Dissolution rate mass transfer

There have been a number of studies on the rate of dissolution of crystals In agitated tanks (eg.26-31). Predominantly the results Indicate dissolution Is mass transfer controlled. For mass transfer In stirred tanks, among the many studies, that of Levins and Glastonbury (32) Is widely considered. 

A plot of the dissolution rate against driving force, AC, is shown in Figure 13. This shows a linear dependence on undersaturation and a slight dependence on temperature (activation energy of 10 kJ/mole). This indicates that the dissolution is mass transfer controlled. The results can be correlated by... 

Different ways of enhancing the solubility of polysaccharides in ionic liquids have been reported. Recently, ultrasound irradiation has been used to increase enzyme activity in lipase-catalysed esterifications of glucose with vinyl laurate or lauric acid in ILs [67]. It was found that ultrasound irradiation significantly enhances the enzyme activity probably due to an increase in the dissolution and mass transfer rates of substrates, without any loss in enzyme stability. 

The limiting current density is an important parameter for the analysis of mass transfer controlled electrochemical processes and represents the maximum possible reaction rate for a given bulk reactant concentration and fluid flow pattern. During anodic metal dissolution, a mass transfer limiting current does not exist because the surface concentration of the dissolving ion (e.g., Cu + when the anode is composed of copper metal) increases with increasing current density, eventually leading to salt precipitation that blocks the electrode surface. 

The kinetic constants of the Tedmon law are obtained by adjustment of experimental results. The external magnetite layer is assumed to dissolve in the liquid metal and that its dissolution is mass transfer-controlled. Its rate thus depends on the dissolved oxygen and dissolved iron concentrations, on the diffusion coefficient and the solubility of iron in the liquid metal or alloy. The code calculates the dissolved iron concentration on each point of the circuit and takes into account the influence of the fluid velocity on the dissolution of the magnetite layer. However, the erosion or the spallations of the oxide layer are not taken into account by the MATLIM code. 

Under natural conditions the rates of dissolution of most minerals are too slow to depend on mass transfer of the reactants or products in the aqueous phase. This restricts the case to one either of weathering reactions where the rate-controlling mechanism is the mass transfer of reactants and products in the soHd phase, or of reactions controlled by a surface process and the related detachment process of reactants. 

Batch Stirred Tanks Tanks agitated by coaxial impellers (turbines, paddles, or propellers) are commonly used for batch dissolution of solids in liquids and may be used for leaching fine solids. Insofar as the controlhng rate in the mass transfer is the rate of transfer of mate-... 

Yagi and Wakao (1959) used mass transfer measurement results to estimate the heat transfer coefficient at the tube wall. Material was coated on the inner surface of the packed tubes and the dissolution rate was measured. 

Flow thins protective film to equilibrium thickness which is a function of both mass transfer rate and growth kinetics. Erosion corrosion rate is controlled by the dissolution rate of the protective film. 

Sundararajan et al. [131] in 1999 calculated the slurry film thickness and hydrodynamic pressure in CMP by solving the Re5molds equation. The abrasive particles undergo rotational and linear motion in the shear flow. This motion of the abrasive particles enhances the dissolution rate of the surface by facilitating the liquid phase convective mass transfer of the dissolved copper species away from the wafer surface. It is proposed that the enhancement in the polish rate is directly proportional to the product of abrasive concentration and the shear stress on the wafer surface. Hence, the ratio of the polish rate with abrasive to the polish rate without abrasive can be written as... 

The intrinsic dissolution rate is the rate of mass transfer from the solid phase to the liquid phase. Information on the intrinsic dissolution rate is important in early drug product development. It has been suggested that drugs with intrinsic dissolution rates of less than 0.1 mg/(min cm2) will have dissolution rate-limited absorption, while drugs with intrinsic dissolution rates greater than 0.1 mg/ (min cm2) are unlikely to have dissolution rate problems. 

The derivation and experimental verification of the MMHS model represented a significant accomplishment and a natural plateau for film models. To be sure, there are general criticisms of film models and more specific criticisms of the MMHS model [6], However, overall the MMHS model should be recognized as a robust but simply applicable model which serves to demonstrate how factors such as intrinsic solubility of the acid drug, ionization and pA of the drug, and concentration of the reactive base all contribute to increasing the dissolution rate and mass transfer. 

Other researchers used flow between two parallel plates as the experimental and theoretical system to incorporate diffusion plus convection into their dissolution modeling and avoid film model approximations [10]. Though they did not consider adding reactions to their model, these workers did show that convection was an important phenomenon to consider in the mass transfer process associated with solid dissolution. In fact, the dissolution rate was found to correlate with flow as... 

When determining the solubility and dissolution rate of amorphous or partially crystalline solids, the metastability of these phases with respect to the highly crystalline solid must be considered. While the low diffusivity of the molecules in the solid state can kinetically stabilize these metastable forms, contact with the solution, for example during measurements of solubility and dissolution rate, or with the vapor, if the solid has an appreciable vapor pressure, may provide a mechanism for mass transfer and crystallization. Less crystalline material dissolves or sublimes whereas more crystalline material crystallizes out. The equilibrium solubility measured will therefore approach that of the highly crystalline solid. The initial dissolution rate of the metastable form tends to reflect its higher... 

However, flow generated by a cylinder rotating at high speed was subsequently used by others, and in particular by King and co-workers (K3, K4a), to demonstrate that dissolution and electrochemical corrosion may both be transport limited. The dependence of the mass-transfer coefficient on the rotation rate and on the diffusivity of the dissolving species was established by correlation of experimental data (see Table VII, System 43). 

Equation (43) describes the transport-controlled dissolution rate of a solid according to the diffusion layer theory in its simplest form. The mass transfer coefficient here is given by k, = kT = Dlh. 

Once the initial equilibrium state of the system is known, the model can trace a reaction path. The reaction path is the course followed by the equilibrium system as it responds to changes in composition and temperature (Fig. 2.1). The measure of reaction progress is the variable , which varies from zero to one from the beginning to end of the path. The simplest way to specify mass transfer in a reaction model (Chapter 13) is to set the mass of a reactant to be added or removed over the course of the path. In other words, the reaction rate is expressed in reactant mass per unit . To model the dissolution of feldspar into a stream water, for example, the modeler would specify a mass of feldspar sufficient to saturate the water. At the point of saturation, the water is in equilibrium with the feldspar and no further reaction will occur. The results of the calculation are the fluid chemistry and masses of precipitated minerals at each point from zero to one, as indexed by . 

In this chapter we consider how to construct reactions paths that account for the effects of simple reactants, a name given to reactants that are added to or removed from a system at constant rates. We take on other types of mass transfer in later chapters. Chapter 14 treats the mass transfer implicit in setting a species activity or gas fugacity over a reaction path. In Chapter 16 we develop reaction models in which the rates of mineral precipitation and dissolution are governed by kinetic rate laws. 

Comparing the development here to the accounting for the kinetics of mineral precipitation and dissolution presented in the previous chapter (Chapter 16), we see the mass transfer coefficients v and so on serve a function parallel to the coefficients v , etc., in Reaction 16.1. The rates of change in the mole number of each basis entry, accounting for the effect of each kinetic redox reaction carried in the simulation, for example,... 

Dissolution can be described as a mass transfer process. Although mass transfer processes commonly are under the combined influence of both thermodynamics and hydrodynamics, usually one of these prevails in terms of the overall dissolution process (1-3). Hydrodynamics is predominant for the overall dissolution rate if the mass transfer process is mainly controlled by convection and/or diffusion, as is usually the case for poorly soluble substances. This is of great... 

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