多组分颗粒凝并是颗粒长大过程的主要物理机制之一。对于双组分凝并，混合程度χ为一重要衡量标准，是预测组分分布的关键参数。针对双组分颗粒团聚的非稳态过程研究混合程度随时间的变化关系，采用颗粒群平衡模拟异权值快速Monte Carlo方法，进行模拟，最终预测出χ与初始条件的关系，得到自由分子区布朗凝并与连续区布朗凝并的指数形式预测公式，并进行验证，从而可以通过合理选择初始参数，优化控制组分分布和实现颗粒定向功能制备。
Multi-component particle aggregation is one of the main physical mechanisms in the process of particle growth. For two-component aggregation, the compositional mixing degree χ is an important criterion and the key to determination of compositional distribution. Now the dynamic evolution of χ before the attainment of a steady-state value is beyond numerical modeling and theoretical research. In this work, the fast differentially-weighted Monte Carlo method for population balance modeling was used to predict the dependence of time-varied χ on initial feeding conditions through hundreds of systematically varied simulations. It is found that χ is subject to exponential decay in the free molecular regime and the continuum regime. By using the explored exponential formulas for the dynamic mixing degree, it is possible to achieve an optimum control over the compositional distributions during two-component aggregation processes through selecting the initial feeding parameters.
[1] Friedlander S K. Smoke, dust, and haze:fundamentals of aerosol dynamics[M].New York:Oxford University Press, 2000.
[2] Hofmann S, Raisch J. Solutions to inversion problems in preferential crystallization of enantiomers. Part Ⅱ:Batch crystallization in two coupled vessels[J]. Chemical Engineering Science, 2013, 88:48-68.
[3] Hosseini A, Bouaswaig A E, Engell S. Novel approaches to improve the particle size distribution prediction of a classical emulsion polymerization model[J]. Chemical Engineering Science, 2013, 88:108-120.
[4] Riemer N, West M, Zaveri R, et al. Estimating black carbon aging time-scales with a particle-resolved aerosol model[J]. Journal of Aerosol Science, 2010, 41(1):143-158.
[5] Fox R O. Higher-order quadrature-based moment methods for kinetic equations[J]. Journal of Computational Physics, 2009, 228(20):7771-7791.
[6] Barrasso D, Ramachandran R. A comparison of model order reduction techniques for a four-dimensional population balance model describing multi-component wet granulation processes[J]. Chemical Engineering Science, 2012, 80:380-392.
[7] Chauhan S S, Chakraborty J, Kumar S. On the solution and applicability of bivariate population balance equations for mixing in particle phase[J]. Chemical Engineering Science, 2010, 65(13):3914-3927.
[8] Lushnikov A. Evolution of coagulating systems:Ⅲ. Coagulating mixtures[J]. Journal of Colloid and Interface Science, 1976, 54(1):94-101.
[9] Matsoukas T, Kim T, Lee K. Bicomponent aggregation with composition-dependent rates and the approach to well-mixed state[J]. Chemical Engineering Science, 2009, 64(4):787-799.
[10] Matsoukas T, Lee K, Kim T. Mixing of components in two-component aggregation[J]. AIChE journal, 2006, 52(9):3088-3099.
[11] Lee K, Kim T, Rajniak P, et al. Compositional distributions in multicomponent aggregation[J]. Chemical Engineering Science, 2008, 63(5):1293-1303.
[12] Zhao H, Kruis F E, Zheng C. Monte Carlo simulation for aggregative mixing of nanoparticles in two-component systems[J]. Industrial & engineering chemistry research, 2011, 50(18):10652-10664.
[13] Marshall C L, Rajniak P, Matsoukas T. Numerical simulations of two-component granulation:comparison of three methods[J]. Chemical Engineering Research and Design, 2011, 89(5):545-552.
[14] Zhao H, Kruis F E. Dependence of steady-state compositional mixing degree on feeding conditions in two-component aggregation[J]. Industrial & Engineering Chemistry Research, 2014, 53(14):6047-6055.
[15] Zhao H, Kruis F E, Zheng C. A differentially weighted Monte Carlo method for two-component coagulation[J]. Journal of Computational Physics, 2010, 229(19):6931-6945.
[16] Zhao H, Kruis F E, Zheng C. Reducing statistical noise and extending the size spectrum by applying weighted simulation particles in Monte Carlo simulation of coagulation[J]. Aerosol Science and Technology, 2009, 43(8):781-793.
[17] Zhao H, Zheng C. A new event-driven constant-volume method for solution of the time evolution of particle size distribution[J]. Journal of Computational Physics, 2009, 228(5):1412-1428.
[18] Zhao H, Zheng C. Two-component Brownian coagulation:Monte Carlo simulation and process characterization[J]. Particuology, 2011, 9(4):414-423.
[19] Zhao H, Zheng C. A population balance-Monte Carlo method for particle coagulation in spatially inhomogeneous systems[J]. Computers & Fluids, 2013, 71:196-207.
[20] Hao X, Zhao H, Xu Z, et al. Population balance-Monte Carlo simulation for gas-to-particle synthesis of nanoparticles[J]. Aerosol science and technology, 2013, 47(10):1125-1133.
[21] Xu Z, Zhao H, Zheng C. Fast Monte Carlo simulation for particle coagulation in population balance[J]. Journal of Aerosol Science, 2014, 74:11-25.
