Batch dispersive growth

The yeast must be so finely dispersed throughout the wort that a quick yeast growth is assured, which leaves no possibiUty for other microorganisms, if any, to develop. The inoculation of yeast occurs through injection directly into the wort pipe. To be used in the next batch of wort, the yeast that is harvested after the end of fermentation must be protected against contamination. 

Although evidence exists for both mechanisms of growth rate dispersion, separate mathematical models were developed for incorporating the two mechanisms into descriptions of crystal populations random growth rate fluctuations (36) and growth rate distributions (33,40). Both mechanisms can be included in a population balance to show the relative effects of the two mechanisms on crystal size distributions from batch and continuous crystallizers (41). 

Both experimental and theoretical work has demonstrated that growth rate dispersion exists, and has a measurable effect on the CSD in both batch and continuous crystallization processes. Further understanding of this phenomenon on a fundamental level will be required to develop methods to make use of or control growth rate dispersion and make it a tool in control of particle size and shape. 

An increase in the spread of sizes in a batch crystallization could be due to size dependent growth or also growth dispersion. Whatever the cause, the spreading decreases substantially for the high alcohol content crystallizations. There seems to be no current explanation for this effect. In practical terms, this means that batch growth from alcoholic solutions should give a more uniform product than from aqueous solution. 

As a preliminary indication of the capability of SEC to qualitatively follow particle growth, the diameters corresponding to the peak retention volume were calculated directly from the calibration curve (without any correction for axial dispersion). "Peak average particle diameters are plotted vs. conversion for the batch runs in Figure 7, where it is clearly shown that runs B10 and Bll are replications, with latex particles smaller than those produced from run B7, as expected. In the continuous run, shown in Figure 8,... 

Erickson et al. (E3) developed a model for batch growth in fermentations with two liquid phases present in which the growth-limiting substrate is dissolved in the dispersed phase. The model accounts for drop size distribution and considers the effect of droplet coalescence and redispersion by an interaction model similar to that of Eq. (110). Droplet interactions were shown to be important if drop size distributions have large variance. 

The quality, productivity, and batch-to-batch consistency of the final crystal product can be affected by the conditions of the batch crystallizer. Several factors considered here include batch cycle time, supersaturation profile, external seeding, fouling control, CSD control, growth rate dispersions, and mixing. 

In order to account for GRD, the population balance needs to be modified, and its solution becomes a very difficult task, in particular for batch crystallization. Recently, Butler et al. (1997) concluded that because different batches of seeds of the same material have different growth rates, it is impossible to assign a growth rate dispersion property for a given material. Instead, they advocated a common history (CH) seed concept. As the name suggests, CH seed comprises crystals of a common history. Furthermore, CH seed has the following properties... 

Erickson, Humphrey, and Prokop (1969) have developed mathematical models which can be used to describe batch growth in hydrocarbon fermentation with two types of dispersed system. In the first type of fermentation, the growth-supporting hydrocarbon substrate is dissolved in inert hydrocarbons, and it is assumed that substrate utilization from the dispersed phase causes little or no change in the interfacial area. 

Erickson et al (1969) developed a mathematical model for the description of fermentations with two liquid phases in both batch and continuous cultivation. The considerations embrace growth at the surface of the drops and in the aqueous phase. Three spedal cases have been examined in the first case it is assumed that growth occurs only at the surface of the dispersed phase in the second and third cases, growth takes place both at the interface and in the continuous phase (water). The second case assumes that the substrate equilibrium is continuously maintained between the two phases, while in the third case the consumption of substrate is limited by the transport path to the aqueous phase. Fig. 13 shows a comparison between the model and experimental data. It is assumed that growth takes place only at the... 

It should be emphasized that in a real crystalhzer the assrmrptions of monodisperse seed material and of absence of nucleation and growth dispersion does not apply. The formation of secondary seeds by abrasion can considerably reduce the reqirired batch time in case of a constant supersaturation but impairs the particle size distribution toward smaller sizes. 

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