Effect of Lateral Mixing

Huber and Hiltbrunner (135) showed that when the column to packing diameter ratio D D is smaller than 10, the effect of lateral mixing is so large that only a strong maldistribution can decrease column efficiency G ut note also that this range of D /Op is uncommon in practice because of wall effects, Sec. 9.2.4). However, when Df/Dp is greater than 30, the lateral mixing becomes too small to counteract the influence of maldistribution, and the effect of variations in L/V ratio dominates. 

In large-diameter towers and long beds, a redistributor may help correct a maldistributed composition profile. For instance, remixing stage 4 liquid of the two columns in Example 9.1 would have alleviated the pinch. Good redistribution practices are discussed elsewhere (40). 

Li the presence of maldistribution, efflcien y becomes a flinction of the following parameters. 

The effects of these variables on ef icien in the presence of maldistribution are complex and interactive, as can be expected from Example 9.1. For instance, it has been shown (116,137) that under some feed composition and reflux conditions, efficiency increases with feed composition under other conditions, the converse occurs. It has also been shown that as LfV was reduced from total reflux, efficiency improved— at least in some cases. Note, however, that the reverse may occur in other columns. 

Liquid profile unevenness is more severe at low liquid flow rates 

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Correlations of nucleation rates with crystallizer variables have been developed for a variety of systems. Although the correlations are empirical, a mechanistic hypothesis regarding nucleation can be helpful in selecting operating variables for inclusion in the model. Two examples are (/) the effect of slurry circulation rate on nucleation has been used to develop a correlation for nucleation rate based on the tip speed of the impeller (16) and (2) the scaleup of nucleation kinetics for sodium chloride crystalliza tion provided an analysis of the role of mixing and mixer characteristics in contact nucleation (17). Pubhshed kinetic correlations have been reviewed through about 1979 (18). In a later section on population balances, simple power-law expressions are used to correlate nucleation rate data and describe the effect of nucleation on crystal size distribution. 

Concentrations of moderator at or above that which causes the surface of a stationary phase to be completely covered can only govern the interactions that take place in the mobile phase. It follows that retention can be modified by using different mixtures of solvents as the mobile phase, or in GC by using mixed stationary phases. The theory behind solute retention by mixed stationary phases was first examined by Purnell and, at the time, his discoveries were met with considerable criticism and disbelief. Purnell et al. [5], Laub and Purnell [6] and Laub [7], examined the effect of mixed phases on solute retention and concluded that, for a wide range of binary mixtures, the corrected retention volume of a solute was linearly related to the volume fraction of either one of the two phases. This was quite an unexpected relationship, as at that time it was tentatively (although not rationally) assumed that the retention volume would be some form of the exponent of the stationary phase composition. It was also found that certain mixtures did not obey this rule and these will be discussed later. In terms of an expression for solute retention, the results of Purnell and his co-workers can be given as follows,... 

First-order means that we consider nothing beyond that described here. In second-order , we would include the effects of mixing between ground and excited states brought about by the magnetic field. This is briefly discussed under second-order Zeeman effects later. 

In Chapter 11, we indicated that deviations from plug flow behavior could be quantified in terms of a dispersion parameter that lumped together the effects of molecular diffusion and eddy dif-fusivity. A similar dispersion parameter is usefl to characterize transport in the radial direction, and these two parameters can be used to describe radial and axial transport of matter in packed bed reactors. In packed beds, the dispersion results not only from ordinary molecular diffusion and the turbulence that exists in the absence of packing, but also from lateral deflections and mixing arising from the presence of the catalyst pellets. These effects are the dominant contributors to radial transport at the Reynolds numbers normally employed in commercial reactors. 

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