Phenomenological Sintering Equations

In most cases, if grain growth is significantly prohibited, shrinkage data can be fitted by the following equation  

There are also various empirical sintering equations that can be found in the open literature. One of them is as follows  

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Considerable amount of work has been done on both charged and uncharged membranes [46-53]. We shall discuss some of the recent data in the context of the conclusion of the thermodynamic theory developed in an earlier section. It may be noted that Eqs. (4.14) and (4.15) are used as axioms in the development of the phenomenological theory. The only justification for these is that these are consistent with the theory developed in the subsequent section. A direct test of the validity of the linear phenomenological equation has been performed recently. For pyrex sinter with water as permeant, (7)totd. (J) 4,=o have been measured individually. It is found... 

Phenomenological equations Empirical or phenomenological derivation of equations to describe sintering data. No reasonable physical basis. 34, 35... 

In the phenomenological approach, empirical equations are developed to fit sintering data, usually in the form of density (or shrinkage) versus time. Although the equations provide little or no help in understanding the process of sintering, they may serve a useful function in some numerical models that require the incorporation of explicit equations for the densification of a powder system. 

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