Micromixing effects

David, R. and Marcant, B., 1994. Prediction of micromixing effects in precipitation Case of double-jet precipitators. American Institution of Chemical Engineers Journal, 40, 424M32. 

Kim, W.-S. and Tarbell, J.M., 1996. Micromixing effects on barium sulphate precipitation in an MSMPR reactor. Chemical Engineering Communications, 146, 33-56. 

Mahajan, A.J. and Kirwan, D.J., 1996. Micromixing effects in a two-impinging-jets precipitator. American Institution of Chemical Engineers Journal, 42, 1801-1814. 

In order to implement the PDF equations into a LES context, a filtered version of the PDF equation is required, usually denoted as filtered density function (FDF). Although the LES filtering operation implies that SGS modeling has to be taken into account in order to capture micromixing effects, the reaction term remains closed in the FDF formulation. Van Vliet et al. (2001) showed that the sensitivity to the Damkohler number of the yield of competitive parallel reactions in isotropic homogeneous turbulence is qualitatively well predicted by FDF/LES. They applied the method for calculating the selectivity for a set of competing reactions in a tubular reactor at Re = 4,000. 

Micromixing effects in the Nicolis-Puhl reaction Numerical bifurcation and stability analysis of the IEM model. Chemical Engineering Science 46, 1829-1847. 

Fox, R. O., G. Erjaee, and Q. Zou (1994). Bifurcation and stability analysis of micromixing effects in the chlorite-iodide reaction. Chemical Engineering Science 49, 3465-3484. 

Weinstein, H. and R. J. Adler (1967). Micromixing effects in continuous chemical reactors. 

Clear distinction between macromixing effects (large scale motions due to average velocities) and micromixing effects (turbulent fluctuations),... 

The effect of coalescence and break-up of droplets on the yield of chemical reactions was studied by Villermaux (33). Micromixing effects may occur even in batch reactors if there is a drop size distribution and mass-transfer control. Although practical rules for the design and scale-up of liquid-liquid reactors are available as Oldshue showed in the case of alkylation (152), many problems remain unsolved (.5) mass transfer effects, high hold-up fractions (> 20 %), large density differences, high viscosities, influence of surfactants. 

It is true that micromixing effects can generally be neglected in the design of reactors for simple and slow reactions. However, as has been pointed out in the preceding Sections in the case of fast reactions with unmixed reactants, chemical conversion could be entirely controlled by mixing, and induce dramatic variations in the distribution of products. The practical examples of combustion and reactions in liquid suspension are especially illuminating in this respect. 

The Eulerian (bottom-up) approach is to start with the convective-diffusion equation and through Reynolds averaging, obtain time-smoothed transport equations that describe micromixing effectively. Several schemes have been proposed to close the two terms in the time-smoothed equations, namely, scalar turbulent flux in reactive mixing, and the mean reaction rate (Bourne and Toor, 1977 Brodkey and Lewalle, 1985 Dutta and Tarbell, 1989 Fox, 1992 Li and Toor, 1986). However, numerical solution of the three-dimensional transport equations for reacting flows using CFD codes are prohibitive in terms of the numerical effort required, especially for the case of multiple reactions with... 

Thus, we recover the Danckwerts model only if no distinction is made between the cup-mixing and spatial average concentrations (with this assumption, the effective axial dispersion coefficient is given by the Taylor-Aris theory). This derivation also shows that the concept of an effective axial dispersion coefficient and lumping the macro- and micromixing effects into one parameter is valid only at steady-state, constant inlet conditions and when the deviation from plug flow is small. [Remark Even with all these constraints, the error in the model because of the assumption (cj) — cym is of the same order of magnitude as the dispersion effect ]... 

For the special case of a simple reaction A — B, the low-dimensional model for a CSTR with premixed feed consists of three differential equations and two algebraic equations. When the mass and thermal micromixing effects are ignored (r) = t]H — 0), cm — (c), (Of) — dfm — (ds), and we get the classical pseudohomogeneous CSTR model... 

In this section, we present examples to illustrate the usefulness of multi-mode homogeneous reactor models in predicting micromixing effects on yield and selectivity, reactor runaway, etc. 

Single Bimolecular Reaction in a CSTR Micromixing Effects on Conversion... 

Prediction of Micromixing Effects on Polymer MWD in Tank Reactors... 

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