Regimes of operation

FIG. 22-28 Regimes of operation of cross-flow-electrofiltration (a) voltage less than critical, (h) voltage equal to the critical voltage, (c) voltage greater than critical. 

Figure 10.38 shows an input window with three triangular fuzzy sets NB, Z and PB. Each set is positioned in its regime of operation by the centre parameter c so that, for example, NB can only operate on the negative side of the universe of discourse. The width of each set is controlled by parameter ri . 

If the data yield a satisfactory straight line passing through the origin, the reaction rate expression assumed in step 1 is said to be consistent with the data and may be accepted as a basis for subsequent work in the same temperature-concentration regime of operation. The slope of this line is equal to the reaction rate constant k. If the data do not fall on a satisfactory straight line, one must return to step 1 and assume a new mathematical form of the reaction rate expression. 

Dense and Patterned Thin Films Confirming 4820 Two Regimes of Operation... 

Figure 51. Three regimes of operation for crossflow electrofiltration (23)...

Terms such as diffusion limited or diffusion controlled are undesirable because a rate may be larger in regimes of heat or mass transfer than in the kinetic regime of operation, i.e., when gradients are negligible. 

In Fig. 13.7 the experimental drain currents are compared with modeled characteristics. Below, the simple nine-term OFET model that is used here will be outlined. Three regimes of operation are distinguished ... 

Fig. 12.4 Relation between the equilibrium pressure Peq and the normalized radius r of the afferent arteriole for different values of the muscular activation level [f. The solid curves represent our analytical approximation and the dashed curves represent the exact numerical solution. The area bounded by dotted lines corresponds approximately to the regime of operation for the model.

In cocurrent-up fluid-particle two-phase flow, the fluid tends to choose an upward path with minimal resistance, while the particles tend to array themselves with minimal potential energy. Stability of the two-phase system calls for mutual coordination, as much as possible, between the fluid and the particles in following their respective tendencies. This applies for all the three broad regimes of operation fixed bed, fluidization and transport. When neither the fluid nor the particles can dominate the system, either has to compromise and yield its intrinsic tendencies to those of the other to reach a stable state. However, if the system is fully dominated by either the fluid or the particles, the intrinsic tendency of the dominant one will be satisfied exclusively, with full suppression of that of the other. 

If we consider the set of six equations on mass and momentum conservation on the one hand, and the characteristic energy extrema for stability of the three broad regimes of operation on the other, mathematical modeling for local hydrodynamics of particle-fluid two-phase flow beyond minimum fluidization needs therefore to satisfy the following constraints ... 

Figure 1. Drain current-drain voltage (Ids-Vds) curve at a given gate voltage (Vqs), illustrating the pre-pinch-off and post-pinch-off regimes of operation, which are distinguished by Vdsat = Vqs - Vx.

Of the three common mobilities used for TTFT assessment, the effective mobility is probably the best channel mobility figure-of merit since (i) it is evaluated in the linear regime of operation where the channel is most uniform and the concept of mobility as a proportionality constant betw een the electric field and carrier velocity is most appropriate, and (ii) the term... 

The different investigators have covered different regimes of operation. Any value of m less than 1.0 indicates the possibihty of heterogeneous regime and Eqs. (87) and (88) are not applicable for such a regime. 

The apparent transfer coefficient of the cathodic reaction, ac, is a measure of the sensitivity of the transition state to the drop in electrostatic potential between electrolyte and metal [109,112]. According to Ref. 113, it is ac = 0.75 for the O2 reduction on Pt in aqueous acid electrolytes. In Ref. Ill the value ac = 1.0 was reported instead. Since the cathodic reaction is a complex multistep process, it might follow several reaction pathways, and the competition between them is affected by the operation conditions (rj, p, T). Therefore, different values of ac have been reported in different regimes of operation. Although in the simple reactions the transfer coefficient is a microscopic characteristic of the elementary act [112], for complex multistage reactions in fuel cell electrodes it is rather an empirical parameter of the model. The dependence of effective a for methanol oxidation on the catalyst layer preparation was recently studied [114]. 

The parameter ah A is dependent on the regime of operation for the spray regime... 

As noted in Section 12.1.1, there are two quite different regimes of operation of distillation trays, the froth regime and the spray regime. In this section we develop detailed models of the hydrodynamic and mass transfer character of these regimes. 

Doraiswamy and Sharma (1984) have given detailed derivations for the overall rates of reaction and the conditions to be satisfied in each regime of operation. The final eqnations and conditions are snmmarized in Table 11.17. It is likely that a reaction falls in the intermediate range or more than one regime. For these cases, expressions for the overall rates are given in Table 11.18. Recently, Doraiswamy (2001) has given similar tables for some complex reactions. 

Theoryof Mass Transfer Accomplished by an Irreversible Chemical Reaction Overall Rates of Reaction and Conditions to Be Satisfied for the Four Regimes of Operation... 

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