Scale of scrutiny

When extracting samples from sampling thieves, it is necessary to specify the sample size. This determination is based on the necessary scale of scrutiny for a particular system. Typically, this scale can be determined from the end use of 

A key point to gather from the textured mixtures above is that the orientation of sampling can have a large impact on mixing measures as well as the sample size. Sampling perpendicular to a striated mixture must be undertaken with care to ensure that the sample size is smaller than the striation size to obtain accurate measures of mixture quality (or lack thereof). 

Clearly, the sampling protocol and extraction technique can have a major impact on the accuracy of the mixing measure. Once samples have been obtained, it then becomes necessary to develop mixing measures that give an accurate representation of mixture quality. 

With these caveats in mind, the intensity of segregation, I, is defined as 

Another mixing measure of importance to powder mixing is the relative standard deviation (RSD), also known as the coefficient of variance (CoV), 

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When determining appropriate sample size, the Scale of Scrutiny must be considered. 

The Scale of Scrutiny must be carefully considered when sampling as both small and large samples can give very misleading results. 

Scale Granulator Vessel The local variables of moisture and shear level vary with volume element, or position in the granulator, which leads to the kinetics of nucleation, growth, consolidation, and breakage being dependent on position in the vessel, leading to a scale of scrutiny of fne vessel size. As shown in Fig. 21-147, moisture levels and drop phase concentration and nucleation will be high at position... 

Danckwerts defined a scale of scrutiny for a mixture as that maximum size of the regions of segregation in the mixture which would cause it to be regarded as imperfectly mixed . The scale of scrutiny provides a vital link between product specification and the state of mixedness of the mixture. Fora particular product it fixes the scale or sample size at which the mixture should be examined. If the eye is able to resolve colour variations in areas greater than, say, 1 mm, then this becomes the scale of scrutiny for the pigment dispersion. 

Great care has to be taken in fixing the scale of scrutiny for a product. If nutrient is fed to animals in the form of cake mixture and the assumption is made that the daily nutrient intake should be nearly constant then the scale of scrutiny of the nutrient mixture would be that of the animal s daily consumption. In the case of the animal nutrient the scale of scrutiny would depend on the consumption of the animal being fed. A suitable feed for a sheep would require a smaller scale of scrutiny than that for a cow. If it was decided that a weekly, rather than daily, intake of nutrient was critical then the scale of scrutiny would increase. It could well be that in this case the scale of scrutiny would be determined not so much by the animals requirements but by the marketing requirement of having a product of uniform appearance. An almost identical analysis of scale of scrutiny could be carried out on the mixture requirements for a pharmaceutical tablet. 

An identification of the scale of scrutiny for a product fixes the size of the sample to be taken from the mixture and assessed for mixture quality. It determines how closely the mixture will be examined. The relationship between mixture quality and scale of scrutiny is difficult to predict and as a result a theoretical scaling up or down of mixture quality with a scale of scrutiny should be avoided. It is much safer to re-sample the mixture at the new scale of scrutiny. 

Once a scale of scrutiny and hence sample size have been fixed a mixture can be sampled and the individual sample compositions compared. These values can be plotted on a histogram or distribution curve (Figure 2.1). 

A final bias has to be avoided when the samples are subjected to composition analysis. A sample withdrawn from a mixture is a point sample at a carefully chosen scale of scrutiny. When this sample is analysed for quality it is unlikely that the quantity required for analysis is the same as the scale of scrutiny for the process and it is vital that any sub-sampling of the point sample is carried out in an efficient spinning riffler. That is, for analytical purposes a bulk sample has to be taken from a point sample. Alternative methods ofobtaining a bulk analysis of the point sample would be to dissolve the entire point sample in a liquid or to grind the sample down to a fine cohesive state and elimate segregation. 

As welt as providing essential limiting variance values, equations (2.1) and (2.2) indicate how the mixture quality will be affected by the scale of scrutiny, or sample size. The variance, and hence the quality, of a completely s regated mixture is independent of the scale of scrutiny. If a fully randomized mixture is attainable then the quality of that mixture is inversely proportional to the number of particles in the sample. In this case a reduction in the particle size of the mixture will increase the number of particles in each Hxed weight sample and produce a predictable improvement in the attainable mixture quality. For a randomized mixture, equation (2.2) quantifles the effect of changes in the scale of scrutiny on mixture quality. Between these extremes of mixture types there is no infallible guide as to the relationship between scale of scrutiny and mixture quality. 

The Tirst step is to define the scale of scrutiny, and hence the sample size, required for the product. In the case of the plastic sheet this will be an area and, once it has been determined, the entire sheet of plastic can be subdivided into potential sample areas. Evidently the smaller the scale of scrutiny becomes the greater the number of potential sample sites. Assume that an analysis for every potential site has been carried out and the result expressed as a percentage of the coloured chips. The results are shown in Figure 2.3. In this case there are 900 potential sample locations each of which can be identified by two coordinates. A three-dimensional mixture analysis would require a third coordinate to identify potential samples. 

Commonly a minor component is to be dispersed within the bulk of the material and then mixture quality analysed at a very small scale of scrutiny. The cohesive mixture is usually of good quality when analysed at a large scale of scrutiny but at a small scale of scrutiny a high, and unacceptable, intensity of segregation can occur. To understand the nature of this problem the mixture and the structure of the mixture have to be examined on a micro as well as a macro scale. 

Figure II. I Effect of scale of scrutiny, (a) Polymer and masterbatch granules on scale of granules (b) on scale ofpigment particles...

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