Efficient solution of a batch crystallization model with fines dissolution

In this paper, an efficient and accurate numerical method is proposed for solving a batch crystallization model with fines dissolution. The dissolution of small crystals (fines dissolution) is useful for improving the quality of a product. This effectively shifts the crystal size distribution (CSD) towards larger crystal sizes and often makes the distribution narrower. The growth rate can be size-dependent and a time-delay in the dissolution unit is also incorporated in the model. The proposed method has two parts. In the first part, a coupled system of ordinary differential equations (ODEs) for moments and solute mass is numerically solved in the time domain of interest. These discrete values are used to get growth and nucleation rates in the same time domain. In the second part, the discrete growth and nucleation rates along with the initial CSD are used to construct the final CSD. The analytical expression for CSD is obtained by applying the method of characteristics and Duhamel's principle on the given population balance model (PBM). A Gaussian quadrature method, based on orthogonal polynomials, is used for approximating integrals in the ODE-system of moments and solute mass. The efficiency and accuracy of the proposed numerical method is validated by a numerical test problem.     

Computational analysis of three-dimensional flow and mass transfer in a non-standard configuration for growth of a KDP crystal

Computational analysis of three-dimensional flow and mass transfer in a non-standard configuration for growth of a KDP crystal was conducted. The results show that the surface shear stress is mainly affected by the inlet velocity, and the distribution of the surface supersaturation is determined by the bulk supersaturation and the inlet velocity. By adjusting the inlet velocity, the homogeneity of surface supersaturation can be improved, which is helpful for reducing the occurrence of inclusions and enhancing the crystal quality. The thickness of solute boundary layer is closely related to the flow intensity, but it is almost free from the impact of the bulk supersaturation.     

Influence of some foreign metal ions on crystal growth kinetics of brushite (CaHPO4·2H2O)

Brushite, CaHPO₄·2H₂O, has been precipitated at 25 °C in the presence of Mg²⁺, Ba²⁺ or Cu²⁺ at concentrations up to 0.5 mM. When initial pH is sufficiently low to exclude nanocrystalline apatite as the initial solid phase, overall crystal growth rate may be determined from simple mass crystallization by recording pH as function of time. A combination of surface nucleation (birth-and-spread) and spiral (BCF) growth was found. Edge free energy was determined from the former contribution and was found to be a linear function of chemical potential of the additive, indicating constant adsorption over a wide range of additive concentrations. Average distances between adsorbed additive ions as calculated from slopes of plots are compatible with lattice parameters of brushite: 0.54 nm for Mg²⁺, 0.43 nm for Ba²⁺ and 0.86 nm for Cu²⁺. With the latter a sharp decrease in growth rate occurred early in the crystallization process, followed by an equally sharp increase to the previous level. When interpreted in terms of the Cabrera–Vermilyea theory of crystal growth inhibition, the results are consistent with an average distance between Cu ions of 0.88 nm, in perfect agreement with the above value.     

Environmental SEM investigation on surface defects in 0.92Pb(Zn1/3Nb2/3)O3–0.08PbTiO3 single crystal

In this paper, the technique of environmental scanning electron microscopy (ESEM) has been employed to investigate the surface defects of the (1 1 1) appearing face in 0.92Pb(Zn_1/3Nb_2/3)O₃–0.08PbTiO₃ (PZN–8%PT) crystals. From the ESEM images, we succeeded in observing and studying the growth hillocks and etch pits, low-angle grain boundaries, and sub-grain boundaries in (1 1 1) face, which were related to the generation of dislocation and stacking faults, respectively. On the other hand, an image of a unique multi-layer lamellar structure and fine step structure obtained in the (1 1 1) face reveals that the dominant fast growth mechanism of PZN–8%PT crystal grown by the flux method is a sub-step mechanism, unlike the screw dislocation growth mechanism.     

Determination of kinetic parameters of crystal growth rate of borax in aqueous solution by using the rotating disc technique

Growth rate of polycrystalline disc of borax compressed at different pressure and rotated at various speed has been measured in a rotating disc crystallizer under well-defined conditions of supersaturation. It was found that the mass transfer coefficient, K, increased while overall growth rate constant, K_g, and surface reaction constant, k_r, decreased with increasing smoothness of the disc. It was also determined that kinetic parameters (k_r,r,K,g) of crystal growth rate of borax decreased with increasing rotating speed of the polycrystalline disc. The effectiveness factor was calculated from the growth rate data to evaluate the relative magnitude of the steps in series bulk diffusion through the mass transfer boundary layer and the surface integration. At low rotating speed of disc, the crystal growth rate of borax is mainly controlled by integration. However, both diffusion and integration steps affect the growth rate of borax at higher rotating speed of polycrystalline disc.     

Numerical study to investigate the effect of partition block and ambient air temperature on interfacial heat transfer in liquid bridges of high Prandtl number fluid

Surface heat transfer at the liquid–air interface in liquid bridges of high Prandtl number fluid is known to affect the transitional characteristics appreciably. The heat transfer characteristics under microgravity conditions become much different from those of normal gravity mainly due to the absence of natural convection. The present study deals with numerical computations of flow and heat transfer characteristics in the liquid and surrounding air and also at the liquid–air interface of thermocapillary flow in liquid bridges of high Prandtl number fluid. The governing equations are solved in the coupled domain of the liquid bridge and the surrounding air with the help of available commercial CFD software. The results obtained for a range of Marangoni numbers indicate that by placing a partition block in the air region under normal gravity conditions, the surface heat transfer characteristics of microgravity conditions could be effectively mimicked. The effect of ambient temperature on the surface heat transfer has also been investigated and it has been found that the behavior of heat transfer at the interface changes from heat loss to heat gain when the ambient temperature is increased. Moreover, the presence of partition block under normal gravity suppresses surface heat loss as well as surface heat gain similar to microgravity conditions. Streamlines and temperature contours have been presented for various conditions in order to clarify the underlying physics more meaningfully. The computed profiles for velocity and temperature at the liquid–air interface have been validated against established experimental results.     

Solution growth of single crystals of 4-hydroxycyanobenzene (4HCB) suitable for electronic applications

Squared, platelet-like single crystals of 4-hydroxycyanobenzene (4HCB) have been grown from solutions based on ethylic ether and petroleum ether. Properly modifying the growth conditions, in terms of both solvent used for the growth and concentration of 4HCB in the starting solution, allowed one to tune the planar dimensions of the platelets in the range 2–6 mm, and their thickness in the range 150–600 μm. In this way samples well suited for desired practical manipulation and electronic measurements may be obtained. Moreover, lowering the growth temperature resulted in larger but still thin 4HCB crystals. The ability to tailor crystal thickness has allowed one to study their Space-Charge Limited Current (SCLC) behaviour along that dimension, showing that the so-contacted samples exhibit intrinsic-like bulk conduction behaviour, and are hence well suitable for electronic studies and applications.