Singular perturbation for a class of coupled chemical reaction and diffusion systems

1995 ◽  
Vol 16 (6) ◽  
pp. 549-556
Author(s):  
Chen Songlin
Keyword(s):  
Singular Perturbation ◽  
Chemical Reaction ◽  
Diffusion Systems ◽  
And Diffusion ◽  
Reaction And Diffusion

scholarly journals Reaction-Diffusion Systems: Self-Balancing Diffusion and the Use of the Extent of Reaction as a Descriptor of Reaction Kinetics

2019 ◽  
Author(s):  
Miloslav Pekař
Keyword(s):  
Reaction Kinetics ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
And Diffusion ◽  
Reaction And Diffusion

Self-balancing diffusion is a concept which restricts the introduction of extents of reactions. This concept is analyzed in detail for mass- and molar-based balances of reaction-diffusion mixtures, in relation to non-self-balancing cases, and with respect to its practical consequences. A note on a recent generalization of the concept of reaction and diffusion extents is also included.<br>

A computational model for diffusion-reaction-deformation coupled problems and its finite element implementation

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Bao Qin ◽  
Yexin Zhou ◽  
Zheng Zhong
Keyword(s):  
Finite Element ◽  
Chemical Reaction ◽  
Reaction Rate ◽  
Diffusion Processes ◽  
Diffusion Reaction ◽  
Governing Equations ◽  
Content Type ◽  
Finite Element Software ◽  
And Diffusion ◽  
Reaction And Diffusion

PurposeA diffusion-reaction-deformation coupled model is employed and implemented as a user-defined element (UEL) subroutine in the commercial finite element software package ABAQUS.Design/methodology/approachChemical reaction and diffusion are treated as two distinct processes by introducing the extent of reaction and the diffusion concentration as two kinds of independent variables, for which the independent governing equations for chemical reaction and diffusion processes are obtained. Furthermore, an exponential form of chemical kinetics, instead of the linearly phenomenological relation, between the reaction rate and the chemical affinity is used to describe reaction process. As a result, complex chemical reaction can be simulated, no matter it is around or away from equilibrium.FindingsTwo numerical examples are presented, one for validation of the model and another for the modeling of the deflection of a plane caused by a chemical reaction.Originality/value1. Independent governing equations for diffusion and reaction processes are given. 2. An exponential relation between the reaction rate and its driving force is employed. 3. The UEL subroutine is used to implement the finite element procedure.

Chemical‐reaction and diffusion rates in solids produced by shock compression

1986 ◽  
Vol 59 (6) ◽  
pp. 1956-1961 ◽  
Author(s):  
J. Kleiman ◽  
P. W. C. Chan ◽  
N. Salansky ◽  
I. I. Glass
Keyword(s):  
Shock Compression ◽  
Chemical Reaction ◽  
Diffusion Rates ◽  
And Diffusion ◽  
Reaction And Diffusion
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