Fluid-mechanical approach

The next step is to derive an expression for the scalar variance defined by 

In Section 3.2, we show that under the same conditions the right-hand side of (1.24) is equal to the negative scalar dissipation rate ((3.45), p. 70). Thus, the micromixing time is related to the scalar dissipation rate e and the scalar variance by 

Choosing the micromixing time in a CRE micromixing model is therefore equivalent to choosing the scalar dissipation rate in a CFD model for scalar mixing. 

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

The FM approach to modeling turbulent reacting flows had as its initial focus the description of turbulent combustion processes (e.g., Chung 1969 Chung 1970 Flagan and Appleton 1974 Bilger 1989). In many of the early applications, the details of the chemical reactions were effectively ignored because the reactions could be assumed to be in local chemical equilibrium.26 Thus, unlike the early emphasis on slow and finite-rate reactions 

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Baldyga, J. and Bourne, J.R., 1984a. A fluid mechanical approach to turbulent mixing and chemical reaction. Part I Inadequacies of available methods. Chemical Engineering Communications, 28, 231-241. 

Both of the above methods belong to a traditional fluid mechanical approach known as dimensional analysis (2). Unfortunately, these methods cannot always achieve results in various manufacturing environments. Therefore, the third method is introduced below and can be easily applied to various research and production situations. This method actually is a combination of the first two methods. 

Additional information on hydrodynamics of bubble columns and slurry bubble columns can be obtained from Deckwer (Bubble Column Reactors, Wiley, 1992), Nigam and Schumpe (Three-Phase Sparged Reactors, Gordon and Breach, 1996), Ramachandran and Chaudhari (Three-Phase Catalytic Reactors, Gordon and Breach, 1983), and Gianetto and Silveston (Multiphase Chemical Reactors, Hemisphere, 1986). Computational fluid mechanics approaches have also been recently used to estimate mixing and mass-transfer parameters [e.g., see Gupta et al., Chem. Eng. Sci. 56(3) 1117-1125 (2001)]. 

The blown film process has been studied analytically since the early 1970s (Table 24.1). The first analysis was proposed by Pearson and Petrie [3, 4], who followed a fluid mechanics approach. However, this model is restricted to Newtonian fluids under isothermal conditions. This first model has been modified several times to consider different aspects of the process, such as temperature variation and rheological behavior of the system. 

Fluid flow pattern may be described in two ways a fluid mechanisms approach and a global phenomenological approach based on the Residence Time Distribution (R. T. D) concept. The fluid mechanics approach tries to determine the velocity, concentration and temperature profiles within the reactor on the basis of fundamental equations of fluid flow hydrodynamics. This approach, when successful, leads to complex mass and heat balance equations requiring cumbersome numerical computations and yielding too detailed informations when a macroscopic description of the process is required by the chemical engineer. 

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