Modeling of a bead mill process for dispersion of coagulated nano particles

A bead mill was used to disperse AlN nanoparticles into coolant-oil to make thermally efficient nanofluids. This apparatus disperses particles by imparting direct impact to the agglomerates of nanoparticles using beads of certain size circulated by added centrifugal forces in the milling vessel. A mathematical model based on population balance was developed to determine optimum operating conditions of the bead mill process. A dimensional analysis for the process model led to two dimensionless groups ηc and ηb, whose ratio (ηc/ηb) represents the relative intensity of the coagulation and breakage phenomena taking place in the mill. Numerical simulations were performed to investigate the effect of process operation variables upon the particle size distribution, and three adjustable model parameters were selected and estimated through regression analysis based on a portion of the experimental data. The population balance model with the estimated parameters yielded prediction results that reasonably matched the rest of the experimental data obtained under different operating conditions, hence is expected to be used as a tool for finding optimal milling conditions.

Graphical abstractA population balance model was developed for a bead mill process that disperses AlN nano particles in a coolant oil. The validity of the model was examined in a two-stage (training and testing) verification procedure using the experimental average particle size evolution data.Figure optionsDownload full-size imageDownload as PowerPoint slideHighlights► A population balance model was developed for a bead mill process. ► Numerical algorithms and MATLAB implementation for the derived model. ► Two-stage (training and testing) model verification based on experimental data. ► Good matches between the calculated and observed particle size evolutions.