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المرحلة 2
أستاذ المادة ظافر قحطان سعيد الامين الماشطة
5/27/2011 1:59:05 PM
In equation (19-1), n is the number of particles in a size range whose midpoint, d, is one of the equivalent diameters mentioned previously. The term p is an index related to the size of an individual particle, because d raised to the power p = 1, p = 2, or p = 3 is an expression of the particle length, surface, or volume, respectively. The value of the index p also decides whether the mean is arithmetic (p is positive), geometric (p is zero), or harmonic (p is negative). For a collection of particles, the frequency with which a particle in a certain size range occurs is expressed by ndf. When the frequency index, f, has values of 0, 1, 2, or 3, then the size frequency distribution is expressed in terms of the total number, length, surface, or volume of the particles, respectively.
Particle-size distribution
When the number, or weight, of particles lying within a certain size range is plotted against the size range or mean particle size, a so-called frequency distribution curve is obtained. Typical examples are shown in Figures 19-1 and 19-2. Such plots give a visual representation of the distribution that an average diameter cannot achieve. This is important because it is possible to have two samples with the same average diameter but different distributions. Also, it is immediately apparent from a frequency distribution curve what particle size occurs most frequently within the sample. This is termed the mode.
An alternative method of representing the data is to plot either the cumulative percentage over or under a particular size versus particle size. This is done in Figure 19-3, using the cumulative percent undersize. A sigmoidal curve results, with the mode being that particle size at the greatest slope.
The standard deviation, ?, is an indication of the distribution about the mean. In a normal distribution, 68% of the population lie ±1? from the mean, 95.5% lie within the mean ±2?, and 99.7% lie within the mean ±3?. The normal distribution, shown in Figure 19-1, is not commonly found in pharmaceutical powders, which are frequently processed by milling or precipitation. Rather, these systems tend to have an nonsymmetric, or skewed, distribution of the type depicted in Figure 19-2. When the data in Figure 19-2 are plotted as frequency versus the logarithm of the particle diameter, a typical bell-shaped curve is frequently obtained. This is seen in Figure 19-4.
Number and weight distributions.
Frequently, we are interested in obtaining data based on a weight distribution of particles, rather than a number distribution. The significant differences in the two distributions is apparent, even though they relate to the same sample. For example, in Figure 19-3, only 12% of the sample by number is greater than 11 ?m, yet these same particles account for 42% of the total weight of the particles. For this reason, it is important to distinguish carefully between size distributions on a weight and a number basis.
Particle number
A significant expression in particle technology is the number of particles per unit weight, N, which is expressed in terms of dvn. The number of particles per unit weight is obtained as follow
Example: The mean volume number diameter of a powder is 2.41 ?m, or 2.41×10–4 cm. If the density of the powder is 3 g/cm3, what is the number of particles per gram? The mean volume number diameter of a powder is 2.41 . The number of particles per unit weight is obtained as follow The mean volume number diameter of a powder is 2.41 . When the frequency index, , has values of 0, 1, 2, or 3, then the size frequency distribution is expressed in terms of the total number, length, surface, or volume of the particles, respectively. The mean volume number diameter of a powder is 2.41
المادة المعروضة اعلاه هي مدخل الى المحاضرة المرفوعة بواسطة استاذ(ة) المادة . وقد تبدو لك غير متكاملة . حيث يضع استاذ المادة في بعض الاحيان فقط الجزء الاول من المحاضرة من اجل الاطلاع على ما ستقوم بتحميله لاحقا . في نظام التعليم الالكتروني نوفر هذه الخدمة لكي نبقيك على اطلاع حول محتوى الملف الذي ستقوم بتحميله .
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