Dissolution model description

The stochastic nature of k (t) allows the description of the fraction of dose dissolved, p (t), in the form of a stochastic differential equation if coupled with the simplest dissolution model described by (5.16), assuming complete dissolution 9 = 1) ... 

In all these derivations, the role of the slurry chemicals during the polish process is not apparent. Even under static conditions, some of the chemicals can dissolve the material as in the case of ferric nitrate and copper or even H202/glycine and copper. This effect can, in principle, be easily included in a model description by adding a nonzero, velocity and pressure independent, intercept to the polish rate expression. In practice, it is more complicated since the relation between this nonzero intercept and static dissolution rates is not simple and is unknown due to, among other things, the effects of the polishing pad. In such cases, the role of a threshold pressure, while perhaps obvious when mechanical abrasion is the only mechanism for material removal, is not evident unless the removal rate can be broken neatly into two independent terms, one for the mechanical abrasion and the second for the chemical removal. Such is the case for the... 

The chemical model is defined in a separate file that must be written by the user. It creates the input file for PRISM and a template for the speciation code, assuring a model description consistent for all parts of the modelling. The input file has a well defined, line-oriented structure. Detailed chemical data for each compartment includes the selected SCM with its intrinsic surface parameter, also pH, Eh and the concentrations for all components. Default reaction constants (for complexation, precipitation/dissolution, sorption) can be modified, and reactions can also be suppressed totally. 

To date, potentiometric titration is still a main approach to study the surface acid base chemistry of clay minerals. Only some papers deal with the dissolution of a solid matrix resulting in various hydrolyzed aluminum species, silicic acid and their product hydrous aluminosilicates, though their interaction with a clay surface should be considered in the modeling description. The surface complexation model (SCM) was successfully applied in a recent paper [6] to interpret surface acid-base reactions involving the dissolution of illite clays during prolonged titration. Voluminous literature on ion adsorption and surface complexation... 

A frequently used example of Oldroyd-type constitutive equations is the Oldroyd-B model. The Oldroyd-B model can be thought of as a description of the constitutive behaviour of a fluid made by the dissolution of a (UCM) fluid in a Newtonian solvent . Here, the parameter A, called the retardation time is de.fined as A = A (r s/(ri + s), where 7]s is the viscosity of the solvent. Hence the extra stress tensor in the Oldroyd-B model is made up of Maxwell and solvent contributions. The Oldroyd-B constitutive equation is written as... 

While the simple stirred tank and plug flow models are adequate to describe convective transport in many cases, a more complete description of fluid flow is sometimes needed. For example, an accurate description of tablet dissolution in a stirred vessel may require information about the changing fluid velocity near the tablet surface. Neither the stirred tank nor the plug flow models can address these velocity changes, since both assume that velocity is independent of position and time. In such cases, a more detailed description of fluid flow can be developed using the Navier-Stokes equations, which describe the effects of pressure, viscos-... 

Model of Dissolution. Based on the results described above, a model for the dissolution of phenolic resins in aqueous alkali solutions 1s proposed. The model 1s adapted from Ueberrelter s description for polymer dissolution 1n organic solvents (.21). In Ueberrelter s model, the dissolution process takes place 1n several steps with the formation of (a) a liquid layer containing the dissolved polymer, (b) a gel layer, (c) a solid swollen layer, (d) an infiltration layer, and (e) the unattacked polymer. The critical step which controls the dissolution process is the gel layer. In adapting h1s model to our case, we need to take into account the dependence of solvation on phenolate ion formation. There 1s a partition of the cation and the hydroxide ion between the aqueous solution and the solid phase. The... 

The model framework for describing the void problem is schematically shown in Figure 6.3. It is, of course, a part of the complete description of the entire processing sequence and, as such, depends on the same material properties and process parameters. It is therefore intimately tied to both kinetics and viscosity models, of which there are many [3]. It is convenient to consider three phases of the void model void formation and stability at equilibrium, void growth or dissolution via diffusion, and void transport. 

Enthalpic and Entropic Contributions to the Excess Free Energy Molecular Picture of the Dissolution Process Model for Description of the Aqueous Activity Coefficient Box 5.1 Estimating Molar Volumes from Structure Illustrative Example 5.2 Evaluating the Factors that Govern the Aqueous Activity Coefficient of a Given Compound... 

Under quite general conditions on the geometry of the flow domain and the data we show that the model has a solution that satisfies the equations and boundary conditions in an integrated or weak sense. Clearly, the fluid velocity q, as well as the electrical charge c are solved independent of the chemistry. This part of the model ((81-3) and (9i 2)) is standard and its solution is straightforward. The challenging non-standard issue is the description of the chemistry ((84) and (93-5)), in particular the multi-valued dissolution rate in (95). Existence is demonstrated by regularization, where (94,5) are replaced by... 

The Boltzmann law computes to a configurational AS governed by Eq. (3.22). A configurational AS represents dissolution of a perfectly ordered, pure solid polymer in pure solvent (Allcock and Lampe, 1981). van Oss (1991) cautions against designating physical processes as AH- or AS-driven unless careful microcalorimetric measurements have been made, because many thermodynamic suppositions (imputed to modeling or intuition) have not been substantiated by experimentation. Although descriptive analyses of... 

In the interfacial barrier model of dissolution it is assumed that the reaction at the solid-liquid interface is not rapid due to the high free energy of activation requirement and therefore the reaction becomes the rate-limiting step for the dissolution process (Figure 5.1), thus, drug dissolution is considered as a reaction-limited process for the interfacial barrier model. Although the diffusion layer model enjoys widespread acceptance since it provides a rather simplistic interpretation of dissolution with a well-defined mathematical description, the interfacial barrier model is not widely used because of the lack of a physically-based mathematical description. 

Cover illustration Left panel Stochastic description of the kinetics of a population of particles, Fig 9.15. Middle panel Dissolution in topologically restricted media, Fig. 6.8B (reprinted with permission from Springer). Right panel A pseudophase space for a chaotic model of cortisol kinetics, Fig.11.11. 

Nonsteady behavior of electrochemical systems was observed by -> Fechner as early as 1828 [ii]. Periodic or chaotic changes of electrode potential under - gal-vanostatic or open-circuit conditions and similar variation of -> current under potentiostatic conditions have been the subject of numerous studies [iii, iv]. The electrochemical systems, for which interesting dynamic behavior has been reported include anodic or open-circuit dissolution of metals [v-vii], electrooxidation of small organic molecules [viii-xiv] or hydrogen, reduction of anions [xv, xvi] etc. [ii]. Much effort regarding the theoretical description and mathematical modeling of these complex phenomena has been made [xvii-xix]. Especially studies that used combined techniques, such as radiotracer (- tracer methods)(Fig. 1) [x], electrochemi-... 

Particularly sophisticated models deal with reactive mass transport, including both the accurate description of the convective and dispersive transport of species, as well as the modeling of interactions of species in water, with solid and gaseous phases (precipitation, dissolution, ion exchange, sorption). 

A quantitative description of the diverse morphological features of PS requires the integration of the aspects discussed above as well as the fundamental reaction processes involved in silicon/electrolyte interface structure, anodic dissolution, and anodic oxide formation and dissolution as detailed in Chapters 2-5. Any mathematical formulation for the mechanisms of PS formation without such a global integration would be limited in the scope of its validity and in the power to explain details. In addition, a globally and microscopically accurate model would also require the full characterization of all of the morphological features of PS in relation to all of the... 

Park [74] studied the efficiency of the ELM with non-Newtonian hquids in the removal of Zn, Pb, Ni and Cd from a simulated industrial wastewater using the Taylor-vortex column. The author adapted the shrinking core mathematical model of Liu and Liu [86] for quantitative description of the mass-transfer kinetics of the process [74]. The LM was prepared by the dissolution of 5 g dm of polyisobutylene in Soltrol 220 (see above). After complete dissolution of the polymer, the membrane phase... 

Haim et al. aim at a description of waves that were observed during the electrodissolution of an Ni wire in sulfuric acid. ° Their starting point is a lumped system, the behavior of which they had previously treated in order to simulate the global dynamics of Ni dissolution. This model falls into the category of HNDR oscillators, with the variables being the double-layer potential and the degree of surface modification. The latter is assumed to be local, and migration currents provide the only communication channel. The potential distribution in the electrolyte is presumed to obey Laplace s equation. Haim et al., however, missed... 

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