Constant rate regime

Figure 6.30. Kinetics of transformation of Co in the ERO fraction in two Israeli soils according to the two-constant rate model (a) and the simple Elovich model (b), respectively. Soils were incubated under the saturation paste regime (modified after Han et al., 2002b. Reprinted from J Environ Sci Health, Part A, 137, HanF.X., Banin A., Kingery W.L., Li Z.P., Pathways and kinetics of transformation of cobalt among solid-phase components in arid-zone soils, p 192, Copyright (2003), with permission from Taylor Francis)...

Using the characteristic parameters shown in the figure, critical transition diameters were calculated. The values obtained were 570 microns for transition from non-inertial to inertial and 1140 microns from inertial to coating, and are seen to be within a factor of 1.5-2 of the experimental data which, in view of the approximate nature of these calculations, is quite remarkable. The constant rate of growth in the non-inertial regime also implies that only growth by nucleation occurred and that coalescence (see Fig. 12) was not prevalent. 

Fed-batch cultures differ from batch cultures by the possibility of additional input of the main substrate. Potentially, fed-batch cultures are very promising since in these cultures the possibility to prolong a hydrogen production phase with approximately constant rate exists. Unfortunately publications reporting the application of this cultivation regime for hydrogen production systems are not known to us. 

Stage II is the quasi-steady-state nucleation regime. During this period, the distribution of clusters has built up into a quasi-steady state and stable nuclei are being produced at a constant rate. 

Initially, when the ApBq layer is very thin, the reactivity of the A surface is realised to the full extent because the supply of the B atoms is almost instantaneous due to the negligibly short diffusion path. In such a case, the condition kom kW]/x is satisfied. Therefore, if the surface area of contact of reacting phases A and ApBq remains constant, chemical reaction (1.1) takes place at an almost constant rate. In practice, this regime of layer growth is usually referred to as reaction controlled. The terms interface controlled regime and kinetic regime are also used, though less suited. 

We notice that the correction to the regime of constant rate of event production decays with the same inverse power law as the correlation function of Eq. (148). Note that the correction is produced by the random walkers that throughout the time interval t did not make any transition from one velocity to the other velocity state. As a consequence, the pdf of the corresponding diffusion process is truncated by two ballistic peaks, in agreement with the theoretical predictions of earlier work [59,73]. 

Similar results have been obtained in the study of foam breakdown by alcohols using a special device for determination of the rate of contact foam breakdown [69]. The foam was supplied at constant rate over the surface of organic solvent. The rate of foam breakdown was determined in two regimes impulse and continuous. In the impulse regime, after contacting the organic solvent, the foam expanded as a consequence of its breakdown in the contact zone and detached itself from the solvent surface. Since the foam was constantly supplied, after a... 

Kinetics can also be studied at surface science conditions. Feed can be leaked at a constant rate into the chamber containing the crystal face, and the gas is removed at a constant rate by the pumps. The composition of the chamber gas can be continuously monitored by mass spectrometry. The pressure in the reaction chamber is low enough to ensure Knudsen flow The gaseous molecules collide almost exclusively with the exposed solid surfaces, and the system behaves as a perfectly mixed flow reactor (CSTR). Experiments in the transient regime with various forcing functions can be performed, and response times can be orders of magnitude smaller than those at atmospheric pressure. The catalytic oxidation of CO on Pt(llO) was one of the first studies of this type (33). 

The radius a of the onions in the intermediate shear-rate regime of lyotropic smectics depends on shear rate, scaling roughly as a A similar texture size scaling rule is found in nematics (see Section 10.2.7) there it reflects a balance of shear stress r y against Frank elastic stress. In smectics, the two important elastic constants B and Ki have differing... 

Moving on to the fourth regime of front generation, we see that with very fast front generation, fronts collide when they are very small. None of the fronts is allowed time to grow. This will result in a grid which is covered by a mixture of small (A, S) and (B, S) islands, separated by hexagonal phase (A, H) and (, H). The AB production will be at a constant rate. 

Note that the steady-state approximation does not imply that [X] is even approximately constant, only that its absolute rate of change is very much smaller than that of [A] and [D], Since according to the reaction scheme d[D]/dt = 2[X][C], the assumption that [X] is constant would lead—for the case in which C is in large excess—to the absurd conclusion that formation of the product D will continue at a constant rate even after the reactant A has been consumed. (2) In a stirred-flow reactor, a steady state implies a regime so that all concentrations are independent of time. 

Regime 1 has been described as erosion-enhanced oxidation, because the scale is thinner than it would have been in the absence of erosion, thus the scaling rate is enhanced. The scale grows under diffusion control but its outer surface is eroded at a constant rate by the erosive flux. This situation can be represented by the relationship given in Equation (9.1) ... 

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