The mass deposition rate dm/dt varies exponentially with supersaturation Delta C, and linearly with crystal surface A (eqn. 2). The constant kg reflects the influence of temperature.
The nucleation rate B0 (eqn. 3) is an exponential function of supersaturation, the specific energy input and the crystal mass mT .
As mentioned earlier, two of the main crystallizer design parameters are fixed, to ensure better control of crystallization. These are the C, which, in practice, is set to about half of the metastable range, and the crystal mass mT (or the crystal surface area A), set to val-ues between 15 and 25%wt magma density.
The remaining design parameters that can influence product quality are the crystallization temperature T and the energy input E. With increasing temperature, the constant kg of eqn. 2 will usually increase. The energy input E affects inversely the secondary nucleation rate. Influencing the CSD and the average crystal size, therefore, remains possible by reducing E and operating the crystallizer at a higher temperature.
Another important factor in determining crystal size is the crystal retention time T, as shown by eqn 4, which describes the linear growth rate G and eqn. 5, which describes the mean crystal size L.
Theoretically, longer retention times are necessary if larger crystals are desired; however, in practice, also the opposite can be observed. The reason is the mechanical attrition rate G
a which reflects the reduction of crystal size due to breakage. The effective linear crystal growth rate Geff , therefore, is the sum of G
k minus G
a. (eq. 6).
Because attrition is increases with increasing crystal size, there is a critical particle size, where the effective crystal growth rate becomes zero (eq. 8). Therefore, under certain conditions, there exists a maximum achievable crystal size and longer retention times may lead to smaller crystal sizes.
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