ACH - Models in Chemistry 132. (1995)

3. szám - RESEARCH ARTICLES - Lakatos Béla G.–Sapundzhiev, Tsvetan J.: Sustaines oscillations in isothermal CMSMPR crystallizers: Effect of size-dependent crystal growth rate

Сл - MODELS IN Chemistry 132 (3), pp 379-394 (1995) Sustained oscillations in isothermal CMSMPR crystallizers: Effect of size-dependent crystal growth rate BélaG. Lakatos1-3 andTsvETANJ. Sapundzhiev2 1 Research Institute of Chemical Engineering, Hungarian Academy of Sciences, Egyetem u. 2., H-8200, Veszprém, Hungary 2Institute of Chemical Engineering, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., B1.103, B-1113, Sofia, Bulgaria 3Department of Chemical Engineering Cybernetics, University of Veszprém, Egyetem и. 10., H-8200, Veszprém, Hungary* Received January 2, 1995 The influence of size-dependent crystal growth rate on the oscillatory behaviour of isothermal CMSMPR crystallizers, described by linear relation in size, is studied by numerical experimentation. The rate of formation of crystals is given by the Volmer kinetic model, and an appropriately scaled moment equations model is used in the analysis. Steady state bifurcation diagrams are computed and presented which show that the willingness of crystallizers to oscillate decreases with increasing values of the parameter describing the size-dependence of the crystal growth rate. The model predicted sustained oscillations only for small and moderate values of the parameter. The phase lags of the oscillating moments of crystal size distribution are ordered as an arithmetic sequence. The normalized variance of the size distribution becomes almost zero at the minima of oscillations, but here the mean crystal size also proves to be very small. Introduction Oscillations of crystal size distribution and solute concentration represent a type of instabilities of continuous crystallizers. These may occur as a consequence of nonrepresentative product removal, or due to the highly nonlinear nature of nucleation and crystal growth, and their interactions with the crystal size distribution. The former phenomenon is termed low-order cycling, while the latter, which is inherent to the crystallization process itself and is a manifestation of its complex dynamics, is termed high-order cycling [1]. Since the observations by Miller and Seaman [2] on oscillations in industrial crystallizers, a number of work has dealt with the problem of their stability and * Present address

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