An Extension to the Incorporation Model of Micromixing and Its Use in Estimating Local Specific Energy Dissipation Rates

• Published in: Industrial & engineering chemistry research 2008-05, Vol.47 (10), p.3460-3469
• Main Authors: Assirelli, M, Wynn, E. J. W, Bujalski, W, Eaglesham, A, Nienow, A. W
• Format: Article
• Language: English
• Subjects: Applied sciences; Chemical engineering; Exact sciences and technology
• ISSN: 0888-5885; 1520-5045
• DOI: 10.1021/ie070754n

The incorporation model of micromixing first developed conceptually and quantified by Villermaux and co-workers has been extended to cover both higher rates of micromixing (higher mean and local specific energy dissipation rates) and higher reaction rates (by using higher acid concentrations in the iodide−iodate model reaction scheme). The extended model has involved the use of Bader and Deuflhard's semi-implicit discretization in the Bulirsch−Stoer method, which is especially suitable for stiff ordinary differential equations. Both exponential and linear rates of incorporation were considered, and polynomial equations for three acid concentrations for micromixedness ratios, α, from ∼1 to ∼100, were determined. It was shown that, though different acid concentrations gave different α values at the same feed position and agitation conditions, the micromixing time estimated from the model was constant (as it should be) with exponential incorporation. With linear incorporation, the micromixing time was much less and not constant and was therefore rejected for further analysis. Subsequently, it was shown that φ, the ratio of the local specific energy dissipation rate, εT, to the average, εT, i.e., φ = εT/εT, was constant at the same reactant feed position except when fed into the region of (εT)max close to the impeller. In this case, φ fell with increasing speed as the reactants were swept more rapidly from this region to regions of lower φ. By comparing estimates of φ from feeding a reactant at equivalent positions with a static pipe and one rotating with the impeller, it was found that Φ = φpoint,max/φensemble,max was ∼2.7, in reasonable agreement with the value of ∼3 very recently obtained by Ducci and Yianneskis (AIChE J. 2005, 51, 2133) based on two-point laser Doppler anemometry (LDA) measurements. The absolute value of φensemble,max was rather high compared to the most recent estimates from LDA or particle image velocimetry (PIV), which may reflect some weakness in the model or in the quality of the chemical kinetics data.