Assumptions testing/validating

The extensive use of the Young equation (Eq. X-18) reflects its general acceptance. Curiously, however, the equation has never been verified experimentally since surface tensions of solids are rather difficult to measure. While Fowkes and Sawyer [140] claimed verification for liquids on a fluorocarbon polymer, it is not clear that their assumptions are valid. Nucleation studies indicate that the interfacial tension between a solid and its liquid is appreciable (see Section K-3) and may not be ignored. Indirect experimental tests involve comparing the variation of the contact angle with solute concentration with separate adsorption studies [173]. 

Whether these assumptions axe valid or not is dependent on a given DTA design. To determine the calorimetric capabilities of a particular instrument, one may simply test the melting en-dotherms of standard materials of known latent heats of fusion. The quantity ... 

The business case is often based on initial assumptions (customers will buy this innovative offering from us, we will recoup our investment on this project, etc.). Just be sure to test these assumptions for validity as you move through the project. Otherwise, you may find out too late that they weren t sound. 

Karlsson and Sheiner have provided excellent examples of the varied assumptions that come into play during population pharmacokinetic analysis. The decomposition of the assumptions into common categories and application of assumption testing to actual data sets are important concepts to grasp, and the manuscript itself is an excellent reference. Table 15.4 summarizes the assumptions discussed in Karlsson et al. and lists testing procedures to examine the validity of these assumptions. 

Many common mathematical formulas used for calculations of uncertainty, detection capability (see Section 10.4), and quality control in the radioanalytical chemistry laboratory are based on the assumption of Poisson counting statistics and are valid only if that assumption is valid. In particular, the formulas depend on the fact that the mean and variance of a Poisson distribution are numerically equal. For this reason it may be a good idea to test the Poisson assumption from time to time. 

The assumption is made here that the kinetics of adsorption are not influenced to any appreciable extent by conditions external to the adsorbent, that is the rate of adsorption is controlled solely by processes which occur inside the adsorbent particles. If this assumption is valid then data from small-scale experiments can be reliably scaled up to other flow rates without running pilot tests in larger columns. 

For interpretation and extrapolation of the experimental results the central role of a computer code as vital analytical tool has been emphasized. In Ref. 7 an attempt is made to identify areas of particular interest. For these great care should be exercised, when scaled experimental results are interpreted and extrapolated with the aid of dimensional analysis of a fypical set of conservation equations normally used in the lumped parameter codes. Two basic assumptions have been made in the course of the dimensional analysis. These are the geometrical similarity of the test fecilify and the prototype plant and performing the experiments with the same fluid compon ts, which are expected to dominate within the containment atmosphere of the prototype plant. Both of the two basic assumptions are valid in the VICTORIA test fecilify. 

It is important to know the micelle aggregation number because this influences the micelle shape, micelle kinetics, and transport properties. Translating the micelle size into the number of monomers in the micelle requires various assumptions the validity of which is difficult to test... 

Measurements have errors. When constructing a model, however, one must assume that systematic errors are absent. Whether this assumption is valid or not has to be the subject for later hypothesis testing. However, the presence of only random errors must be postulated a priori. 

It would clearly be desirable to extend the scope of the Kelvin method to include a range of adsorptives having varied physical properties, especially surface tension, molar volume, molecular shape and size. This would enable the validity of the method and its attendant assumptions to be tested more adequately, and would also allow a variation in experimental technique, for example by permitting measurements at 298 K rather than 77 K. 

The performanee tests must be run as mueh as possible to meet the ASME performanee eodes. These eodes are very well written and fully delineate the tests required. Meetings should be held in advanee with the vendors to deeide whieh part of the eode would not be valid and what assumptions and eorreetion faetors must be undertaken to meet the various power and effieieney guarantees. The determination of speeial data or verifieation of partieular guarantees, whieh are outside the seope of the eodes, should be made only after written agreement of both parties to the test, espeeially regarding methods of measurement and eomputation, whieh should be eompletely deseribed in the test report. 

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