4.2 MSZW in membrane-free operation.
The measured MSZW data of thiourea aqueous solution in membrane-free cooling crystallization under different cooling rate and stirring rate were listed in Table S1 as supporting materials. The measured MSZW data were calibrated using the least-squares method, which is,
\(\Delta T_{\max}=40.9\times\nu^{0.2625}{N_{r}}^{-0.4757}\), R2=0.964 (26)
Comparison of experimental MSZW data and fitted ones also provided as supporting materials in Figure S1. According to the classical nucleation theory, high stirring intensity will accelerate the probability of particle collision to generate nucleation. It can also be seen that the MSZW tend to increase with the increase of the cooling rate due to the existence of the induction period. MSZW results provide the operation up limit for both membrane-free operation and membrane involved operation. MSZW under the membrane involved operation will be definitely lower than that of the membrane-free crystallization due to the inducing nucleation function of membrane. In this work, the rotating speed was set at 200 rpm to avoid the sever crystal breakage and secondary nucleation.