Kawakita equation

The Kawakita equation [13] describes the relationship between volume reduction and applied pressure according to Equation (4), where P is the applied pressure, V, is the initial bulk volume, V is the volume at pressure P, a and b are the constants characteristic of the powder under compression, and C is the degree of volume reduction [Equation (5)] ... 

In the Kawakita equation the particle density is not introduced in the calculations since the model operates on the relative change in volume, which gives the same result whether the relative or the absolute volume is used. The problem in the calculation of this equation is to find the correct initial volume V0. 

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]... 

The Kawakita equation was developed to. study powder densification using the degree of reduction in volume, C, and expressed as (70) ... 

The degree of volume reduction of a powder column as a function of the applied pressure has also been modeled with the Kawakita equation. 

Ramberger, R. and Burger, A. 1985. On the application of the Heckel and Kawakita equations on powder compaction. Powder Technol. 43, 1-9. 

The Kawakita Equation. Because the value of / in Eq. (2.55) depends on the catalytic effect of the degradation product, a more general form ofEq. (2.60) is Eq. (2.62). Kawakita reported that the reduction of ferric oxide can be described by Eq. (2.62) with various values of /, depending on temperature.278... 

From tablet height, volume, porosity, and relative density at different stages of densification can be deduced. These variables are plotted as a function of pressure. For analysis, for example, the equations of Heckel [118-120], Kawakita, [121,122], Cooper and Eaton [123], Walker [124], Bal shin [125], and Spnnergaard [126,127] can be used. The equations are given in Table 7. A further overview of these and other equations used can be found in Celik [88],... 

The equation of Kawakita describes volume reduction with pressure in the form of a hyperbolic equation. Walker and Bal shin [125] postulated a logarithmic relation between applied pressure and volume reduction, which was further modified by Spnnergard [126], Cooper and Eaton [123] use an exponential function, which can also be linearized. Pressure thresholds for deformation mechanisms are determined. It should be noted that all of these equations and tableting models determine descriptive parameters. 

Kawakita, K., and Ltidde, K. H. (1970/71), Some considerations on powder compression equations, Powder Tech., 4, 61-68. 

Many equations have been derived in attempts to provide a mathematical expression of Fig. 9. These have been reviewed by Kawakita and Ludde. " It must be stressed that such equations are simply mathematical descriptions of the data, and they have no underlying physical significance. 

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. 

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