Micromixing time determination

For non-linear chemical reactions that are fast compared with the local micromixing time, the species concentrations in fluid elements located in the same zone cannot be assumed to be identical (Toor 1962 Toor 1969 Toor and Singh 1973 Amerja etal. 1976). The canonical example is a non-premixed acid-base reaction for which the reaction rate constant is essentially infinite. As a result of the infinitely fast reaction, a fluid element can contain either acid or base, but not both. Due to the chemical reaction, the local fluid-element concentrations will therefore be different depending on their stoichiometric excess of acid or base. Micromixing will then determine the rate at which acid and base are transferred between fluid elements, and thus will determine the mean rate of the chemical reaction. 

As mentioned above, to determine one value for fM needs an experimental curve of X, versus u0 for the case where the impinging velocity m() is taken as the governing variable. The plot of a set of typical data is indicated in Fig. 10.12. From the curve the critical point at which Xs turns from a varying value to a small constant is found at u -0.184 m/s. With the known reaction rate constant at 298 K, the micromixing time can be calculated as... 

The data determined for the micromixing time, rM, from various curves are illustrated in Fig. 10.13, which meet approximately the relationship below ... 

The reaction system, the experiment procedure, and the analytical method used for the determination of micromixing in the TIJ mixer are the same as those described in the last section of this book but Mahajan et al. correlated their experimental data not with impinging velocity w() but with the jet Reynolds number Re. Also, the researchers employed the measure of increasing both the initial concentration CBo and the reaction temperature to raise the sensitivity of the procedure. The characteristic reaction time constant tK = 200 ms at 25 °C and CBo = 2.5 mM, while rR = 65 ms at 35 °C and CB0 = 4.7 mM, which can be used to bound the micromixing times, rM, no greater than them, respectively. 

Fournier, M. C., Falk, L. and Villerrmaux, J. (1996). A new parallel competing reaction system for assessing micromixing efficiency— Determination of micromixing time by a simple mixing model. Chemical Engineering Science, 51(23) 5187-5192. 

The method, which makes use of simple and cheap chemicals, is amenable to a quantitative exploitation for the determination of micromixing times. 

One of the principal difficulties faced when employing Lagrangian micromixing models is the determination of tm based on properties of the turbulent flow fields. Researchers have thus attempted to use the universal nature of high-Reynolds-number isotropic turbulence to link tm to the turbulence time scales. For example, in the E-model (Baldyga and Bourne 1989) the engulfment rate essentially controls the rate of micromixing and is defined by... 

The reaction scope is further enlarged to unsymmetrically disubstituted derivatives. Using one mole equivalent of two different aryllithium precursors at a time in a sequence of four micromixers and microtube reactors (MRi ), it was possible to obtain an unsymmetrically disubstituted final diarylethene. The yield was determined after solvent evaporation and sample purification on the column. 

The activity of [i-galactosidasc (P-Gal) was studied on a quartz chip using a static micromixer to mix the enzyme and substrate on the ms time scale. Inhibition by phenylethyl-P-D-thio-galactoside was also studied [1048]. In another report, the enzyme P-Gal was assayed on a chip in which P-Gal would convert a substrate, resoruhn-P-D-galactopyranoside (RBG), to resoruhn to be detected fluorescently [1049]. By varying the substrate concentrations and monitoring the amount of resoruhn by LIF, Michaelis-Menten constants could be determined. In addition, the inhibition constants of phenylethyl-P-D-thiogalactoside, lactose, and p-hydroxymercuribenzoic acid to the enzyme P-Gal were determined [1049]. 

In a detailed process optimization study, the impact of the type of micromixers and process parameters was determined [56]. As a result, a pilot with a Toray Hi-mixer connected to a shell and tube microheat exchanger was constructed. Continuous operation for 24 h was carried out to obtain pentafluorobenzene (PFB) after protonation (92% yield). In this time, 14.7 kg of the product was produced, that is, about 5 t/a. Thus, the industrial-scale production carried out using a batch reactor (10 m3) can be replaced by adding only four microflow systems of the scale investigated. The pilot plant produces 0.5 kg in 6h continuous operation, thus about 730kg/a (see Figure 5.19). The name of the industrial company was not disclosed. 

---