Zeldovich equation

A number of relations between rate of activated adsorption and coverage have been proposed. Of these, one has been particularly frequently used, the Roginskii-Zeldovich equation sometimes called the Elovich equation,... 

In the oxidation field this equation was first used by Tammann and Koster (33)> but we shall refer to it in this article as the Roginsky-Zeldovich equation, since we are mainly concerned here with chemisorption. 

Equation (3) is the w ell-known Roginsky-Zeldovich equation (7). The integrated form is... 

As emphasized elsewhere 8), the Roginsky-Zeldovich equation is obeyed so frequently in chemisorption that for its interpretation in terms of any one chosen model, the mere linearity of trial plots such as those in Figs. 2 and 3 is not a particularly satisfactory criterion of validity. It is therefore important to examine the form of the pressure and temperature dependence of the parameters. 

Zeldovich Equation for NO Synthesis in Quasi-Equilibrium Thermal Systems. 

Using the Zeldovich equation (6-62), calculate the time required for reaching quasiequilibrium concentration of nitrogen oxides (NOx) in stoichiometric N2-O2 atmospheric-pressure mixture at different thermal plasma temperatures 3000, 3500, and 4000 K. Analyzing activation energies in the Zeldovich equation, find out the limiting reaction responsible for establishing of the quasi-equilibrium concentration of NOx. 

The following Zeldovich equation is valid for I m the formation of a critical cluster... 

Thermal plumes above point (Fig. 7.60) and line (Fig. 7.61) sources have been studied for many years. Among the earliest publications are those from Zeldovich and Schmidt. Analytical equations to calculate velocities, temperatures, and airflow rates in thermal plumes over point and line heat sources with given heat loads were derived based on the momentum and energy conservation equations, assuming Gaussian velocity and excessive temperature distribution in... 

A reaction mechanism is a series of simple molecular processes, such as the Zeldovich mechanism, that lead to the formation of the product. As with the empirical rate law, the reaction mechanism must be determined experimentally. The process of assembling individual molecular steps to describe complex reactions has probably enjoyed its greatest success for gas phase reactions in the atmosphere. In the condensed phase, molecules spend a substantial fraction of the time in association with other molecules and it has proved difficult to characterize these associations. Once the mecharrism is known, however, the rate law can be determined directly from the chemical equations for the individual molecular steps. Several examples are given below. 

As implied in the previous section, the Russian investigators Zeldovich, Frank-Kamenetskii, and Semenov derived an expression for the laminar flame speed by an important extension of the very simplified Mallard-Le Chatelier approach. Their basic equation included diffusion of species as well as heat. Since their initial insight was that flame propagation was fundamentally a thermal mechanism, they were not concerned with the diffusion of radicals and its effect on the reaction rate. They were concerned with the energy transported by the diffusion of species. 

This procedure is sometimes referred to as the Schvab-Zeldovich transformation. Mathematically, what has been accomplished is that the nonhomogeneous terms (m and H) have been eliminated and a homogeneous differential equation [Eq. (6.7)] has been obtained. 

In the Zeldovich method of spark ignition, the spark is replaced by a point heat source, which releases a quantity of heat. The time-dependent distribution of this heat is obtained from the energy equation... 

The explosion of gaseous methyl nitrate subjected to the influence of an electric spark at 25°C was investigated by Zeldovich and Shaoulov [4] who found that it differs from an explosion initiated by heat. According to these authors, the fo low-ing equations express the decomposition reaction caused by an electric spark ... 

Equation 19.17 may be interpreted in a simple way. If the equilibrium concentration of critical clusters of size Afc were present, and if every critical cluster that grew beyond size Mc continued to grow without decaying back to a smaller size, the nucleation rate would be equal to J = (3CNexp[-AQc/(kT)]. However, the actual concentration of clusters of size Mc is smaller than the equilibrium concentration, and many supercritical clusters decay back to smaller sizes. The actual nucleation rate is therefore smaller and is given by Eq. 19.17, where the first term (Z) corrects for these effects. This dimensionless term is often called the Zeldovich factor and has a magnitude typically near 10-1. 

Following Zeldovich and Ovchinnikov [35], let us consider the role of reactant diffusion in establishing equilibrium in a reversible A B + B reaction. In terms of formal kinetics, it is described by the equations... 

Let us consider now the irreversible A + B —> C reaction in the case of equal reactant concentrations, tj-a = nB, following Ovchinnikov and Zeldovich [35], The reaction kinetics obeys the equations... 

As it was first noted by Zeldovich [33] it is not easy to distinguish experimentally between exponents 1 and 3/4 (equations (2.1.8) and (2.1.77)). The approach just presented cannot be applied to charged reactants since their electrostatic attraction cuts off spatial fluctuation spectrum at the Debye radius. 

The formal secondary quantisation procedure presented first by Doi [107], Zeldovich and Ovchinnikov [35] reduces equations (2.3.67) into... 

In diffusion combustion of unmixed gases the combustion intensity is limited by the supply of fuel and oxidizer to the reaction zone. The basic task of a theory of diffusion combustion is the determination of the location of the reaction zone and of the flow of fuel and oxidizer into it for a given gas flow field. Following V. A. Schvab, Ya.B. considered (22) the diffusion equation for an appropriately selected linear combination of fuel and oxidizer concentrations such that the chemical reaction rate is excluded from the equation, so that it may be solved throughout the desired region. The location of the reaction zone and the combustion intensity are determined using simple algebraic relations. This convenient method, which is universally used for calculations of diffusion flames, has been named the Schvab-Zeldovich method. 

It should be mentioned that, as is often the case in a first draft, the author based his treatment of the turbulent convection on certain assumptions which in fact were not necessary, in particular the semi-empirical concept of L. Prandtl. Moreover, even in the analysis of laminar convection, the author [cf., for example the transition from equation (9) to equation (10)], to derive the asymptotic laws, resorts to simplifications of the equations which are really not necessary. Actually, it is possible to manage without these assumptions so that Zeldovich s asymptotic laws (8), (8a), (11), and (11a) may be obtained by simple dimensional analysis under the most general assumptions. 

Changes with time in the isotopic exchange reaction rate between H2 and HDO(v) over a hydrophobic Pt-catalyst induced by the addition of HN03 were studied experimentally The HN03 poisoning was found to be reversible and was well explained in terms of the competitive adsorption of HNO, with H2 or HDO onto the catalytic active sites. The adsorption equilibrium for HN03 could be expressed by the Frumkin-Temkin equation and the time evolution of the activity was well expressed by the Zeldovich rate equation. 

---