Reaction-Kinetic Systems

In this chapter we consider the simulation of reaction-kinetic systems. The following examples illustrate the modeling of various reaction systems. 

Differential pulse voltanmietry and square-wave voltammetry are the main pulsed techniques used in biosensing. The main advantage exhibited by these techniques is the low capacitive current, which can improve the sensitivity of the voltammetric procedures. Differential pulse voltammetry is usually applied in irreversible systems and in systems that present slow-reaction kinetics. Square-wave voltammetry is usually applied in reversible systems and in rapid reaction kinetics systems. 

It is clear that, based on small perturbations of concentrations, lifetimes can be related to chemical kinetic systems. These lifetimes do not belong to species, however, but to combinations of species concentrations defined by the left eigenvectors of the Jacobian, called modes. A matrix Jacobian of size x has eigenvalues, and therefore, the number of modes is identical to the number of variables. In the case of a linear system (in reaction kinetics, this means that the mechanism consists of first-order and zeroth-order reactions only), the Jacobian is constant and does not depend on the values of variables (concentrations). If the system is nonlinear, which is the case for most reaction kinetic systems, the Jacobian depends on the values of variables, i.e. the timescales depend on the concentrations. In other words, the set of timescales belong to a given point in the space of concentrations (phase space) and are different from location to location (or from time point to time point if the concentrations change in time). 

The computer codes described above are able to simulate spatially homogeneous reaction kinetics systems, which are either characterised by spatially and temporally constant rate coefficients or utilise user-defined functions for the rate parameters (e.g. in the case of KPP). For the simulation of high-temperature gas kinetic systems, such as combustion, pyrolytic and other chemical engineering problems, the rate coefficients may change substantially as a function of temperature and pressure and maybe also as a function of gas composition. Typically, the temperature and pressure is not constant during such simulations due to heat release, and their change has to be calculated during the course of the reaction. Several computer codes are available for such types of simulations. 

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