Analysis of holdups in continuous ball mills

A theoretical study is made on holdups of particulate material in continuous ball mills. The analysis is based on a consideration that holdups are influenced by the discharge properties at the mill exit, the existence of media balls interrupting the material to flow towards the mill exit and the dead space generated depending on the exit configuration. As a result, the linear relation between holdup and feed rate obtained experimentally is derived to be valid under specific discharge properties. Further, the effects of other operating variables such as ball filling, ball diameter, mill speed and slurry density on holdups are clarified based on physical backgrounds deduced from the theory. The derived equation to predict holdups includes three constants relating to the discharge properties of mill exit, the resistance of media balls against material flow and the dead space, respectively. These constants are estimated by the least square regression to give a best fit to data of various operating conditions within reasonable convergence between calculated holdups and experimental ones. Also, the effect of material kind on holdup is discussed using existing data.

Graphical abstractAn equation to predict mass holdup MH showing a linear relationship to feed rate F is derived and its validity is confirmed with data of various operating conditions and materials.Figure optionsDownload full-size imageDownload as PowerPoint slideHighlights► A theory to predict holdups in continuous ball mills is developed. ► A linearity between holdup and feed rate observed in data is proved theoretically. ► The calculated holdups are verified with data of various operating conditions. ► The effect of material kind on holdup is discussed with existing data.