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Population growth steady state kinetics

The population balance analysis of the idealized MSMPR crystallizer is a particularly elegant method for analysing crystal size distributions at steady state in order to determine crystal growth and nucleation kinetics. Unfortunately, the latter cannot currently be predicted a priori and must be measured, as considered in Chapter 5. Anomalies can occur in the data and their subsequent analysis, however, if the assumptions of the MSMPR crystallizer are not strictly met. [Pg.79]

For limiting nutrients, cellular concentrations are constant under conditions of steady-state growth. To ensure that the limiting nutrient is not diluted in the microbial population, kmt must be greater than the maximal growth rate, /imax. This limiting condition sets a minimum for the value of the Monod constant, Kmd = / max /[7]- Note that while Monod kinetics are more applicable than first-order kinetics for many ecological uptake processes, solutions of the above equations require considerably more a priori information [48]. [Pg.497]

The development and refinement of population balance techniques for the description of the behavior of laboratory and industrial crystallizers led to the belief that with accurate values for the crystal growth and nucleation kinetics, a simple MSMPR type crystallizer could be accurately modelled in terms of its CSD. Unfortunately, accurate measurement of the CSD with laser light scattering particle size analyzers (especially of the small particles) has revealed that this is not true. In mar cases the CSD data obtained from steady state operation of a MSMPR crystallizer is not a straight line as expected but curves upward (1. 32. 33V This indicates more small particles than predicted... [Pg.4]

The most common method for obtaining crystal growth kinetics involving suspensions involves the use of a mixed suspension, mixed product removal continuous crystallizer operating at steady state. By using the population balance concepts developed and described by Randolph and Larson (1986), growth rates can be obtained. The population balance method and the use of the crystal size distribution in obtaining kinetic parameters will be discussed in detail in Chapter 4 of this volume. [Pg.60]

Since t is fixed by the choice of experimental conditions, nucle-ation and growth rates can be determined simultaneously by a single measurement of the CSD at steady-state. Example 4.3 shows the use of the population balance in determination of nucleation and growth kinetics. [Pg.105]

As a test of the range of applicability of the kinetics determined in the steady-state measurements, the transient population balance equation has been solved, using the kinetics determined from steady state, to simulate the sequence of protein content frequency functions obtained in synchronous growth of this organism. The simulation results are in very good qualitative agreement with the experimental measurements of the corresponding quantities (28). [Pg.150]

Similarly, several authors have presented MSMPR methods for kinetics determination from continuous crystallizer operation (Chapter 3), which have become widely adopted. In an early study, Bransom etal. (1949) anticipated Randolph and Larson (1962) and derived a crystal population balance to analyse the CSD from the steady state continuous MSMPR crystallizer for growth and nucleation kinetics. Han (1968) proposed a method of kinetics determination from the moments of the CSD from a cascade of continuous crystallizers and assessed the effect of sample position. Timm and Larson (1968) suggested the use of the extra information present in transient response data to determine kinetics, followed by Sowul and Epstein (1981), Daudey and de Jong (1984) and Jager etal. (1991). Tavare (1986) applied the j-plane analysis to the precipitation of calcium oxalate, again assuming nucleation and growth only. [Pg.136]

This readjustment takes place by the attachment of single kinetic units in accordance with the reaction scheme (1). These net growth processes take time, and the readjustment of the number of critical nuclei of size takes time. There is therefore a time-lag before a stationary population of critical nuclei is built up. The rate of nucleation J t) increases during this time-lag until it approaches Jq, the steady-state rate. [Pg.138]


See other pages where Population growth steady state kinetics is mentioned: [Pg.84]    [Pg.100]    [Pg.497]    [Pg.9]    [Pg.278]    [Pg.168]    [Pg.145]    [Pg.155]    [Pg.155]    [Pg.155]    [Pg.286]   
See also in sourсe #XX -- [ Pg.73 ]




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