A non-extensive statistical model for time-dependent multiple breakage particle-size distribution

• Non-extensive statistical model.
• Fractionary time evolution.
• Particle size distribution.
• Multiple breakage processes.

A general formulation for the statistical description of time-dependent multiple particle breakage processes is presented in terms of a purposely constructed dimensionless quantity that contains the main physical magnitudes involved in the problem. The approach combines the Tsallis non-extensive entropy with a kinetic equation with fractionary index for the time evolution of the size/mass of the fragments. The obtained distribution function is tested by fitting some experimental reports. It is found that the better adjustment corresponds, in all cases, to values of the time index equal or below 0.6, whereas the parameter of nonextensivity ranks between 1 and 2, as previously reported in other studies involving some kind of fragmentation. The work could be the first example of a non-extensive maximum-entropy statistical description based on a purposely constructed dimensionless quantity, as well as of the derivation of a fragment size distribution function explicitly dependent on measurable system variables. As a result, the role of quantities such as viscosity, velocity gradient and others becomes explicit in the formulation.