The concept of the limiting step is extended to the asymptotology of multiscale reaction networks. Complete theory for linear networks with well separated reaction rate constants is developed. We present algorithms for explicit approximations of eigenvalues and eigenvectors of kinetic matrix. Accuracy of estimates is proven. Performance of the algorithms is demonstrated on simple examples. Appl...

In a previous paper, Brouwers and Van Eijk [1] presented a theoretical study on the dissolution (reaction) of pulverised powder coal fly ash. This fly ash was modelled as hollow spheres, and a shrinking core model was derived for these hollow spheres that contain two regions (an outer hull and an inner region). The obtained analytical equations were applied to the dissolution experiments by Pie...

Siphons in a chemical reaction system are subsets of the species that have the potential of being absent in a steady state. We present a characterization of minimal siphons in terms of primary decomposition of binomial ideals, we explore the underlying geometry, and we demonstrate the effective computation of siphons using computer algebra software. This leads to a new method for determining wh...

We consider absorbing chemical reactions in a fluid flow modeled by the coupled advection-reaction-diffusion equations. In these systems, interplay between diffusion and transportation causes enhanced dissipation phenomenon. show that time scale, together with reaction coupling strength, determines characteristic scale of reaction.

In this paper, the bioconvective flow in a porous square cavity containing oxytactic microorganism in the presence of chemical reaction is investigated. The bioconvection flow and heat transfer in porous media are formulated based on the Darcy model of Boussinesq approximation. The governing partial differential equations are solved using the Galerkin finite element method. The computational nu...