Mass Balance of the Continuously Operated Crystallizer

In crystallization technology it is common to use mass concentrations c in kg/m apart from mass fractions and loadings. In Fig. 8.3-1, a continuously operated crystallizer is shown. At steady-state conditions, the mass flow Lq of the solution with the concentration Cq entering the crystallizer is equal to the sum of the mass 

it is assumed, that the exhaust vapors do not contain any dissolved substance and no droplets from the solution are entrained. The leaving suspension consists of solution with the concentration Cj and crystals. The suspension density is rrij (in kg crystal/m suspension). The balance for the dissolved substance (with (pj being the volume fraction of the crystals in suspension) is 

In this equation, the quantity is the density of the compact ciystals, i.e., the density of the solid. If the suspension density (/ j 200 kg / is common in industrial ciystallizeis) is much lower than the density of the suspension and if the densities p (solution) and p (suspension) are nearly the same, the combination of (8.3-1) and (8.3-3) leads to 

the term is the evaporation ratio which is zero for cooling-crystal- 

Hence in cooling crystallizers the concentration difference Cq - c, precipitates as crystals of suspension density = (cq - c,). In case of a batch cooling crystallizer the suspension density is /Wj = (c - c ,) with the initial concentration c and the final concentration.  

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