Quasisteady-state approach

In the absence of convection the behavior can often be analyzed using a quasi-steady-state solution to the diffusion equations because the time required for diffusion to produce equilibration in the drop, which is of order d lD with a the drop radius (typically 25 to 50 pm) and D the diffusivity, is normally much less than the time of the experiment (several minutes). This quasisteady-state approach predicts that drop composition is uniform but varies with time and that the time required for intermediate phase formation to begin for given drop and solution compositions is proportional to the square of the initial drop radius. Results obtained using the oil drop technique that are consistent with these predictions are discussed below. 

The quasisteady-state approach can be applied in transient simulations, in a similar fashion to the ID models discussed in Section 3.1. The only retained transient term is that of solid heat conduction in Eq. (3.29). Quasisteady-state and fully transient 2D channel simulations have been recendy compared for fuel-lean hydrogen hetero-Zhomogeneous combustion over Pt in Brambiha et al. (2014). Requirements for the appUcability of quasisteady-state approach have been elaborated in Schneider et al. (2008) and Karagiannidis and Mantzaras (2010). 

Another conceivable limiting case, though one less likely to be approached in practical cases, is that where the total hydrogen concentration always remains far below that of the traps, which continue to capture hydrogen irreversibly. For this case, as Corbett et al. (1986) have pointed out, the concentration of free monatomic hydrogen will approach a quasisteady-state profile that decays exponentially with the depth x. The concentration of trapped hydrogen, of course, will at any point of space approach a linear increase with time. 

An extremely useful intermediate approach, which is capable of handling the whole flame reaction zone, is that employing the quasisteady state (q.s.s.) assumption, referred to in Sect. 5.4.2. In this case a radical pool consisting only of H, OH and O is considered. The growth of the overall pool is now effectively determined by reaction (ii), and its decay by the recombination steps. Its sub-division into the separate components is carried out in rich flames by way of the q.s.s. assumptions on OH and O. In more precise terms, the overall mass flux of free radicals... 

Reaction mechanisms in the literature are often direct, because physical intuition encourages avoidance of excess steps. In considering the mechanism of a reaction, one often postulates ahead of time an implicit quasisteady state, i.e., a combination of steps that explains the observed net reaction and conserves all intermediate species. In our approach, however, we are interested in identifying all possible direct mechanisms that are consistent with the postulated set of steps. 

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