In this paper, we suggested a simple modeling equation to predict the performance of a bead mill and verified it by carrying out milling experiments at various conditions. The comminution process in bead mills is determined by the number of collisions between the beads in the grinding chamber, kinet...
In this paper, we suggested a simple modeling equation to predict the performance of a bead mill and verified it by carrying out milling experiments at various conditions. The comminution process in bead mills is determined by the number of collisions between the beads in the grinding chamber, kinetic energy transfer during bead-to-bead collisions, mechanical strength of particles, and milling time. The number of collisions can be estimated by the collision cross section and the concentration of the beads; whereas the kinetic energy depends on the rotational speed of the rotor as well as the bead size. Considering these parameters, we introduced the concept of the “number of effective collisions” in the modeling equation. The number of effective collisions represents the number of collisions between the beads that cause the breakage of particles in the grinding chamber. In other words, fineness of particles increases with the number of effective collisions during the milling process. To validate the modeling, we comminuted a slurry of tubular halloysite particles with an average size of 6.68 μm as a starting material and investigated the effect of grinding parameters such as bead size (0.3, 0.1, 0.03 mm), rotational speed of the rotor (830~4975 rpm), and milling time (10~300min) on the particle size, which was measured with a laser diffraction size analyzer. According to the calculation using the modeling equation, 0.3 mm beads among the three sizes of the beads have the highest number of effective collisions in case of the rotor speed below 4,150 rpm. Over 4,150 rpm, however, 0.1 mm beads have higher number of effective collisions than 0.3 mm beads. Our experiments agreed well with the estimate from the modeling qualitatively. Below the rotor speed of 4,150 rpm, smaller particle size was obtained with 0.3 mm beads; on the other hand, at the rotor speed over 4,150 rpm, smaller particles were observed for 0.1 mm beads. As a result, halloysite nanoparticles of a narrow particle size distribution with an average size of 0.19 μm could be obtained by using 0.1 mm beads at 4,975 rpm of the rotor speed. Our results imply that higher number of effective collisions leads to higher grinding efficiency during the milling process. Consequently, this modeling equation succeeded in determining an optimal condition of bead milling for tubular halloysite particles. Furthermore, our modeling can be applied for predicting the milling performance with other micrometer range particles.
In this paper, we suggested a simple modeling equation to predict the performance of a bead mill and verified it by carrying out milling experiments at various conditions. The comminution process in bead mills is determined by the number of collisions between the beads in the grinding chamber, kinetic energy transfer during bead-to-bead collisions, mechanical strength of particles, and milling time. The number of collisions can be estimated by the collision cross section and the concentration of the beads; whereas the kinetic energy depends on the rotational speed of the rotor as well as the bead size. Considering these parameters, we introduced the concept of the “number of effective collisions” in the modeling equation. The number of effective collisions represents the number of collisions between the beads that cause the breakage of particles in the grinding chamber. In other words, fineness of particles increases with the number of effective collisions during the milling process. To validate the modeling, we comminuted a slurry of tubular halloysite particles with an average size of 6.68 μm as a starting material and investigated the effect of grinding parameters such as bead size (0.3, 0.1, 0.03 mm), rotational speed of the rotor (830~4975 rpm), and milling time (10~300min) on the particle size, which was measured with a laser diffraction size analyzer. According to the calculation using the modeling equation, 0.3 mm beads among the three sizes of the beads have the highest number of effective collisions in case of the rotor speed below 4,150 rpm. Over 4,150 rpm, however, 0.1 mm beads have higher number of effective collisions than 0.3 mm beads. Our experiments agreed well with the estimate from the modeling qualitatively. Below the rotor speed of 4,150 rpm, smaller particle size was obtained with 0.3 mm beads; on the other hand, at the rotor speed over 4,150 rpm, smaller particles were observed for 0.1 mm beads. As a result, halloysite nanoparticles of a narrow particle size distribution with an average size of 0.19 μm could be obtained by using 0.1 mm beads at 4,975 rpm of the rotor speed. Our results imply that higher number of effective collisions leads to higher grinding efficiency during the milling process. Consequently, this modeling equation succeeded in determining an optimal condition of bead milling for tubular halloysite particles. Furthermore, our modeling can be applied for predicting the milling performance with other micrometer range particles.
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