Prediction of average shape values of quartz particles by vibrating disc and ball milling using dynamic image analysis based on established time-dependent shape models

Abstract

Although grinding kinetics has been the subject of many researches, there is no research examining the shape kinetics of particles ground by different mills using dynamic image analysis (DIA) in the literature. In this investigation, how the shapes of quartz particles change over time at two different size fractions in two different mills is modeled using the latest image analysis technique, since particle shape of mineral is important in flotation and hydraulic fracturing processes. Empirical time-dependent shape models based on the correlation between average circularity (C_av.) and bounding rectangle aspect ratio (BRAR_av.) parameters and grinding time for vibratory disc mill and ball milled particles are established with high R² values by different fitting. Furthermore, average shape values of particles ground by the mills depending on grinding time were predicted for two size fractions. It was found that, C_av. data can be better described by linear fitting equations, on the other hand BRAR_av. data can be better represented by power fitting equations. Since predicted and measured shape values were found close to each other, this approach provides useful information for estimating the milling time required to produce the particles by milling (with less energy and cost) appropriately for intended use.

Keywords:

• Quartz
• shape
• dynamic image analysis
• circularity
• vibratory disc mill
• ball mill

Acknowledgement

The authors thank to Professor Zhiyong Gao, who is a professional editor at Physicochemical Problems of Mineral Processing, for checking of the revised manuscript regarding English language and grammar.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Nomenclature
A	=	the area of the particle image
BRAR	=	bounding rectangular aspect ratio
BRARav.	=	average value of bounding rectangular aspect ratio
C	=	circularity
Cav.	=	average value of circularity
DBC	=	bounding circle diameter
DIA	=	dynamic image analysis
sd	=	shape distribution