对于两组分颗粒系统,某组分 A 在整个颗粒群中的混合均匀程度是一个非常重要的物理量。采用异权值蒙特卡罗方法研究有限系统中凝并核与组分相关的两组分颗粒凝并混合程度问题。首先,验证了核函数齐次性指数 lambda 对系统凝并混合的影响,并得到了有限系统中分散指数与 lambda 的变化规律。其次,发现并总结了有限系统中考虑不同组分间吸引或排斥作用时颗粒凝并混合规律：临界时间之前系统在吸引排斥因素以及核函数的共同作用下发生颗粒凝并,且排斥作用的影响远远大于吸引作用的影响;临界时间之后系统在核函数的单独作用下进行颗粒凝并,排斥或吸引作用的影响可以忽略不计。最后,拟合得到了临界时间与吸引排斥指数 alpha 的幂函数关系,以及临界时间与齐次性指数 $\lambda$ 的指数函数关系。研究结果对药物混合工业过程的设计具有一定的理论指导意义。

The mixing state of a bicomponent population of granules is characterized by the total variance of component A, which measures the deviation of the composition of each granule from the overall mean. By means of the multi-weighted Monte Carlo method, first the fundamental influence of the homogeneity index lambda of the kernel is verified, and the scaling rate of segregation index, which is a function of homogeneity index lambda, is obtained. Second, two stages in the evolution of mixing are identified. Before the critical time, both interaction between components and the kernel take important effects on the coalescence. And the repulsive interaction is much stronger than the attractive interaction. After the critical time, only the kernel itself affects the coalescence and the effects of interaction between components are ignored. Finally, a power-law function between the critical time and alpha is obtained, whereas an exponential function relationship between the critical time and $\lambda$ is identified by a curve fitting technique. The results are of great importance in the pharmaceutical engineering.