Dissolution rate constants

In a typical research and development setting, in the event that a new drug candidate is recognized by the drug-discovery group, then the dissolution rate constant K for that compound under specified hydro-dynamic conditions can be determined from powder dissolution data and practical size analysis by microscopy. 

Formulation Apparent permeability rate constant, kp SE, h 1 First-order dissolution rate constant, kd SE, h-1 = SE... 

It can be seen that the dissolution rate constant kD is equivalent to the diffusion coefficient divided by the thickness of the diffusion layer (D/h). 

The diffusion coefficient is linked to the intrinsic dissolution rate constant ( i) as expressed by the term... 

Level B Correlation A predictive mathematical model for the relationship between summary parameters that characterize the in vitro and in vivo time courses, e.g., models that relate the mean in vitro dissolution time to the mean in vivo dissolution time, the mean in vitro dissolution time to the mean residence time in vivo, or the in vitro dissolution rate constant to the absorption rate constant. 

M = mass of solid remaining at a specific time k= cube root dissolution rate constant, which is represented as... 

According to W. Nernst,298 the dissolution-rate constant can be expressed as follows... 

Indeed, it seems obvious that a variation of the concentration of any dissolving solid substance in a liquid is directly proportional to both the area of its surface contacting with the liquid and the difference between the saturation concentration (solubility) at a given temperature and the instantaneous concentration of A in B, and is inversely proportional to the volume of the liquid phase. Therefore, the general form of equation (5.1) remains unchanged for either dissolution regime of any solid in any liquid. The difference lies in the character of the dependence of the dissolution-rate constant, k, upon the thickness, 5, of the diffusion boundary layer. 

It is clear that under conditions of decomposition control the rate of dissolution of a solid in a liquid is independent of the thickness of the diffusion boundary layer and hence of the intensity of agitation of the liquid. By contrast, in the case of diffusion control the intensity of agitation of a liquid has a strong effect on the thickness of the diffusion boundary layer, thus influencing the value of the dissolution-rate constant, k. 

This equation allows the determination of the diffusion coefficient, D, of the atoms of the dissolving substance across the diffusion boundary layer, knowing the value of the dissolution-rate constant, k, and vice versa. It is essential to remember, however, that equation (5.6) holds for Schmidt s numbers, Sc, exceeding 1000. 

To determine precise values of the dissolution-rate constant, thorough investigations of initial portions of the c - St/v curves like those shown in Figs 5.4 and 5.6 are to be carried out. Figure 5.7 shows the experimental... 

In contrast to the solubility, the values of the dissolution-rate constants of different metals and alloys in liquid aluminium are very close. At least, they are of the same order of magnitude, namely 10 5 m s1, although the solubility values may differ by two orders of magnitude or more (see Table 5.2). This is also typical of dissolution of other solid substances in liquids.299 301... 

Table 5.8. Values of the dissolution-rate constant, k (xlO 5 m s ), of transition metals in liquid aluminium at an angular speed of the disc rotation of 25 rad s 1 303 The mean relative error of their determination is around 5 %...

It should be emphasised that accurate calculations of the dissolution-rate constant, k, can only be carried out if the difference between c and cs is sufficiently large. At c —> cs, the error in computing this constant rapidly increases due to the low value of the denominator (cs-c) in equations (5.9) and (5.10). In such a case, even small errors in determining the instantaneous concentration, c, which are clearly unavoidable, lead to very large errors in calculating the values of k. 

From equations (5.6) and (5.7), it follows that under conditions of diffusion control the dissolution-rate constant should depend linearly on the square root of the angular speed of the disc rotation. As seen in Fig. 5.9, this is indeed the case (see also Refs 197, 300, 301, 303, 304, 307, 308). 

Fig. 5.9. A plot of the dissolution-rate constant of tungsten in liquid aluminium against the square root of the angular speed of the disc rotation at 750°C.309...

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