Mixing in continuous systems

The mixing problems considered so far have related to batch systems in which two materials are mixed together and uniformity is maintained by continued operation of the agitator. 

Frequently, stirred tanks are used with a continuous flow of material in on one side of the tank and with a continuous outflow from the other. A particular application is the use of the tank as a continuous stirred-tank reactor (CSTR). Inevitably, there will be a very wide range of residence times for elements of fluid in the tank. Even if the mixing is so rapid that the contents of the tank are always virtually uniform in composition, some elements of fluid will almost immediately flow to the outlet point and others will continue circulating in the tank for a very long period before leaving. The mean residence time of fluid in the tank is given by  

In a completely mixed system, the composition of the outlet stream will be equal to the composition in the tank. 

The variation of time for which fluid elements remain with the tank is expressed as a residence time distribution and this can be calculated from a simple material balance if mixing is complete. For incomplete mixing, the calculation presents difficulties. 

The problem is of great significance in the design of reactors because a varying residence time will, in general, lead to Afferent degrees of chemical conversion of various fluid elements, and this is discussed in some detail in Volume 3, Chapter 1. 

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Reac tors that are nominally CSTRs or PFRs may in practice deviate substantially from ideal mixing or nonmixing. This topic is developed at length in Sec. 23, so only a few summary statements are made here. More information about this topic also may be found in Nauman and Buffham (Mixing in Continuous Flow Systems, Wiley, 1983). 

Nauman, E. B. and Buffliam, B. A., Mixing in Continuous Elow System, John Wiley Sons, 1983. 

Nauman E. B. andBuffham, B. A. Mixing in Continuous Flow Systems, Wiley, New York, 1983. 

Yeung, P. K., S. Xu, and K. R. Sreenivasan (2002). Schmidt number effects on turbulent transport with uniform mean scalar gradient. Physics of Fluids 14, 4178 -191. Zwietering, T. N. (1959). The degree of mixing in continuous flow systems. Chemical Engineering Science 11, 1-15. 

Most chemical reaction engineering textbooks contain material on residence time distribution theory. Levenspiel [17] and Hill [18] present particularly useful introductions as do refs. 9 and 16. The proceedings of a recent summer school [19] contains a brief overview of the field [8] as well as papers describing many specific applications of RTD theory in chemical engineering contexts. Nauman s comprehensive invited review cited earlier [4] is an extremely thorough and yet highly readable contribution to the literature. The book by Nauman and Buffham [20], will no doubt fill a most important gap in the literature on mixing in continuous flow systems. 

Diffusive mixing in continuous laminar flow systems. Chem. Eng. Set. 21,... 

Graessley and his co-workers have made calculations of the effects of branching in batch polymerizations, with particular reference to vinyl acetate polymerization, and have considered the influence of reactor type on the breadth of the MWD (89, 91, 95, 96). Use was made of the Bamford and Tompa (93) method of moments to obtain the ratio MJMn, and in some cases the MWD by the Laguerre function procedure. It was found (89,91) that narrower distributions are produced in batch (or the equivalent plug-flow) systems than in continuous systems with mixing, a result referrable to the wide distribution of residence times in the latter. 

Levenspiel, O. Chemical Reactor Omnibook (OSU Book Stores, Corvallis, Oregon, 1989). Nauman, E. B. and Buffham, B. A. Mixing in Continuous Flow Systems (Wiley, 1983). Wen, C. Y. and Fan, L. T. Models for Flow Systems and Chemical Reactors (Dekker, 1975). 

Crystallization from an overall viewpoint represents transfer of a material from solution (or even a gas) to a solid phase by cooling, evaporation, or a combination of both. But there is more to it. Of considerable importance are economics, crystal size distribution, purity, and the shape of the crystals. Impurities or mother solution are carried along only in the surface or occlusions in the crystals. The partical size distribution depends on the distribution of seed crystals, which are injected into the crystallizer prior to initiation of crystallization (batch) or continuously from recycled undersized particles, the mixing in the system, the crystal growth rate, and the degree of supersaturation of the mother liquor. As in shown in the figures, both batch and continuous crystallization are used in industry. 

E.B. Nauman and B. A. Buffham, Mixing in Continuous Flaw Systems,... 

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