In general, breakage matrix is an analysis technique, which is potentially useful in describing any degradation process. The application is widespread and unconstrained to model an intentional degradation process such as the study of the material breakage efficiency in a milling operation or capable of identifying which parts in a transport system contribute most to attrition problems. Breakage matrix approach is however, often limited to linear breakage assumption neglecting the nature of the many body of inter-particle interaction of individual species and the surrounding particles within mixture assembly.

Linear breakage assumption has received to open criticism for more than a century and as matter of fact, it is not necessarily held true in many degradation scenarios. Broadbent and Calcott, 1956 a&b observed linear or independent breakage for their case of coal transporting system even tough they remarked earlier, “..Breakage in an assembly is partly due to interaction between particles in the assembly”. Therefore, it can be reasoned at small extent, inter-particle interaction may result in abnormal breakage effects of the output size distribution. The successfulness of breakage matrix as a prediction tool is no doubt for self-governing condition, in fact, Campbell and Webb, 2001 in their work essentially suppose the breakage matrix approach is worthless for significant interacting mixture. Non-interacting conditions are sensible for some degradation scenarios for example during roller milling process in which each particle passing through the two rotating rolls and break independently, or in dilute phase pneumatic conveyor where the particles impact on pipe bends one at a time. Consider an example of dense phase condition where dense assemblies are subjected under compression loads/ shear, the breakage of individual particles within the mixture obviously far from negligible and are supposedly influenced by the presence of particles in other size classes.

This paper attempts to demonstrate the usefulness of breakage matrix as a more versatile tool in predicting degradation than it has been appreciated to date with additional feature of coefficient of interaction as a function of micro-structural limit fines composition and size ratio to account for the role of inter-particle interaction in influencing the binary mixture output size distribution after degradation. The prediction capability of this proposed more flexible breakage matrix approach is verified with some degradation data set obtained from a compression test bed of dense particulate mixtures.

References:

1-) Broadbent, S.R., Callcott, T.G.,(1956-a) J. Inst Fuel., pp: 524-528

2-) Broadbent, S.R., Callcott, T.G.,(1956-b) J. Inst Fuel., pp: 528-539

3-) Campbell G.M., Webb C., (2001), J. Powder Technol., 115, pp: 243-255

4-) Tuzun U., Artega P., (1992), Chem. Eng. Sci., 47, pp:1619-1630