两组分颗粒系统中凝并混合程度问题的多重蒙特卡罗模拟

Monte Carlo simulation for mixing degree in two-component system

多组分颗粒凝并问题有重要应用背景,如制药过程中有效成分分散、雨滴形成和晶体结晶过程等,因而对其深入研究有重要理论和实际意义.采用多重蒙特卡罗方法研究两组分颗粒系统中布朗凝并问题,其中凝并核与组分有关.数值结果表明:两组分颗粒系统的矩统计量与单组分颗粒系统中的矩统计量有相同的渐近行为.当系统混合度达到稳定值并且分散指数以1/v下降时,系统趋于自保持状态.另外,还得到了不同初始条件下某组分总偏差的渐近稳定值与"凝并效率"参数的函数关系式.

Multi-component aggregation has important applications in areas such as dispersion of active ingredients in a pharmaceutical process,formation of raindroplets,and crystallization.In this paper,a population balance equation with composition dependent kernel is numerically simulated using multiple Monte Carlo methods.The results show that the moments of a two-component system have a scaling behavior similar to a single component system regardless of the kernel type.While the degree of mixing reaches a constant value and the segregation index decreases by 1/v,the system approaches a self-preserving state.A fitted function of the stable value of the power density of excess component A on collision efficiency is derived.