Continuous crystallization process, dynamic

The observed transients of the crystal size distribution (CSD) of industrial crystallizers are either caused by process disturbances or by instabilities in the crystallization process itself (1 ). Due to the introduction of an on-line CSD measurement technique (2), the control of CSD s in crystallization processes comes into sight. Another requirement to reach this goal is a dynamic model for the CSD in Industrial crystallizers. The dynamic model for a continuous crystallization process consists of a nonlinear partial difference equation coupled to one or two ordinary differential equations (2..iU and is completed by a set of algebraic relations for the growth and nucleatlon kinetics. The kinetic relations are empirical and contain a number of parameters which have to be estimated from the experimental data. Simulation of the experimental data in combination with a nonlinear parameter estimation is a powerful 1 technique to determine the kinetic parameters from the experimental... 

The close relationship between cell membranes and liquid crystals has already been cited as a stimulus for research on transport of ions and various uncharged molcules in liquid crystals. However, dynamic behavior of membranes is not limited to transport processes. Ambrose (50) has provided a fascinating description of cell surfaces in constant motion with pseudopodia continually forming, growing, and disappearing. He also noted that such behavior is quite different for normal and cancer cells, at least for the cell types he studied. 

A continuous production process requires the separation of gel precipitation and crystallization stages. The latter step lasts three times longer then gel precipitation and aging. High-shear forces are employed during gel precipitation and aging, whereas low flow velocity is advisable during crystallization [15,99,104]. Nevertheless, continuous crystallization tends to be difficult due to the metastability of the crystallization and dynamic processes, which result in the unforeseeable formation of impurities [108]. 

The design and implementation of control systems for both batch and continuously operated industrial crystallisers can be achieved by mathematical and physical structured models for the process dynamic behaviour and from on-line measurements of the crystal distribution (CSD). 

To prove that the equilibrium is dynamic, we could add to the equilibrium mixture some radioactive iodine-131 as iodide ion, as illustrated in Figure 15-2. If both the forward and reverse processes stopped at equilibrium, radioactivity would be confined to the solution. What we find, though, is that radioactivity shows up in the solid as well. Over time, the radioactive iodide ions are distributed throughout the solution and undissolved solid. The only way this can happen is if the dissolving and crystallization processes continue indefinitely. 

These apparent restrictions in size and length of simulation time of the fully quantum-mechanical methods or molecular-dynamics methods with continuous degrees of freedom in real space are the basic reason why the direct simulation of lattice models of the Ising type or of solid-on-solid type is still the most popular technique to simulate crystal growth processes. Consequently, a substantial part of this article will deal with scientific problems on those time and length scales which are simultaneously accessible by the experimental STM methods on one hand and by Monte Carlo lattice simulations on the other hand. Even these methods, however, are too microscopic to incorporate the boundary conditions from the laboratory set-up into the models in a reahstic way. Therefore one uses phenomenological models of the phase-field or sharp-interface type, and finally even finite-element methods, to treat the diffusion transport and hydrodynamic convections which control a reahstic crystal growth process from the melt on an industrial scale. 

According to Cairns-Smith, the first primitive gene materials could have been clay minerals these crystallize out everywhere on Earth from dilute silica solutions and hydrated solutions of metal ions. Both groups of substances are continually being formed by weathering processes. Two cycles keep this dynamic process going ... 

The ionic atmosphere moves continually, so we consider its composition statistically. Crystallization of solutions would occur if the ionic charges were static, but association and subsequent dissociation occur all the time in a dynamic process, so even the ions in a dilute solution form a three-dimensional structure similar to that in a solid s repeat lattice. Thermal vibrations free the ions by shaking apart the momentary interactions. 

In a saturated solution, an equilibrium exists between the rate of precipitation of solute particles and the rate of dissolution of solute particles. The rate of precipitation equals the rate of dissolution. The shape of a crystal of solute added to a saturated solution will change after a period of time at a constant temperature and pressure, but its mass will remain the same. The equilibrium between dissolving and precipitation is dynamic, a continuous process. 

Steven Strogatz is the best teaclier 1 know. From his own course he has crystallized the perfect textbook for a first undergraduate course in nonlinear dynamics, covering both continuous and discrete processes plus fractals, with wonderfully seductive examples and problem sets. The book would also serve well for higher level courses. I would love to teach out of it." —Arthur T. Winfree, University of Arizona, and author of... 

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