摘要
This paper presents a simple but informative mathematical model to describe the mixing of three dissimilar components of particulate solids that have the tendency to segregate within one another. A nonlinear Markov chain model is proposed to describe the process. At each time step, the exchange of particulate solids between the cells of the chain is divided into two virtual stages. The first is pure stochastic mixing accompanied by downward segregation. Upon the completion of this stage, some of the cells appear to be overfilled with the mixture, while others appear to have a void space. The second stage is related to upward segregation. Components from the overfilled cells fill the upper cells （those with the void space） according to the proposed algorithm. The degree of non-homogeneity in the mixture （the standard deviation） is calculated at each time step, which allows the mixing kinetics to be described. The optimum mixing time is found to provide the maximum homogeneity in the ternary mixture. However, this “common” time differs from the optimum mixing times for individual components. The model is verified using a lab-scale vibration vessel, and a reasonable correlation between the calculated and experimental data is obtained
This paper presents a simple but informative mathematical model to describe the mixing of three dissimilar components of particulate solids that have the tendency to segregate within one another. A nonlinear Markov chain model is proposed to describe the process. At each time step, the exchange of particulate solids between the cells of the chain is divided into two virtual stages. The first is pure stochastic mixing accompanied by downward segregation. Upon the completion of this stage, some of the cells appear to be overfilled with the mixture, while others appear to have a void space. The second stage is related to upward segregation. Components from the overfilled cells fill the upper cells （those with the void space） according to the proposed algorithm. The degree of non-homogeneity in the mixture （the standard deviation） is calculated at each time step, which allows the mixing kinetics to be described. The optimum mixing time is found to provide the maximum homogeneity in the ternary mixture. However, this “common” time differs from the optimum mixing times for individual components. The model is verified using a lab-scale vibration vessel, and a reasonable correlation between the calculated and experimental data is obtained
