Compaction equations

With this, a compact equation is found for the coefficients of the MSO expansions in the atomic basis, for each initial state /, as... 

For adsorption rate, LeVan considered four models axial dispersion (this is not really a rate model but rather a flow model), external mass transfer, linear driving force approximation (LDF) and reaction kinetics. The purpose of this development was to restore these very compact equations with the variables of Wheeler equation for comparison. 

Figure 3.2 illustrates the relatively complex nature of the compressibility factor s dependence on temperature and pressure. It is evident that there can be very substantial departures from ideal-gas behavior. Whenever possible, it is useful to represent the equation of state as an algebraic relationship of pressure, temperature, and volume (density). Certainly, when applied in computational modeling, the benefits of a compact equation-of-state representation are evident. There are many ways that are used to accomplish this objective [332], most of which are beyond our scope here. 

The Kawakita compaction equation is another equation which is often used for ceramic powder pressing. It can be derived by considering that compaction is similar to packing by tapping, where the compaction pressure, P, is directly substituted for the number of taps, N, in the analysis in Section 13.5.1. The Kawakita equation is a special case, where the value of m in the Weibul distribution function for tapping is 1. In the Kawakita equation, the compaction, C, defined as the relative reduction in volume is given by [72]... 

Using a compaction equation valid for the material of interest,... 

A new model was compared to known compaction equations, including Kawakita and Heckel, for some mineral salts. Panelli and Filho (2001) concluded that Equation 12 best represents the density-pressure relationship for powders, obtaining a linear correlation coefficient close to the unity. 

Chen, M. and Malgham, S.G. 1994. Investigation of compaction equation for powder. Powder Technol. 81, 75-81. 

Panelli, R. and Filho, F.A. 2001. A study of a phenomenological compacting equation. Powder Technol. 114, 255-261. 

This model leads to a compact equation for the breakthrough curve. With the expressions... 

Morgan and co-workers (26) derived the following compact equation for predicting microemulsion pol3rmerization kinetics. 

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