Dissolution general discussion

One-dimensional diffusive dissolution With the above general discussion, we now turn to the special case of one-dimensional crystal dissolution. Use the interface-fixed reference frame. Let melt be on the right-hand side (x > 0) in the interface-fixed reference frame. Crystal is on the left-hand side (x < 0) in the interface-fixed reference frame. Properties in the crystal will be indicated by superscript "c". For simplicity, the superscript "m" for melt properties will be ignored. Diffusivity in the melt is D. Diffusivity in the crystal is D. The concentration in the melt is C (kg/m ) or w (mass fraction). The initial concentration in the crystal is or simplified as or if there would be no confusion from the context. It is assumed that the interface composition rapidly reaches equilibrium. In the following, diffusion in the melt is first considered, and then diffusion in the crystal. 

Table 5.1 displays dissolution reactions for oxides and hydroxides whose ceramics have potential practical applications. Also included is the pH range in which these reactions are valid. The pH range can be derived by the method described above, or as was done in Chapter 4, it can be calculated by equating the two subsequent equations at the transition boundary where these equations are equally valid. This table shows only the dissolution equations that are valid in acidic and neutral pH. For details covering the entire pH range and general discussions, the reader is referred to Ref. [5]. 

The mineral dissolution reactions discussed in this chapter are generally surface controlled. For these reactions, the rate of diffusion of reaction products from the reaction surface into the bulk solution is more rapid than the rate of release of products from the surface (Berner, 1981 Dibble and Tiller, 1981). Consequently, reaction rates are independent of the rate of stirring and measured Arrhenius activation energies (determined from the temperature dependence of measured rates) are greater than the activation energies for the diffusion of reaction products in solution. Activation energies for some soil minerals are shown in Table 7-1. 

It will be shown later that the values of icrit, Epp, and ip, which are the important parameters defining the shape of the active-passive type of polarization curve, are important in understanding the corrosion behavior of the alloy. In particular, low values of icrit enhance the ability to place the alloy in the passive state in many environments. For this reason, the maximum that occurs in the curve at B (Fig. 5.4) is frequently referred to as the active peak current density or, in general discussion, as the active peak. It is the limit of the active dissolution current density occurring along the A region of the polarization curve. 

A natural way to generalize the non-relativistic many-body Schrodinger equation is to combine the one-electron Dirac operators and Coulomb and Breit two-electron operators. However such an equation would have serious defects. One of them is the continuum dissolution first discussed by Brown and RavenhaU [36]. This means that the Schrodinger-type equation has no stable solutions due to the presence of the negative energy Dirac continuum. A constrained variational approach to the positive energy states becomes therefore necessary. 

The physical chemist is very interested in kinetics—in the mechanisms of chemical reactions, the rates of adsorption, dissolution or evaporation, and generally, in time as a variable. As may be imagined, there is a wide spectrum of rate phenomena and in the sophistication achieved in dealing wifli them. In some cases changes in area or in amounts of phases are involved, as in rates of evaporation, condensation, dissolution, precipitation, flocculation, and adsorption and desorption. In other cases surface composition is changing as with reaction in monolayers. The field of catalysis is focused largely on the study of surface reaction mechanisms. Thus, throughout this book, the kinetic aspects of interfacial phenomena are discussed in concert with the associated thermodynamic properties. 

The most important mechanism involved in the corrosion of metal is electrochemical dissolution. This is the basis of general metal loss, pitting corrosion, microbiologically induced corrosion and some aspects of stress corrosion cracking. Corrosion in aqueous systems and other circumstances where an electrolyte is present is generally electrochemical in nature. Other mechanisms operate in the absence of electrolyte, and some are discussed in Section 53.1.4. 

Biopharmaceutical issues to be addressed will include a discussion of the pharmaceutical development process as it relates to in vivo and in vitro performance and the general approach taken concerning bioavailability, bioequivalence, and in vitro dissolution profiles. There should be a comparative analysis of relevant studies—objectives, study design, conduct, outcome, and data analyses. The effects of formulation changes (including different strengths of product and... 

The diffusion layer theory, illustrated in Fig. 15B, is the most useful and best-known model for transport-controlled dissolution. The dissolution rate here is controlled by the rate of diffusion of solute molecules across a diffusion layer of thickness h, so that kT kR in Eq. (40), which simplifies to kx = kT. With increasing distance, x, from the surface of the solid, the concentration, c, decreases from cs at x = 0 to cb at x = h. In general, c is a nonlinear function of x, and the concentration gradient dddx becomes less steep as x increases. The hyrodynamics of the dissolution process has been fully discussed by Levich [104]. In a stirred solution, the flow velocity of the liquid dissolution medium increases from zero at x = 0 to the bulk value at x = h. 

Note that in the mechanistic schemes presented, the dissolution steps of reactant and products have been omitted for the sake of brevity. These include, for example CO (g) <-> CO (1), C02 (1) <-> C02 (g), and H2 (1) <-> H2 (g). From the standpoint of thermodynamics, when the equilibrium lies far to the right, reactions are deemed to be irreversible and may be denoted with a forward arrow - symbol. In cases where the reaction is considered to be reversible (i.e., equilibrium lies somewhere in the middle), the forward and backward arrows (e.g., <-> ) are employed. In some cases, however, we do not specify reversible/irreversible steps, and therefore arrows (e.g., or <-> ) might be used in a general sense. From a kinetic standpoint, in some cases a step will be defined that is considerably slower than the others (i.e., the rate determining step) in those cases, the remaining steps may be considered to be pseudo-equilibrated. The reader must therefore use discretion in interpreting the mechanistic schemes. The context of the discussion should clue the reader into how to interpret the arrows. 

This book deals only with the chemistry of the mineral-water interface, and so at first glance, the book might appear to have a relatively narrow focus. However, the range of chemical and physical processes considered is actually quite broad, and the general and comprehensive nature of the topics makes this volume unique. The technical papers are organized into physical properties of the mineral-water interface adsorption ion exchange surface spectroscopy dissolution, precipitation, and solid solution formation and transformation reactions at the mineral-water interface. The introductory chapter presents an overview of recent research advances in each of these six areas and discusses important features of each technical paper. Several papers address the complex ways in which some processes are interrelated, for example, the effect of adsorption reactions on the catalysis of electron transfer reactions by mineral surfaces. 

During the dissolution test, the hydrodynamic aspects of the fluid flow in the vessel have a major influence on the dissolution rate (1). Therefore, the working condition of the equipment is of critical importance. In this chapter, the qualification and calibration of the equipment referred to in the two USP General Chapters related to dissolution, < 711 > Dissolution and < 724 > Drug Release (2), will be discussed. Sources of error when performing dissolution... 

Periodic discussions among the EP, JP, and USP, with the World Health Organization as observer, facilitate compendial harmonization. This association is known as the Pharmacopeial Discussion Group (PDG). The PDG has prioritized the harmonization effort for individual general test chapters based originally on those identified within ICH Q6A (1). Dissolution is prominent on the PDG work agenda. 

Dissolution-based biowaivers for generic IR and MR drug products are discussed in the General BA and BE Guidance (4). 

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