Time scale mixing, reaction

Laser-based pump strategies are generally necessary to study reactions taking place on time scales faster tlian microseconds. Lasers can be used to produce L-jumps on time scales faster tlian microseconds or to initiate reactions tlirough rapid photochemical or photophysical processes. Lasers can also initiate ultrarapid mixing via a wide variety... 

First, let us consider batch mixing processes, as exemplified by ordinaiy laboratory practice in solution kinetics. A portion of one solution (say, of the substrate) is added by pipet to a second solution (containing the reagent) in a flask, the flask is shaken to achieve homogeneity, and then samples are withdrawn at known times for analysis, or the solution is subjected to continuous observation as a function of time, for example, by spectrophotometry. For reactions on a time scale (measured by the half-life) of hours or even several minutes, the time consumed in these operations is a negligible portion of the reaction time, but as the half-life of the reaction decreases, it becomes necessary to consider these preliminary steps. Let us distinguish three stages ... 

Revisions of the continuous-flow method have been made to allow observations along the length of the flow tube rather than at right angles.5 This method, fast continuous flow, eliminates the dead time during which the reaction cannot be observed. Kinetic data can be extracted to a time resolution of nearly 10 p,s, but the mathematics is more complicated in this limit, because the mixing and chemical reaction occur on the same time scale. Rate constants nearly as large as the diffusion-controlled value have been determined in favorable cases.6... 

This process does not lead to net ozone depletion because it is rapidly followed by reaction 2, which regenerates the ozone. Reactions 2 and 3 have, however, another important function, namely the absorption of solar energy as a result, the temperature increases with altitude, and this inverted temperature profile gives rise to the stratosphere (see Figure 1). In the lower layer, the troposphere, the temperature decreases with altitude and vertical mixing occurs on a relatively short time scale. In contrast, the stratosphere is very stable towards vertical mixing because of its inverted temperature profile. 

The spatio-temporal variations of the concentration field in turbulent mixing processes are associated wdth very different conditions for chemical reactions in different parts of a reactor. This scenario usually has a detrimental effect on the selectivity of reactions when the reaction time-scale is small compared with the mixing time-scale. Under the same conditions (slow mixing), the process times are increased considerably. Due to mass transfer inhibitions, the true kinetics of a reaction does not show up instead, the mixing determines the time-scale of a process. This effect is known as mixing masking of reactions [126]. 

Micro reactors show, under certain conditions, low axial flow dispersion reactions with unstable intermediates can be carried out in a fast, stepwise manner on millisecond time-scales. Today s micro mixers mix on a millisecond scale and below [40]. Hence in micro reactors reactions can be carried out in the manner of a quench-flow analysis, used for determination of fast kinetics [93]. 

Table 5.4-24 summarises the various characteristic time constants for reaction and mixing. Instantaneous (very rapid), fast (rapid) and slow (very slow) reactions have been classified based on characteristic time constants (time scales) for mixing and reaction. Denoting the mixing time scale by xm (t99, to, xms, xds, or x ,) reactions can be classified as follows from the viewpoint of competition with individual stages of mixing tm xf => instantaneous TM XR => fast TM XR => slow... 

Fig. 5. Multiple phases in the reduction of xanthine oxidase by xanthine at pH 8.2. Intensities of the Rapid (circles) and Slow (triangles) molybdenum EPR signals expressed as electron/mole enzyme (i-e. per 2 atom Mo) are plotted as a function of time. Note the changes in the time scale. Rapid freezing was used for reaction times (at 22°) up to 1 sec. and manual mixing for longer times (at 25°) enzyme concentrations (immediately after mixing) were 0.09 mM and 0.13 mM respectively. The enzyme had Activity/A45o 125 corresponding to 63% of active enzyme and 20 mole xanthine/mole enzyme was used. (Data from ref. 67.)...

In a general way, the ions in the first two classes would be considered labile while those in the last two classes would be considered inert. Labile complexes are regarded as those in which the reaction is complete on a time scale that would be comparable to the time necessary to mix the solutions of the reacting species. Such reactions can be studied by flow techniques or by NMR line broadening. Inert complexes are those that can be followed by conventional kinetic techniques. 

In CL techniques, after mixing of the reagents and the sample, the CL reaction starts and the emission intensity is being produced, decreasing once the reactants are consumed. This implies a transient character of the CL emission, the time scale of which depends on the specific reaction, and which can range from a short flash to a continuous glow. This fact is crucial for selection of the most convenient systems of reagent addition. 

The acid-base reaction is a simple example of using the mixture fraction to express the reactant concentrations in the limit where the chemistry is much faster than the mixing time scales. This idea can be easily generalized to the case of multiple fast reactions, which is known as the equilibrium-chemistry limit. If we denote the vector of reactant concentrations by and assume that it obeys a transport equation of the form... 

In most applications, the first reaction in each set is an acid-base reaction so that k is very large. For Eq. (59), B and C are premixed and added to A under conditions such that B is in stoichiometric excess to A. Likewise, for Eq. (58), B is reacted in stoichiometric excess with A to produce the desired product R. Under these conditions, the first reaction in each set is favored. However, if mixing occurs with the same time scale as the second reaction, the undesired byproduct (S in Eq. (58) and P2 in Eq. (59)) will be produced. Thus, the amount of by-product produced is a sensitive measure of the quality of mixing in the chemical reactor. 

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