The model equations consider axial dispersion, interfacial mass transfer, intraparticle diffusion, and multi-component Langmuir isotherm.
Three different modelling and simulation approaches are presented and compared: an analytical solution of the equilibrium model, a closed-form solution of model equations considering both axial dispersion and mass transfer resistance, and a numerical solution of the general rate model.
Four model equations are considered: linear advection, non-linear advection, diffusion, and advection diffusion, with cases chosen to mimic features present in compressible gas dynamics.
Our method relies on accurate, essentially noise-free, solutions of the basic microscopic kinetic equation, e.g. the Boltzmann equation or a kinetic model equation; in this paper, the BGK model and the ES-BGK model equations are considered.
The mixed model equations were considered converged when the relative difference between the left-hand and right-hand sides of the mixed model equations was smaller than 1.0 * 10-10.
The outline of the paper is the following: first, we present the constitutive equations considered in the model.
To describe the model equations, we consider (Omegasubsetmathbb{R}^{3}) a bounded and regular open set of (mathbb{R}^{3}).
However, microscopically these models are distinct from the Lotka-Volterra equations considered above.
The model is based on equations considering reaction and diffusion components.
In the model, the cage dynamic equations considering six degree-of-freedom and the balls dynamic equations considering two degree-of-freedom were solved.
