Crystallization kinetics transport

Adsorption Kinetics. In zeoHte adsorption processes the adsorbates migrate into the zeoHte crystals. First, transport must occur between crystals contained in a compact or peUet, and second, diffusion must occur within the crystals. Diffusion coefficients are measured by various methods, including the measurement of adsorption rates and the deterniination of jump times as derived from nmr results. Factors affecting kinetics and diffusion include channel geometry and dimensions molecular size, shape, and polarity zeoHte cation distribution and charge temperature adsorbate concentration impurity molecules and crystal-surface defects. 

There are basically three, rate-limiting mechanisms for mineral dissolution assuming a fixed degree of undersaturation. They are (1) transport of solute away from the dissolved crystal or transport-controlled kinetics. 

For example, when we consider the design of specialty chemical, polymer, biological, electronic materials, etc. processes, the separation units are usually described by transport-limited models, rather than the thermodynamically limited models encountered in petrochemical processes (flash drums, plate distillations, plate absorbers, extractions, etc.). Thus, from a design perspective, we need to estimate vapor-liquid-solid equilibria, as well as transport coefficients. Similarly, we need to estimate reaction kinetic models for all kinds of reactors, for example, chemical, polymer, biological, and electronic materials reactors, as well as crystallization kinetics, based on the molecular structures of the components present. Furthermore, it will be necessary to estimate constitutive equations for the complex materials we will encounter in new processes. 

The formalism introduced in the previous subsections is able to incorporate the effect of these influences in the crystallization kinetics, thus providing a more realistic modeling of the process, which is mandatoiy for practical and industrial purposes. Due to the strong foundations of our mesoscopic formalism in the roots of standard non-equilibrium thermodynamics, it is easy to incorporate the influence of other transport processes (like heat conduction or diffusion) into the description of crystallization. In addition, our framework naturally accounts for the couplings between all these different influences. 

The crystallization kinetics of heat polymers are governed by the energy barriers that must be overcome to form a critical nucleus on the crystal surface, AF, and to activate the transport of the segments across the solid-liquid interface, H. The accepted expression for the radial growth rate is... 

Another example of this class is solvent-induced crystallization (142). The effects of crystallization kinetics and rate of movement of the boundary between penetrated and impenetrated regions have been treated. Moreover, effects of increasing impediments to diffusion caused by the increasing crystalline fraction during the same time scale as that of the solvent transport are included in the model of the system. Such models become exceedingly complex and fall outside the domain of the present discussion however, they clearly require the input of information related to transport properties and their dependence on local conditions. 

Based on our previous studies of the dissolution and crystallization kinetics of potassium inorganic compounds based on linear nonequilibrium thermodynamics (Ji et al, 2010 Liu et al, 2009 Lu et al, 2011), we proposed to assume that the kinetic process of CO2 absorption by ILs comprised two steps surface reaction and diffusion, as shown in Fig. 17. Figure 17 demonstrates that when CO2 in the vapor phase and the ILs were in contact, the chemical reaction of CO2 with ILs occurred for the chemical absorption process of CO2 by ILs in the first step, which was named as the surface reaction layer, while for the physical mass transport process of CO2 by ILs in the first step, CO2 in the vapor phase would be transported into the IL phase, which was also named as the assumed surface reaction layer. As for the surface reaction layer, the driving force of the surface reaction was the chemical potential gradient of CO2 between CO2 at the vapor—Hquid interface and gas CO2. After that, in the second step, CO2 in the IL phase would... 

As mentioned before, nonequilibrium thermodynamics could be used to study the entropy generated by an irreversible process (Prigogine, 1945, 1947). The concept ofhnear nonequilibrium thermodynamics is that when the system is close to equilibrium, the hnear relationship can be obtained between the flux and the driving force (Demirel and Sandler, 2004 Lu et al, 2011). Based on our previous linear nonequihbrium thermodynamic studies on the dissolution and crystallization kinetics of potassium inorganic compounds (Ji et al, 2010 Liu et al, 2009 Lu et al, 2011), the nonequihbrium thermodynamic model of CO2 absorption and desorption kinetics by ILs could be studied. Figure 17 shows the schematic diagram of CO2 absorption kinetic process by ILs. In our work, the surface reaction mass transport rate and diffusion mass transport rate were described using the Hnear nonequihbrium thermodynamic theory. 

The usual practice for avoiding the plugging of production facilities by hydrates is to add thermodynamic inhibitors, such as methanol or glycol. A newer concept is the injection of low-dosage additives either kinetic inhibitors, which delay nucleation or prevent the growth of hydrate crystals, or hydrate dispersants, which prevent the agglomeration of hydrate particles and allow them to be transported within the flow [880,1387]. Hydrate control is discussed extensively in Chapter 13. Classes of hydrate control agents are shown in Table 11-9, and additives are shown in Table 11-10. 

Molecular transport junctions differ from traditional chemical kinetics in that they are fundamentally electronic rather than nuclear - in chemical kinetics one talks about nucleophilic substitution reactions, isomerization processes, catalytic insertions, crystal forming, lattice changes - nearly always these are describing nuclear motion (although the electronic behavior underlies it). In general the areas of both electron transfer and electron transport focus directly on the charge motion arising from electrons, and are therefore intrinsically quantum mechanical. 

From the above statements it follows that it should be possible to derive the growth kinetics and calculate the growth rate of uncontaminated electrolyte crystals when the following parameters are known molecular weight, density, solubility, cation dehydration frequency, ion pair stability coefficient, and the bulk concentration of the solution (or the saturation ratio). If the growth rate is transport controlled, one shall also need the particle size. In table I we have made these calculations for 14 electrolytes of common interest. For the saturation ratio and particle size we have chosen values typical for the range where kinetic experiments have been performed (29,30). The empirical rates are given for comparison. 

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