Semenov’s model

The model presented here is based on extending Semenov s model (2) of the induction period to cover the period of heat release. 

Semenov s model considers any branching chain reaction. It assumes that some initial dissociation of fuel leads to an intermediate species. This species, or some of its products, reacts with the fuel to create more of the intermediate species, implying branching reactions. If recombination, or other chain breaking reactions, are allowed one gets a rate equation for the concentration of the intermediate species [r]. 

Creighton ( 3,5) has shown that the induction period of methane oxidation is described by Semenov s model. Analysis of the results of numerical calculations using a detailed chemical kinetics reaction scheme showed that about eight reactions were dominant, and that the rate of creation and consumption of... 

Figure 1. Calculated mole fractions of fuel, intermediate species, and products using Semenov s model for a stoichiometric methane-air mixture initially at 1200 K and atmospheric pressure...

Figure 2. Reaction trajectories calculated with Semenov s model for a stoichiometric mixture at atmospheric pressure and various initial temperatures and radical concentration (-----), B C calculated using constant initial fuel and oxygen con-...

Semenov s model is the first of the stationary state theories that have dominated thermal combustion studies up to the present day. It characterizes exothermic chemical systems by ... 

We shall first review, in section 2, some experimental evidence of inhomogeneity-induced transitions. In section 3 we present a phenomenological model and apply it to two reaction systems exhibiting bistability and oscillatory behavior, respectively. Finally, in section 4, we outline a more fundamental approach to the problem of chemical reactions in a non-uniform medium, and illustrate its applicability on Semenov s model of thermal ignition. 

Or, would it be supposed in Semenov s formulation that the walls of the container were of infinite thickness, of infinite heat content or of infinite thermal conductivity, so that To was kept constant over a long time Such a situation will not be realistic. Besides, it seems that such a supposition that the container wall has a large overall coefficient of heat transfer is inconsistent with the Semenov model that the rate of heat transfer from a self-heating fluid filled in a container and placed in the atmosphere under isothermal conditions, through the whole fluid surface, across the container walls, to the atmosphere is far less than the rate of thermal conduction in the fluid. 

In this connection, there arc cases where the very ultimate of the Semenov model, in which the condition, UH A - 0, holds, is referred to as the Semenov s boundary conditions or the Semenov extreme [12]. 

Semenov, S. G., and N. V. Khodureva. 1992. Quantum-chemical estimate of nonspecific solvent effect on the electronic structure and spectra of molecules modeling nucleophilic fragments of lignin. Opt. Spektrosk. 73(2) 280-290. 

Ksenzhek, O.S., Gerod, V.S., Omel Chenko, A.M., Semenov, S.N., Sotnichenkov, A.I., and Miro-schinikov, A.I., 1978, Interaction of the cardiotoxin of the venom of the cobra Naja naja oxiana with phospholipid membrane model system, A/b/. Biol. 12 1057-1065. 

This deals with purely convective heating, but defining 6 by Equation (5.12), we take h = k/r0 and r0 = V/S of the Semenov model. Equation (5.18) approximates the constant surface temperature case. Also, here the initial temperature is taken as Too- If we allow no convective cooling, the adiabatic equation becomes... 

Aggeli, A., Nyrkova, I.A., Bell, M., Harding, R., Carrick, L., McLeish, T.C.B., Semenov, A.N., and Boden, N. "Hierarchical self-assembly of chiral rod-like molecules as a model for peptide beta-sheet tapes, ribbons, fibrils, and fibers". Proc. Nat. Acad. Sci. U.S.A. 98(21), 11857-11862 (2001b). 

Another model based on Emery and Drickamer s theory (Schimpf and Semenov, 2004) yields... 

Shevchenko, S. M., T. J. Elder, S. G. Semenov, andM. Ya.Zarubin. 1995. Conformational effects on the electronic structure and chemical reactivity of lignin model p-quinone methides and benzyl cations. Res. Chem. Inter. 21(3-5) 413 23. 

SEMENOV developed a model of this phenomenon in about 1930, which is still used in studies on industrial safety. A batch reactor of volume V equipped with a heat exchanger of area S is considered. The reaction medium is assumed to be perfectly-stirred and an exothermic chemical reaction (AjH < 0) with the following kinetic law is... 

Cho et al. (2000) studied the segregation dynamics of block copolymers to the interface of an immiscible polymer blend and compared experimental results to the predictions of various theories for a poly(styrene-b-dimethylsiloxane) [P(S-b-DMS) M = 13,000] symmetric diblock copolymer system added to a molten blend of the corresponding immiscible homopolymers. They used the pendant drop technique at intermediate times and compared their results to the predictions of diffusion-limited segregation models proposed by Budkowski, Losch, and Klein (BLK) and by Semenov that have been modified to treat interfacial tension data. The apparent block copolymer diffusion coefficients obtained from the two analyses fall in the range of 10 -10 cm /s, in agreement with the estimated self-diffusion coefficient of the PDMS homopolymer matrix. 

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