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
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摘要
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.
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.
引文
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[22]Haibo Z,Chuguang Z,Minghou X.Multi-Monte Carlo approach for general dynamic equation considering simultaneous particle coagulation and breakage[J].Powder Technology,2005,154(2):164-178.
[23]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.
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[27]Yu M,Zhang X,Jin G,et al.A new analytical solution for solving the population balance equation in the continuum-slip regime[J].Journal of Aerosol Science,2015,80:1-10.
[28]Xie M L,Wang L P.Asymptotic solution of population balance equation based on TEMOMmodel[J].Chemical Engineering Science,2013,94:79-83.
[2]Kuang C,Mc Murry P H,Mc Cormick A V.Determination of cloud condensation nuclei production from measured new particle formation events[J].Geophysical Research Letters,2009.DOI:10.1029/2009GL037584.
[3]Senior C L,Zeng T,Che J,et al.Distribution of trace elements in selected pulverized coals as a function of particle size and density[J].Fuel Processing Technology,2000,63(2):215-241.
[4]Riemer N,West M,Zaveri R A,et al.Simulating the evolution of soot mixing state with a particle-resolved aerosol model[J].Journal of Geophysical Research:Atmospheres,2009,114:D09202.
[5]Liu Y,Jiang Y,Zhang X,et al.Structural and magnetic properties of the ordered FePt3,FePt and Fe3Pt nanoparticles[J].Journal of Solid State Chemistry,2014,209:69-73.
[6]Singh J,Patterson R I A,Kraft M,et al.Numerical simulation and sensitivity analysis of detailed soot particle size distribution in laminar premixed ethylene flames[J].Combustion and Flame,2006,145(1):117-127.
[7]Rajniak P,Mancinelli C,Chern R T,et al.Experimental study of wet granulation in fluidized bed:impact of the binder properties on the granule morphology[J].International Journal of Pharmaceutics,2007,334(1):92-102.
[8]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.
[9]Puel F,F′evotte G,Klein J P.Simulation and analysis of industrial crystallization processes through multidimensional population balance equations.Part 1:a resolution algorithm based on the method of classes[J].Chemical Engineering Science,2003,58(16):3715-3727.
[10]Krapivsky P L,Ben-Naim E.Aggregation with multiple conservation laws[J].Physical Review E,1996,53(1):291-298.
[11]Lushnikov A A.Evolution of coagulating systems:Ⅲ.Coagulating mixtures[J].Journal of Colloid and Interface Science,1976,54(1):94-101.
[12]Gelbard F M,Seinfeld J H.Coagulation and growth of a multicomponent aerosol[J].Journal of Colloid and Interface Science,1978,63(3):472-479.
[13]Vigil R D,Ziff R M.On the scaling theory of two-component aggregation[J].Chemical Engineering Science,1998,53(9):1725-1729.
[14]Fern′andez-D′?az J M,G′omez-Garc′?a G J.Exact solution of Smoluchowski’s continuous multi-component equation with an additive kernel[J].EPL(Europhysics Letters),2007,78(5):56002.
[15]Fern′andez-D′?az J M,G′omez-Garc′?a G J.Exact solution of a coagulation equation with a product kernel in the multicomponent case[J].Physica D:Nonlinear Phenomena,2010,239(5):279-290.
[16]Piskunov V N.Analytical solutions for coagulation and condensation kinetics of composite particles[J].Physica D:Nonlinear Phenomena,2013,249:38-45.
[17]Yu M,Lin J,Chan T.A new moment method for solving the coagulation equation for particles in Brownian motion[J].Aerosol Science and Technology,2008,42(9):705-713.
[18]Matsoukas T,Lee K,Kim T.Mixing of components in two-component aggregation[J].AIChEJournal,2006,52(9):3088-3099.
[19]Lee K,Kim T,Rajniak P,et al.Compositional distributions in multicomponent aggregation[J].Chemical Engineering Science,2008,63(5):1293-1303.
[20]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.
[21]Zhao H B,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.
[22]Haibo Z,Chuguang Z,Minghou X.Multi-Monte Carlo approach for general dynamic equation considering simultaneous particle coagulation and breakage[J].Powder Technology,2005,154(2):164-178.
[23]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.
[24]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.
[25]Mller H.Zur allgemeinen theorie ser raschen koagulation[J].Fortschrittsberichte ber Kolloide und Polymere,1928,27(6):223-250.
[26]Wright D L,McGraw R,Rosner D E.Bivariate extension of the quadrature method of moments for modeling simultaneous coagulation and sintering of particle populations[J].Journal of Colloid and Interface Science,2001,236(2):242-251.
[27]Yu M,Zhang X,Jin G,et al.A new analytical solution for solving the population balance equation in the continuum-slip regime[J].Journal of Aerosol Science,2015,80:1-10.
[28]Xie M L,Wang L P.Asymptotic solution of population balance equation based on TEMOMmodel[J].Chemical Engineering Science,2013,94:79-83.
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