, an enhancement of the intensity of concentration fluctuations in the presence of a temperature gradient is predicted. The nonequilibrium concentration fluctuations are spatially long ranged, with an intensity depending on the wave number q. The intensity exhibits a crossover from a ϰq −4 to a ϰq −2 behavior depending on whether the corresponding wavelength is smaller or larger than the penetration depth of the reacting mixture. This opens a possibility to distinguish between diffusion-or activation-controlled regimes of the reaction by measuring these fluctuations. In addition, the possible observation of these fluctuations in nonequilibrium molecular dynamics simulations is considered.

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Section: B Nonequilibrium Structure Factormentioning

confidence: 59%

Section: A the Stationary Solutionmentioning

confidence: 80%

Section: A the Stationary Solutionmentioning

confidence: 99%

“…9 The dimensionless parameter in Eq. ͑47͒ has been used by Demirel 36 when solving the nonlinear ͑Arrhen-ius͒ version of Eq. ͑45a͒ and ͑45b͒.…”

Section: A the Stationary Solutionmentioning

confidence: 99%

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Concentration fluctuations in nonisothermal reaction-diffusion systems

Zárate

Sengers

Bedeaux

et al. 2007

The Journal of Chemical Physics

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“…(10) with v = 0 but with a non-vanishing diffusion flux J at the boundary. 40 We shall not consider boundary conditions for the fluctuating fields in this paper. In general, fluctuations in fluids subjected to a temperature gradient at large wavelengths comparable to the size of the system are affected by the presence of boundaries.…”

Section: B Equations For the Fluctuationsmentioning

confidence: 99%

Concentration fluctuations in non-isothermal reaction-diffusion systems. II. The nonlinear case

Bedeaux

Zárate

Pagonabarraga

et al. 2011

The Journal of Chemical Physics

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In this paper, we consider a simple reaction-diffusion system, namely, a binary fluid mixture with an association-dissociation reaction between two species. We study fluctuations at hydrodynamic spatiotemporal scales when this mixture is driven out of equilibrium by the presence of a temperature gradient, while still being far away from any chemical instability. This study extends the analysis in our first paper on the subject [J. M. Ortiz de Zárate, J. V. Sengers, D. Bedeaux, and S. Kjelstrup, J. Chem. Phys. 127, 034501 (2007)], where we considered fluctuations in a non-isothermal reactiondiffusion system but still close to equilibrium. The present extension is based on mesoscopic nonequilibrium thermodynamics that we recently developed [D. Bedeaux, I. Pagonabarraga, J. M. Ortiz de Zárate, J. V. Sengers, and S. Kjelstrup, Phys. Chem. Chem. Phys. 12, 12780 (2010)] to derive the law of mass action and fluctuation-dissipation theorems for the random contributions to the dissipative fluxes in the nonlinear macroscopic description. Just as for non-equilibrium fluctuations close to equilibrium, we again find an enhancement of the intensity of the concentration fluctuations in the presence of a temperature gradient. The non-equilibrium concentration fluctuations are in both cases spatially long ranged, with an intensity depending on the wave number q. The intensity exhibits a crossover from a ∝ q −4 to a ∝ q −2 behavior depending on whether the corresponding wavelength is smaller or larger than the penetration depth of the reacting mixture. This opens a possibility to distinguish between diffusion-or activation-controlled regimes of the reaction experimentally. The important conclusion overall is that non-equilibrium fluctuations in non-isothermal reaction-diffusion systems are always long ranged.

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A Non-Isothermal Constitutive Model for Chemically Active Elastoplastic Rocks

Roshan

Oeser

2011

Rock Mech Rock Eng

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Hydration/dehydration of water-active rocks under non-isothermal conditions is encountered in many industries, in particular the drilling industry. Water-active rocks can adsorb water on their basal crystal surfaces on both the external, and, in the case of expanding lattice clays, the inter-layer surfaces. There are two main mechanisms in which the instability may occur for a structure built in water-active rocks. First mechanism is the change in stresses resulted from mechanical, hydraulic, chemical and thermal interaction, which we formulate based on the concept of non-equilibrium thermodynamics. Second mechanism illustrates the change in mechanical properties of the rock due to physic-chemical interaction between the rock and exposed fluid. We postulate the later mechanism in terms of chemically active plastic deformation by using the modified Cam Clay model. The complete governing equations for non-isothermal chemo-poro-elastoplastic rock are therefore presented. A three-dimensional finite element model is then developed to solve the obtained governing equations. From the numerical results, it was found that the effect of temperature coupling term on stress cannot be ignored when non-isothermal conditions are encountered. However, this effect is almost trivial on pore pressure. It was also revealed that the effect of change in the shale's mechanical properties on stability due to physic-chemical interaction is as important as change in stresses due to mechanical, hydraulic, chemical and thermal interactions.

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Non-isothermal reaction-diffusion systems with thermodynamically coupled heat and mass transfer

Cited by 30 publications

References 21 publications

Concentration fluctuations in nonisothermal reaction-diffusion systems

Concentration fluctuations in nonisothermal reaction-diffusion systems

Concentration fluctuations in non-isothermal reaction-diffusion systems. II. The nonlinear case

A Non-Isothermal Constitutive Model for Chemically Active Elastoplastic Rocks

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