Mixed population kinetics

Mixed populations of microorganisms (Aris and Humphrey, 1977 Jannasch and Mateles, 1974 Yoon and Blanch, 1977) occur, for example, in waste water treatment, in which the variation of organism composition with time plays a central role. The connection between various environmental circumstances (such as substrate choice and organism species composition) is shown in Figs. 5.54 and 5.55. 

In analogy to natural systems, some technical processes involving mixed populations have recently been introduced. In a situation where the optimal strategy for the production of ethanol from sugars involves batch fermentation of highly concentrated sugar solutions, the use of dual organisms that possess 

---

Mixed Populations. Considerable literature has evolved on mixed populations kinetics. Virtually every possible biological interaction from the classical prey-predator model of Lotka (35) to various forms of commensalism, synergism, etc. have been modelled. Virtually all models end up exhibiting stable oscillations. Solutions are often expressed in triangular phase plane plots of the limiting substrate and the two species. Invariably the plots have a limit cycle as one of the stable steady state solutions. From this one gains the impression that oscillatory behavior is the norm rather than the exception in biological reactors. 

Pharmacokinetic/pharmacodynamic model using nonlinear, mixed-effects model in two compartment, best described time course of concentration strong correlation with creatinine clearance predicted concentration at the efi ect site and in reduction of heart rate during atrial fibrillation using population kinetic approach... 

For the former case (Equation (3)), which is environmentally more relevant for low contamination situations, the rate obeys first-order kinetics with respect to substrate and biomass (second-order overall), whereas in the latter case (Equation (4)), the kinetics have a first-order relationship to biomass but are independent of substrate concentration. Methods for measuring of biomass, B, have varied widely, and, for studies involving mixed populations, in which only a fraction of the organisms can degrade the substrate, a means for quantifying the responsible fraction is not available. 

Kinetics of growth. In order to derive the correct version of Equation (75) using the Reynolds transport theorem, the kinetics of growth needs to be discussed. Let [Z] be the concentration of mixed population of microorganisms ntiUzing an organic waste. The rate of increase of [Z] fits the first order rate process as follows ... 

The process-engineering comparison between simple fermentation and a complex bioprocess such as that used for waste water treatment, shown in detail in Table 1.2, brings out the problems involved in quantifying practices used in complex cases multiple substrate kinetics operating in either sequential or parallel form mixed populations dependence on pH and temperature the influence of homogeneous or heterogeneous reactor operation in discontin-... 

Choice of inadequate submodels of the kinetic processes, for example, unknown influences from endogenous metabolism, inhibitors, the use of homogeneous rather than heterogeneous models, multisubstrate limitations, mixed population interactions. 

To a large extent, the formal kinetic analysis techniques presented in this chapter relate to discontinuous batch operations. Even if the goal is a continuous operation, the batch process kinetic model serves as a start-up. The most significant element of a kinetic analysis is the time dependence of the macroscopic process variables mentioned in Chap. 2. Bacteria, molds, viruses, and yeasts all have different reproduction mechanisms, and formulating a structured kinetic model more closely related to the actual mechanism is a desirable goal. More structured models are desirable not only to deal with active cells but also to extend kinetic analysis to more complex situations involving inactive cells, mixed populations of cells, multiple substrates, and... 

These infinitely variable problems in bioreactor operation are waiting to be solved. There have been relatively few systematic tests of the principles of interaction of mixed populations. Experimental work on the basis of the understanding from kinetic model theories should be encouraged by studies utilizing a CSTR, a CSTR cascade, or a CPFR. 

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. 

The CSD from the continuous MSMPR may thus be predicted by a combination of crystallization kinetics and crystallizer residence time (see Figure 3.5). This fact has been widely used in reverse as a means to determine crystallization kinetics - by analysis of the CSD from a well-mixed vessel of known mean residence time. Whether used for performance prediction or kinetics determination, these three quantities, (CSD, kinetics and residence time), are linked by the population balance. 

The model is able to predict the influence of mixing on particle properties and kinetic rates on different scales for a continuously operated reactor and a semibatch reactor with different types of impellers and under a wide range of operational conditions. From laboratory-scale experiments, the precipitation kinetics for nucleation, growth, agglomeration and disruption have to be determined (Zauner and Jones, 2000a). The fluid dynamic parameters, i.e. the local specific energy dissipation around the feed point, can be obtained either from CFD or from FDA measurements. In the compartmental SFM, the population balance is solved and the particle properties of the final product are predicted. As the model contains only physical and no phenomenological parameters, it can be used for scale-up. 

The process opposite to vesicle division is that of fusion, when two or more vesicles come together and merge with each other, yielding a larger vesicle. As outlined in the previous chapter, vesicle fusion is generally not a spontaneous process. If two populations of POPC liposomes with different average dimensions are mixed with each other, they do not fuse to produce a most stable intermediate structure - they stay in the same solution as stable, distinct species. This is connected to the notion of kinetic traps, as discussed previously, and is supported by theoretical and experimental data from the literature (for example, Hubbard etal, 1998 Olsson and Wennerstrom, 2002 Silin et al, 2002). 

Similar mixed-ligand complexes of the type (R, R2Dtc)2(MNT)Fe have been synthesized. The complexes were obtained initially as dianions, [(RiR2-Dtc)2(MNT)Fe]J", and were subsequently oxidized either by air or Cu(II) ions in acetonitrile (510). They also exhibit the singlet- triplet equilibrium however, they show a higher population of the triplet state than is found for the TFD analogues. The complexes are stereochemically nonrigid and display the same type of kinetic processes as their TFD counterparts. Thermodynamic activation parameters for inversion of the two complexes (TFD versus MNT) do not differ within experimental error. 

---