THEORETICAL SEARCH FOR OPTIMUM HOLD-UP IN A BATCH MIXER OF PARTICULATE SOLIDS

The objective of the study is to investigate how the hold-up of particulate solids to be mixed in a batch mixer influences the mixture quality and mixer capacity. It is known that a small amount of components (i.e., a small hold-up) allows reaching better quality of a mixer but leads to small capacity of a mixer. It is particularly appreciably when it is necessary to mix the components, which have a strong tendency to segregate into each other. In this case the perfect mixture cannot be reached, and there exists the optimum mixing time, at which the mixture homogeneity reaches maximum. This optimum time increases with the hold-up increase. Thus, from the mixing as such viewpoint, it is better to mix components not in big portions one time but in small portions several times. However, the total time of a mixing process consists of the loading time, mixing time and discharge time. The loading time depends on many factors such as a dosage device design, feeders design, and others, while the discharge time is usually much smaller. Thus, the mixer capacity is determined not only by the mixing time but also by the loading time at least. In order to estimate the mixer capacity at a required mixture quality, a cell model based on the theory of Markov chains is used. It is shown that the optimum hold-up exists that provides the maximum mixer capacity, and this optimum hold-up strongly depends on the loading time.