Dear Ahmad

Breakage function is generally difficult to measure in the laboratory. One should make sure that batch grinding is done for a time short enough to avoid re-breakage of particles. If this is done, then one will produce accurate data for breakage function. Typically no more than 30 % of the initial monosized feed should be milled.

Now, the problem is that the broken particles (i.e. less than 30 % of the initial feed sample) may not spread well enough across of the sieve sizes that retained masses will be measured with a fair level of error. In addition to this, the grinding time is so short that it is prone to being measured with high inaccuracy compared to longer grinding times. So, all this contributes to the breakage function being challenging to accurately measure. That is partly the reason why the breakage function is assumed normalisable.

Finally, by assuming non-normalisation, one additional parameter need to be included to cater for this besides the 4 fitting parameters for the selection function and the 3 fitting parameters for the breakage function. Again here, the additional parameter is not always straightforward to measure. Hence, normalised breakage function is used for simplicity.

Francois

Generally, breakage function is found to be normalizable for only pure single component minerals such as limestone and quartz. In the case of complex multicomponent ores and cement clinker breakage function has been found to be non-normalizable. You may refer to my papers on complex pyritic ore (Pow Tech 28(1981) 97-106 and V. K, Gupta, A. Tripathy, J.P. Patel, An experimental and computational

methodology for estimation of breakage rate and distribution parameters for batch ball milling operation, in: Proceedings, XXVI International MineralProcessing Congress (IMPC), New Delhi, 2012, pp. 1800–1810. The last one is the best paper on this subject.

Dear Mulenga and Gupta,

I truly appreciate your recommendations and remarks that will be surely helpful for the future research studies.

Sincerely yours,

Ahmad