The G-M-H size distribution function contains three parameters and can describe the major features of size distribution used today.
The authors apply this equation to batch ball mill grinding process and study the subject from some angles of the comminution kinetics.
By using the Lewis' equation, comminution energy is represented in terms of a parameter of the Lewis' equation and those of the G-M-H function.
From the above result, size distributions of the batch ball mill grinding product is represented by the following equation. y={1-(x/x₀)^α}^C₁tm……(25) where E₁ and m are defined by parameters of the G-M-H function and that of the Lewis' equation.
Kinetics of disappearance of feed size is studied by using eq. (25).
This equation is also derived as an analytical solution of the mass balance equation where some assumptions are made about the breakage function and the selection function.
Eq. (25) is confirmed experimentally and a practical application of this equation is tried. A method for determining three parameters of the G-M-H distribution function is also shown.

View full abstract

Some statistical quantities were experimentally evaluated for a system of droplets, which, because of their spherical shape, might be considered as idealized particles.
The droplets were prepared by atomizing an aqueous 5% NaCl solution through an atomizer of the paintspraying gun type or of the Lauterbach's nozzled-air flow type, and were allowed to stand tranquil or stirred for aging in a cylindrical mist chamber of a volume of about 0.23m³. The droplet size was measured by means of our chemical spot method taking advantage of the formation of AgCl precipitate from a NaCl solution droplet, and was found to be heterogeneous in the limits of 0.5 and 6μ in diameter, depending on the conditions of atomization.
The results obtained are as follows: (1) The relation between a droplet diameter (D_d) and its spot diameter (d_s) is expressed as D_d³=0.541d_s². (2) There is a close connection between the number of the droplets measured and the smoothness of the size distribution curve drawn; for a smooth curve to be found, it would be required to measure 500 droplets or more. (3) It is only necessary, in order to aquire a reliable number-averaged diameter for a comparatively homogeneous system having the relative standard deviation of 0.27, to measure 200 droplets or so, whereas it is needed to measure more than 500 droplets with definitely heterogeneous systems of the relative standard deviations larger than 0.46.

View full abstract