Length reduction of fibres subject to breakage

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Abstract
A statistical analysis of the breakage of essentially one-dimensional materials (fibres) has been performed. This breakage process has been characterized by two independent frequency functions, one specifying the proportion of fibres of a certain length that are broken per unit of time, and the other specifying the number and distribution of fragments. From these two functions the process equation giving the fibre length distribution at any instant has been derived. With certain limiting conditions this equation has been solved with respect to the moments of the fibre length distribution function. One of the main purposes of the analysis was to examine the dependence of the fibre length distribution at an arbitrary operating time on the type of fragment distribution function and the initial fibre length distribution. It was found that the quotient between the weight average and the number average fibre length approached an asymptotic value that was independent of the initial fibre length distribution.

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