Crystallization process systems simulation

Thus, methods are now becoming available such that process systems can be designed to manufacture crystal products of desired chemical and physical properties and characteristics under optimal conditions. In this chapter, the essential features of methods for the analysis of particulate crystal formation and subsequent solid-liquid separation operations discussed in Chapters 3 and 4 will be recapitulated. The interaction between crystallization and downstream processing will be illustrated by practical examples and problems highlighted. Procedures for industrial crystallization process analysis, synthesis and optimization will then be considered and aspects of process simulation, control and sustainable manufacture reviewed. 

A detailed examination of phosphate distribution between solution and solid phase during calcite crystallization in a simulated natural water shows that phosphorus adsorbs as a mono-layer, causing slight changes in the solution phosphorus concentration. It appears that under the conditions examined in this study, calcite- mediated phosphorus mineralization has a role in the movement of phosphorus from the water column to bed sediments, although the extent and rates of the process in natural systems remain to be determined. 

The essential feature of PC materials is the ultrafast phase transition between amorphous and crystalline structures that occurs on a nanosecond time scale. In the previous sections, we have discussed extensively the amorphous and crystalline structures of GST and their properties. These correspond to the starting and end points for the actual phase transition, which are crucial to understand the function of PC materials. We now present results for the nucleation-driven crystallization process of GST using DF calculations combined with MD [31], A sample of fl-GST with 460 atoms was studied at 500, 600, and 700 K, and a second sample of 648 atoms was simulated at 600 K. In all cases we used a fixed crystalline seed (58 atoms, 6 vacancies) in order to speed up the crystallization process. More recent experience has shown that the time scale for the crystallization is of the order of several nanoseconds for these system sizes in the absence of a fixed seed, while those here are of the order of 0.3-0.6ns. This means that we cannot discuss the onset of nucleation, but this is also true in the case of smaller systems (<200 atoms) discussed by other groups. In very small systems, periodic boundary conditions bias the process severely. Our larger samples reduce finite-size effects, and we show the effect of choosing different annealing temperatures. Simulations of this scale (up to 648 atoms over 1 ns) are near the limit of present day DF/MD calculations. 

Simulating the crystallization process is a computational challenge, precisely because crystal nucleation is an activated process. This implies that the formation of small crystal nuclei in a supersaturated liquid is infrequent but, when it happens, the process is quite fast, i.e. it proceeds on a time scale that can be followed in a molecular simulation. For instance, experimentally measured nucleation rates are typically on the order of (9(10 ) to (9(10 ) nuclei per cm per sec. We can estimate the number of time steps needed in a molecular dynamics (MD) simulation to observe one nucleation event. In a large-scale computer simulation, it is feasible to study the dynamics of (9(10 ) particles, but the number of particles in a typical simulation is some two to three order of magnitude less. For an atomic liquid, the volume of a simulation box containing one million particles is of order (9(10 ) cm. If a million nuclei form per second in one cubic centimeter, then it will take, on average, 10 seconds for a nucleus to form in a system of a million particles. As the typical time step in a molecular simulation (MD) is on the order of femto seconds, this implies that it would take some 10 " MD time-steps to observe a single nucleation event under experimental conditions. 

Computational fluid dynamics (CFD) is the numerical analysis of systems involving transport processes and solution by computer simulation. An early application of CFD (FLUENT) to predict flow within cooling crystallizers was made by Brown and Boysan (1987). Elementary equations that describe the conservation of mass, momentum and energy for fluid flow or heat transfer are solved for a number of sub regions of the flow field (Versteeg and Malalase-kera, 1995). Various commercial concerns provide ready-to-use CFD codes to perform this task and usually offer a choice of solution methods, model equations (for example turbulence models of turbulent flow) and visualization tools, as reviewed by Zauner (1999) below. 

Rousseau, R.W. and Howell, T.R., 1982. Comparison of simulated crystal size distribution control systems based on nuclei density and super-saturation. Industrial and Engineering Chemistry Process Design and Development, 21, 606. 

The orientational relationships between the martensite and austenite lattice which we observe are partially in accordance with experimental results In experiments a Nishiyama-Wasserman relationship is found for those systems which we have simulated. We think that the additional rotation of the (lll)f< c planes in the simulations is an effect of boundary conditions. Experimentally bcc and fee structure coexist and the plane of contact, the habit plane, is undistorted. In our simulations we have no coexistence of these structures. But the periodic boundary conditions play a similar role like the habit plane in the real crystals. Under these considerations the fact that we find the same invariant direction as it is observed experimentally shows, that our calculations simulate the same transition process as it takes place in experiments. The same is true for the inhomogeneous shear system which we see in our simulations. 

An SMB-type process has been disclosed to extract the 26DMN using liquid phase adsorption in a simulated moving bed two stage system [45, 46]. The source of the 26DMN is not specified but could be by one of the methods outlined by Lillwitz. Currently almost all separation of 26DMN is by crystallization. 

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