Steady-state size distribution

Randolph, A.D. and Larson, M.A., 1962. Transient and steady state size distribution in continuous mixed suspension crystallizers. American Institution of Chemical Engineers Journal, 8, 639-649. 

A comparison of the measured mean relative size with the model in Eq. (101) is shown in Fig. 28. The material was monosize glass beads. The data fit the model quite well, with the exception of fine 0.038-mm powder. It is evident that the steady-state size distribution is a function of the liquid content, and consequently, as shown by Sherrington (S9), there is an optimal granulating liquid for maximum granulation efficiency, that is, percentage of the product-grade material. 

The resulting steady-state size distribution functions were compared with experiments, and it was demonstrated that size distributions were indeed self-similar, and the functionality deduced in the development of the model was observed. 

Data from [WiJ - particularly figures 3, 6, 8, 10, 18, 19, and 21 - leave no doubt that, at least for certain populations of algae, individual cell volume varies significantly during the course of experiments in the chemo-stat. These data also suggest that steady-state size distributions are reached which have remarkably stable shapes with respect to changes in the control parameters for the chemostat (flow rates, temperature, CO2). 

In Section 4, competition between two populations is analyzed. Again, the equations can be reduced to a system that can be directly compared to the systems derived in Chapters I and 2. Section 5 explores the evolution in time of the population average length, surface area, and volume in Section 6 we formulate the conservation principle, which played such a crucial role in earlier chapters. The steady-state size distribution of a population is determined in Section 7. Our findings are summarized in a discussion section, where a comparison is made between the conclusions derived from the size-structured model and the unstructured models considered in Chapters 1 and 2. 

Figure 7.1. Eight steady-state size distributions observed under different experimental conditions (flow rate, temperature, CO2), scaled for equal means and areas. The mean cell size for each graph is indicated next to the graph. (From [Wi, fig. 19], Copyright 1971, Academic Press. Reproduced by permission.)...

The reason for osdllations in conversion and surface tension become dear whea one considers particle formation and growth phenomena. If a single CSTR is started empty or by adding initiator to a full vessel of inactive emulsion, a conversion overshoot occurs. The first free radicals generated are almost entirdy utilized to ibrm new particles. Since these partides do not grow rapidly to the steady-state size distribution, radical... 

Jiang Q., Logan B.E. (1991), Fractal dimensions of aggregates determined from steady-state size distributions. Environ. Sci. TechnoL, 25,12, 2031-2038. 

Figure 11. Computer simulation of a population using 2000 unstructured cell models. There were 20 size classes with 100 cells per class in the simulation. The steady state size distributions are considerably more stable than the simulation with 200 cells CSee Figure 10).

Another notable contribution was made by Saeman (1956) was derived equations, based on a first-order growth law, for the form of the steady-state size distribution in mixed suspensions. The assumption of size-independent growth was also made and the cumulative mass-size distribution was expressed in the form... 

What are the mechanics of a textured liquid crystal How does the steady state size distribution of domains (or density of defects) change with shear in Region I, and what is the effect on transient and steady state rheology ... 

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