Fres Residence time

Our aim is to determine the concentration of A in the reactor as a function of time and in terms of the experimental conditions (inflow concentrations, pumping rates, etc.). We need to obtain the equation which governs the rate at which the concentration of A is changing within the reactor. This mass-balance equation will have contributions from the reaction kinetics (the rate equation) and from the inflow and outflow terms. In the simplest case the reactor is fed by a stream of liquid with a volume flow rate of q dm3 s 1 in which the concentration of A is a0. If the volume of the reactor is V dm3, then the average time spent by a molecule in the reactor is V/q s. This is called the mean residence time, tres. The inverse of fres has units of s-1 we will call this the flow rate kf, and see that it plays the role of a pseudo-first-order rate constant. We denote the concentration of A in the reactor itself by a. 

In choosing a timescale, we could take the residence time ties as our basis. However, if the experiments envisaged involve the variation of fres as discussed in 6.1.3 above, this is not so convenient. It is better that we should choose a constant In the present case we are rather limited for other possibilities. However, the rate constant k1 can be recruited if treated properly. 

The reaction rate curve R is zero at complete conversion and also has low (but non-zero) values close to 1 — a = 0, with a maximum close to two-thirds conversion (actually at 1 — a = — / 0). Importantly, R does not depend on the residence time rres, although it does vary if / 0 is changed. The flow line L is zero when 1 — a = 0 since the inflow and outflow have the same composition (no conversion of A to B). The gradient of the flow line (Fig. 6.7(b)) is given by 1 /Tres, so it is steep for short residence times (fast flow rates) and relatively flat for long rres. (Note how tres actually compares fres and lch, so short residence times are those that are much less than the chemical timescale etc.) The flow line is, however, unaffected by the inflow concentration of the autocatalyst f 0. 

In closed systems, or even in systems with large residence times, it is possible to make further simplifications to the above scheme. In such cases it can be assumed that /c 5[H2] > 1/fres and the steady-state concentrations for O and OH reduce to... 

Provided r, is small, then the critical inflow concentration for this branching-termination model under CSTR conditions differs slightly from the so-called pool chemical result which is obtained by assuming [A] = constant. For typical chemical systems the residence time will be such that k, > 1/fres, SO the two results are not significantly different but the extra influence of the flow is clearly evident in the above forms. In neither of the analyses above, however, is there a discontinuous jump in the steady-state response as the parameters are varied. 

Fig, 5.28. The p-T. ignition diagram for a stoichiometric 2H2 + O2 mixture with mean residence time fres = 2.0 0.2 s showing additional region of complex oscillatory ignition. (Reprinted with permission from reference [33], Royal Society of Chemistry.)... 

The ignition limit lies in the region of the p-T plane, corresponding to the second limit in classical closed vessels, and so we may surmise that the dominant features of the mechanism will be the competition between the branching cycle (1-3) and the gas-phase termination step producing HO2, step (5). A full steady-state analysis on the intermediates OH and O would introduce (out)flow terms for each species and a fairly complex polynomial in terms of fres- The full analysis appears in Chapter 4 of this volume. For now, we can note that the typical residence times of interest, 1 to 10 s,... 

Again, ions in FAIMS experience directed drift, anisotropic diffusion, and Coulomb repulsion. The drift proceeds along E that is orthogonal to electrodes (3.2.3). The diffusion and Coulomb force transpose ions in aU directions, but the separation is due to ions hitting electrodes and, at fixed residence time fres, the motion parallel to them... 

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