Dissolution rate, calculation

The steady-state convective dissolution rate calculated above applies only when the unperturbed diffusion distance is greater than the boundary... 

Normalized to unstrained calcite. Dissolution rate calculation as a function of radius r of the hollow core, based on Eq. 11, for p = 10locm-2 (ST = total perfect surface area Sd = total surface area of hollow cores). 

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... 

Investigation of the differences in crystal packing between (431) and (426) from comparison of their respective X-ray structures, revealed that (431) was more tightly packed than (442), reflected in their respective melting points of 235 and 170 °C. It was postulated that the absence of in vivo activity for (431) may be explained by the resultant reduction in water solubility and dissolution rate compared with (426). The comparatively high calculated polar surface area of (431) (122.5A ) compared with (426) (89.3 A ) was also proposed as a factor influencing the marked difference in bioavailability between the two related compounds. Compound (426) (SLV-319) is currently being developed with Bristol-Myers Squibb for the potential treatment of obesity and other metabolic disorders. Phase I trials for obesity were started in April 2004. Earlier Phase I clinical trials for the treatment of schizophrenia and psychosis, which commenced in April 2002, appear to have been abandoned. 

Fig. 1.4 The calculated results for one acoustic cycle when a bubble in water at 3 °C is irradiated by an ultrasonic wave of 52 kHz and 1.52 bar in frequency and pressure amplitude, respectively. The ambient bubble radius is 3.6 pm. (a) The bubble radius, (b) The dissolution rate of OH radicals into the liquid from the interior of the bubble (solid line) and its time integral (dotted line). Reprinted with permission from Yasui K, Tuziuti T, Sivaknmar M, Iida Y (2005) Theoretical study of single-bubble sonochemistry. J Chem Phys 122 224706. Copyright 2005, American Institute of Physics...

Bisrat et al. concluded that for sparingly soluble, suspended drugs, diffusional transport plays a major role in the dissolution kinetics [19]. They studied the effect of particle size and viscosity on dissolution rate and apparent diffusional distance (.h-App) of oxazepam and griseofulvin. The term apparent diffusional distance was used as a simplified measure of the distance over which diffusion dominates and was calculated as follows ... 

The intrinsic dissolution rates of pharmaceutical solids may be calculated from the dissolution rate and wetted surface area using Eq. (36) or (37). For powdered solids, two common methods are available the powder intrinsic dissolution rate method, and the disc intrinsic dissolution rate method. In the former method, the initial dissolution rate of one gram of powder is determined by a batch-type procedure as illustrated in Fig. 13A. The initial wetted surface area of one gram of powder is assumed to equal the specific surface area determined by an established dry procedure, such as monolayer gas adsorption by the Brunauer, Emmett, and Teller (BET) procedure [110]. 

Fig. 8-7. Steady-state profiles of the saturation index, omegadel = omega-1, the dissolution rate, and the respiration rate to a depth of 40 centimeters. This calculation uses a finer depth resolution. 

Fig. 16.1. Results of reacting quartz sand at 100°C with deionized water, calculated according to a kinetic rate law. Top diagram shows how the saturation state Q/K of quartz varies with time bottom plot shows change in amount (mmol) of quartz in system (bold line). The slope of the tangent to the curve (fine line) is the instantaneous reaction rate, the negative of the dissolution rate, shown at one day of reaction.

In the calculation results (Fig. 26.6), the initial segment of the path is marked by the disappearance of the amorphous silica as it reacts to form cristobalite. The amorphous silica is almost completely consumed after about 10000 years of reaction. The mineral s mass approaches zero asymptotically because (as can be seen in Equation 26.1) as its surface area As decreases, the dissolution rate slows proportionately. During the initial period, only a small amount of quartz forms. 

Fig. 27.2. Concentration of dissolved silica and the quartz dissolution rate along a quartz sand aquifer being recharged at left by rainwater, for the scenario considered in Figure 27.1. Results were calculated assuming a range of flow velocities rapid flow corresponds to a Damkohler number Da less than one, whereas Da is greater than one for slow flow.

The calculations are similar and the result is displayed in Fig. 5.14b for pH = 4.4. Obviously Pb-adsorption is accompanied by an increase in net charge and a marked decrease in surface protonation [sFeOHg]. Plausibly, this reduction in Cji, can decrease the dissolution rate. 

Many mass balance studies which report weathering rates as a function of unit area of landscape surface do not permit comparison of those rates with laboratory dissolution rates, and cannot, therefore, contribute to the objectives of this paper. Only two published studies have thus far attempted to renormalize such calculated rates to mineral surface area. Discussion of these studies therefore forms the basis for comparisons of laboratory rates with natural weathering rates. 

PK-Map and PK-Sim (Bayer Technology Services, Wuppertal, Germany), that are based on the models described by Willman et al. [54], In these software packages, the intestinal permeability coefficient can be calculated using a compound s lipophilicity and molecular weight [52,54] and hence, no experimental permeability data is needed. Different to the model described by Willman et al. [54], the commercial prediction tools model the dissolution rate taking the particle size distribution of the solid particles into account (www.pk-sim.com). 

The main input parameter used to define the highest possible drug concentration in the intestine and to calculate the dissolution rate in the GI tract is the solubility of the dmg in the GI fluids. As described earlier (Sect. 21.2) there are several, both physiological and physicochemical, factors that can affect the solubility in the GI tract and it is therefore important to consider the relevance of the solubility data generated in the early drug discovery phase. A common approach is to use in silico models to predict the solubility of drugs (e.g., [5]). The advantage of this approach is that only the chemical... 

In silico models should also be used with care when it comes to predicting the absorption properties of salts and bases with low solubility in the intestinal fluids. All models use the thermodynamic solubility to calculate the dissolution rate and the saturation solubility in the different parts in the GI tract. However,... 

Results of the field experiment are shown in Eig. 16.27a, which is based on combined discharge from five extraction weUs. After about 50 days, TCM concentrations decreased. In contrast, concentrations of TCE fluctuated but remain relatively high. PCE concentrations continued to increase over time, exhibiting a higher dissolution rate over the first 100 days of the experiment. These results were used to plot (Eig. 16.27b) the observed relationship between concentration ratio and source transformation by dissolution-induced depletion, together with the equivalent theoretical relationships. Source depletion was calculated from the cumulative mass removed, as determined from monitoring of effluent at specific times, divided by the initial source mass. 

For the dissolution of a crystal into a melt, if one wants to predict the interface melt composition (that is, the composition of the melt that is saturated with the crystal), the dissolution rate, and the diffusion profiles of all major components, thermodynamic understanding coupled with the diffusion matrix approach is necessary (Liang, 1999). If the effective binary approach is used, it would be necessary to determine which is the principal equilibrium-determining component (such as MgO during forsterite dissolution in basaltic melt), estimate the concentration of the component at the interface melt, and then calculate the dissolution rate and diffusion profile. To estimate the interface concentration of the principal component from thermod5mamic equilibrium, because the concentration depends somewhat on the concentrations of other components, only... 

Equation 4-127 is from Zhang and Xu (2003). Therefore, with Sh and 8 calculated, the convective dissolution rate can be calculated. The calculation procedure is summarized next. 

Based on the above results, the following is a summary of steps to calculate the convective dissolution rate of a single falling or rising crystal in an infinite melt reservoir ... 

If the purpose is to calculate the dissolution rate for this crystal size, then we are done. If the purpose is to find how the crystal size changes as the crystal moves in the melt, then one chooses a small time interval dt, and obtains new depth as h + U dt and new crystal radius as a —u dt. 

For the calculation of convective dissolution rate of a falling crystal in a silicate melt, the diffusion is multicomponent but is treated as effective binary diffusion of the major component. The diffusivity of the major component obtained from diffusive dissolution experiments of the same mineral in the same silicate melt is preferred. Diffusivities obtained from diffusion-couple experiments or other types of experiments may not be applicable because of both compositional effect... 

The calculated result is in good agreement with experimental KCl dissolution rate at this temperature ( 0.025 mm/s, Zhang and Xu, 2003). 

The calculated result is in good agreement with CO2 droplet dissolution rate obtained by in situ experiments (1.44 um/s, Brewer et al., 2002). 

---