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.
A review of the deterministic and diffusion approximations for stochastic chemical reaction networks
