Time scale micromixing

In the CRE literature, turbulence-based micromixing models have been proposed that set the micromixing time proportional to the Kolmogorov time scale ... 

The limiting case where the chemical time scales are all large compared with the mixing time scale r, i.e., the slow-chemistry limit, can be treated by a simple first-order moment closure. In this limit, micromixing is fast enough that the composition variables can be approximated by their mean values (i.e., the first-order moments (0)). We can then write, for example,... 

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... 

If the characteristic micromixing time scale is much smaller than Atf, then care must be taken in implementing tiie intra-cell processes. For example, several smaller time steps may be required to represent mixing and chemical reactions at each iteration. 

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]. 

The issue of multiple time scales is also present in the case of homogeneous tank reactors. As in Fig. 2, a tank reactor consists of several circulating flow loops which exchange material with each other and within which micromixing occurs at the continuum scale. Therefore, there are three physical length scales present in a tank reactor. The size of the reactor is the macroscale. The meso length scale could be anywhere from the size of a circulation loop to the size of an eddy (or cell). The continuum scale is the microscale. The time scales... 

Da 1 flows where the time scale for chemical conversion L is relatively large compared to the time scale for turbulent micromixing t ... 

For the first two cases Da << 1 (slow reactions) and Da >> 1 (very fast reactions) adequate closure models are available in many commercial CFD codes. For the third case, where the time scale for chemical conversion approximately equals the time scale for turbulent micromixing, moment methods are inappropriate and other methods should be used. In this situation the reactor performance may be significantly affected by mixing efficiency. Here the engineer is faced with the difficult problem of predicting the overall conversion and/or selectivity of the chemical process. In the last three decades this problem has received considerable attention in three scientific areas, namely, chemical reaction engineering, fluid mechanics and combustion, and various approaches have been followed. 

When local micromixing is slow compared to the reaction time scale and the macromixing time scale is smaller than the process time scale, the performance of a reactive flow process is controlled only by the micromixing. In such cases, though there is no macroscopic segregation, reactants are not mixed on a molecular scale (see the right bottom case of Fig. 5.5). Several micromixing models have been developed to simulate such reactive flow processes. Some of the widely used models are ... 

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