基于Matlab平台的絮凝体分形仿真模拟
摘要
在水处理絮凝过程中,水中细小粒子相互碰撞、凝聚、破碎以及再凝聚过程是一个随机的过程,形成的絮凝体具有分形构造特征。研究絮凝体的成长过程以及内部构造,对提高水处理固液分离效果具有重要意义。
论文借助Matlab工具,考虑了具有一定粒径分布的初始颗粒的絮凝体聚集情况,对絮凝体颗粒初始粒径呈正态分布、对数正态分布以及卡方分布的二维有限扩散凝聚(DLA)模型进行了研究,并分析计算了分形维数以及孔隙率。
研究表明二维空间中的DLA模拟中,在初始粒子粒径为均一分布的情况下,模拟所得到的絮凝体具有典型的分形构造特征,分形维数随模拟絮凝体尺寸的增加其分形维数有减小的趋势,而其密度随尺寸的增加而呈幂指数减小规律,孔隙率则是呈幂指数增大规律。相比较而言,具有一定粒径分布的初始颗粒之间的聚集体,其分形维数随着粒子数目的增多也逐渐变小,与均一分布颗粒见凝聚的分形维数计算数值并无很大差异。在孔隙率分析方面,对数正态分布的孔隙率比较接近实际情况的,在0.3～0.5之间。
在模拟过程中,考虑了Matlab工具使用过程出现伪随机数的情况。论文在程序中考虑了因伪随机数的产生而造成的模拟结果偏离情况,改进了以往程序的相关缺陷,提高了模拟结果的精度。
Solid/liquid separation is of crucial importance in the water treatment process.As a traditional separation method,flocculation/coagulation followed by sedimentation prevails nowadays.To improve the separation efficiency,it is necessary to study the floc structure.In this paper,fractal simulation is used to investigate the floc structure and its characteristic parameters.Computer simulation is an effective method to study the floc structure.
With the popular software Matlab 7.1 as the development platform,the simulation has been carried out based on DLA floc growing model,when the initial diameter of floc partical presents as a normal distribution,then analyzed the fractal dimensionality and porosity.
In this paper,two-dimensional DLA model is studied on the morphological structure,the fractal dimensionality,and the porosity of the resulting flocs.Further more,the changes of the fractal dimensionality,porosity with respect to the floc characteristic length are studied.And two-dimensional image has been compared by their fractal dimensionality.Comparing to it,when the initial particle diameter presents as other distributions,the fractal dimensionality of floc diminishes obviously as the number of particles increases.It has not too much different with the initial particle diameter presents as a equal distribution.As the porosity,the value of logarithmic normal distribution is nearest the natural situation,and the value is between 0.3 to 0.5.
When we simulate,we think of the influence of the pseudo-random number. Because of the pseudo-random number,the particle diameters are not stochastic,but orderliness.And then we innovate the program,improve the precision of outcome..
论文借助Matlab工具,考虑了具有一定粒径分布的初始颗粒的絮凝体聚集情况,对絮凝体颗粒初始粒径呈正态分布、对数正态分布以及卡方分布的二维有限扩散凝聚(DLA)模型进行了研究,并分析计算了分形维数以及孔隙率。
研究表明二维空间中的DLA模拟中,在初始粒子粒径为均一分布的情况下,模拟所得到的絮凝体具有典型的分形构造特征,分形维数随模拟絮凝体尺寸的增加其分形维数有减小的趋势,而其密度随尺寸的增加而呈幂指数减小规律,孔隙率则是呈幂指数增大规律。相比较而言,具有一定粒径分布的初始颗粒之间的聚集体,其分形维数随着粒子数目的增多也逐渐变小,与均一分布颗粒见凝聚的分形维数计算数值并无很大差异。在孔隙率分析方面,对数正态分布的孔隙率比较接近实际情况的,在0.3～0.5之间。
在模拟过程中,考虑了Matlab工具使用过程出现伪随机数的情况。论文在程序中考虑了因伪随机数的产生而造成的模拟结果偏离情况,改进了以往程序的相关缺陷,提高了模拟结果的精度。
Solid/liquid separation is of crucial importance in the water treatment process.As a traditional separation method,flocculation/coagulation followed by sedimentation prevails nowadays.To improve the separation efficiency,it is necessary to study the floc structure.In this paper,fractal simulation is used to investigate the floc structure and its characteristic parameters.Computer simulation is an effective method to study the floc structure.
With the popular software Matlab 7.1 as the development platform,the simulation has been carried out based on DLA floc growing model,when the initial diameter of floc partical presents as a normal distribution,then analyzed the fractal dimensionality and porosity.
In this paper,two-dimensional DLA model is studied on the morphological structure,the fractal dimensionality,and the porosity of the resulting flocs.Further more,the changes of the fractal dimensionality,porosity with respect to the floc characteristic length are studied.And two-dimensional image has been compared by their fractal dimensionality.Comparing to it,when the initial particle diameter presents as other distributions,the fractal dimensionality of floc diminishes obviously as the number of particles increases.It has not too much different with the initial particle diameter presents as a equal distribution.As the porosity,the value of logarithmic normal distribution is nearest the natural situation,and the value is between 0.3 to 0.5.
When we simulate,we think of the influence of the pseudo-random number. Because of the pseudo-random number,the particle diameters are not stochastic,but orderliness.And then we innovate the program,improve the precision of outcome..
引文
[1]Goodarz N I.Floc simulation:Prolate spheroidal particles[J].J Colloid Interface Sci,1979,70(2):306-319.
[2]Mandelbrot B B.分形--自然界的几何学[M].李后强译.成都:四川大学出版社,1993.
[3]Lorenz E M.混沌的本质[M].刘式达译.北京:气象出版社,1997.
[4]Mandelbrot B B.分形对象--形、机遇和维数[M].文志英,苏 红译.北京:世界图书出版公司,1999.
[5]张济忠.分形[M].北京:清华大学出版社,1995.
[6]Da□Hong Li,and J.Ganszarczyk.Fractal Geometry of Particle Aggregates Generated in Water and Wastewater Treatment Processes.Environ.Sci.Technol.1989,23(11):1385-1389.
[7]王晓昌,丹保宪仁.絮凝体形态学和密度的探讨--1.从絮凝体分形构造谈起[J].环境科学学报,2000,20(3):257-262.
[8]王东升,汤鸿霄。分形理论在混凝研究中的应用与展望[J].工业水处理,2001,21(7):16-19.
[9]Vold M J.Computer simulation of floc formation in a colloidal suspension[J].J Colloid Interface Sci,1963,18:684-695.
[10]Sutherland D N.A theoretical model of floc structure[J].J Colloid Interface Sci,1967,25:373 - 380.
[11]T A Witten,L M Sander.Diffusion-Limited Aggregation,a Kinetic Critical PhenoMenon[J].Phys.Rev.Lett.,1981,47:1400-1403
[12]Francois R J,Van H A A.Structure of hydroxide flocs[J].Wat Res,1985,19(10):1249-1254.
[13]Firth B A,Hunter R J.Flow properties of coagulated colloidal suspensions[J].J Colloid Interface Sci,1976,57(2):248-265.
[14]Higashitani K,Kubota T.Pelleting flocculation of colloidal latex particles[J].Powder Tech,1987,51:61 - 69.
[15]Tambo N,Wang X C.The mechanism of pellet flocculation in a fluidized - bed operation[J].J Wat SRT - Aqua,1993,42(2):67 - 76.
[16]Tambo N,Wang X C.Control of coagulation condition for treatment of highturbidity water by fluidized pellet - bed operation[J]J War SRTAqua,1993,42(4):212-222.
[17]Tambo N,Wang X C.Application of fluidized pellet - bed technique in the treatment of highly colored and turbid water[J].J Wat SRT -Aqua,1993,42(5):301-309.
[18]Thomas D N,J udd S J,Fawceet N.Flocculation modeling:A review[J].Wat Res,1999,33(7):1579-1592.
[19]Ernest A N et al.Determination of particle collision efficiencies for flocculent transport models[J].J.Environmental Engineering,1995,121(4):320-329
[20]Meakin P.Fractal aggregates[J].Advances in Colloid Interface Science,1988,28:249-331.
[21]Li Dh,Ganczarczyk J.Fractal geometry of particle aggregates generated in waste and wastewater treatment processes.Environ Science & Technology,1989,23:1385-1389.
[22]Logan B E,Wilkinson DB.Fractal dimensions and porosities of Zoogloea ramigera and Saccharomyces cerevisae aggregates.Biotechnol Bioengin 1991,38(4):389-396.
[23]Kim J W and Kramer T A..Improved models for fractal colloidal agglomeration:computationally efficient algorithms.Colloids and Surfaces A:Physicochem.Eng.Aspects,2005,253:330-349.
[24]Li X & Logan B E.Collision frequencies between fractal aggregates and small particles in a turbulently sheared fluid[J].Environmental Science & Technology,1997,31(4):1237-1242.
[25]Lee DG,Bonner JS,Garton LS et al.Modeling coagulation kinetics incorporating fractal theories:a fractal rectilinear model[J].Water Research,2000,34(7):1987-2000.
[26]Lee D G,Bonner J S,Garton L S et al.Modeling Coagulation kinetics incorporating fractal theories:comparison with observed data[J].Water Research,2002,36(4):1056-1066.
[27]Lattuada M,Wu H,and Morbidelli M.A simple model for the structure of fractal aggregates[J].Journal of Colloid and Interface Science,2003,268:106-120.
[28]赵海波,郑楚光,徐明厚.求解考虑颗粒凝聚的通用动力学方程的多重MonteCarlo算法[J].应用数学和力学.2005,7(26):875-882.
[29]Wu R M,Lee D.J.,Waite T.D.et al.Multilevel structure of sludge flocs[J].J.Colloid and Interface Science,2002,252:383-392.
[30]Wang X C,Jin P K and Gregory J.Structure of Al-humic flocs and their removal at slightly acidic and neutral pH.Water Science & Technology:Water Supply,2002,2(2):99-106.
[31]T.A.Witten,L.M.Sander,Phys.Rev.Lett.47(1981)1400.
[32]黄昀.百科知识,1992,6-54
[33]Meakin P.远离平衡态的分形动力学,1987
[34]P Meakin.A historical introduction to computer models for fractal aggregates[J].J Sol-Gel Sci Tech,1999,15:97-117
[35]Meakin P.Fractal aggregates.Advances in Colloid and interface science,1988,28:249-331
[36]刘华杰,分形的艺术,1997
[37]H.Choi,G.Gervais,K.Yawata,T.M.Haard,Superfluid He in Aerogel.National Science Foundation DMR-0244099
[38]A.S.Kim,K.D.Stolzenbach,J.Colloid Interface Sci.253(2002)315.
[39]Rafael Salazar,Lev D.Gelb,Molecular Phyics,10-20 May 2004,Vol.102,Nos.9-10,1015-1030.
[40]蒋新,Matlab平台上的DLCA过程模拟,计算机仿真,2003.
[41]M.Kolb,R.Botet,R.Jullien,Phys.Rev.Lett.51(1983)1123.
[42]R.Jullien and R.botet,Aggregation and Fractal Aggregates,World Scientific,1987.
[43]Remi Jullien and Anwar Hasmy,Fluctuating Bond Aggregation:a Model for Chemical Gel Formation,2004.
[44]S.Kiez Orrite,S.Stoll and P.Schurtenberger.Study of the Structure of Fractal Aggregates:Off-lattice Monte Carlo Simulation,2001.
[45]S.Kim,Dynamics of Particle Accumulation at Engineered and Natural Interfaces,Ph.D.thesis,University of Califonia,Los Angeles,2000
[46]P.C.Hiemenz,Principles of Colloid and Surface Chemistry,Dekker,New York,1986.
[47]F.Family and D.P.Landau,Kinetics of Aggregation and Gelation,North-Holland,1984.
[48]M Kostoglou and A G Konstandopolulos.Evolution of aggregate size and fractal dimension during Brownian coagulation[J].J Aerosol Sci,2001,32:1399-1460
[49]A Rzepiela,J H Opheusden and T Vliet.Brownian Dynamics simula-tion of aggregation kinetics of hard spheres with flexible bonds[j].J Colloid Interface Sci,2001,244:43-50.
[50]A M Brasil,T L Farias and M G Carvalho.Numerical characterization of the morphology of aggregated particles[J].Aerosol Sci,2001.
[51]Jiang Q,Logan B E.Fractal dimensions of aggregates determined from steadystate size distributions[J].Environ Sci Tech,1991,25:2031-2038.
[52]Clifford P J,Li X Y,Logan B E.Settling velocities of fractal aggregates[J].Environ Sci Tech,1996,30:1911-1981.
[53]Matlab7.0从入门到精通.人民邮电出版社.2006.
[2]Mandelbrot B B.分形--自然界的几何学[M].李后强译.成都:四川大学出版社,1993.
[3]Lorenz E M.混沌的本质[M].刘式达译.北京:气象出版社,1997.
[4]Mandelbrot B B.分形对象--形、机遇和维数[M].文志英,苏 红译.北京:世界图书出版公司,1999.
[5]张济忠.分形[M].北京:清华大学出版社,1995.
[6]Da□Hong Li,and J.Ganszarczyk.Fractal Geometry of Particle Aggregates Generated in Water and Wastewater Treatment Processes.Environ.Sci.Technol.1989,23(11):1385-1389.
[7]王晓昌,丹保宪仁.絮凝体形态学和密度的探讨--1.从絮凝体分形构造谈起[J].环境科学学报,2000,20(3):257-262.
[8]王东升,汤鸿霄。分形理论在混凝研究中的应用与展望[J].工业水处理,2001,21(7):16-19.
[9]Vold M J.Computer simulation of floc formation in a colloidal suspension[J].J Colloid Interface Sci,1963,18:684-695.
[10]Sutherland D N.A theoretical model of floc structure[J].J Colloid Interface Sci,1967,25:373 - 380.
[11]T A Witten,L M Sander.Diffusion-Limited Aggregation,a Kinetic Critical PhenoMenon[J].Phys.Rev.Lett.,1981,47:1400-1403
[12]Francois R J,Van H A A.Structure of hydroxide flocs[J].Wat Res,1985,19(10):1249-1254.
[13]Firth B A,Hunter R J.Flow properties of coagulated colloidal suspensions[J].J Colloid Interface Sci,1976,57(2):248-265.
[14]Higashitani K,Kubota T.Pelleting flocculation of colloidal latex particles[J].Powder Tech,1987,51:61 - 69.
[15]Tambo N,Wang X C.The mechanism of pellet flocculation in a fluidized - bed operation[J].J Wat SRT - Aqua,1993,42(2):67 - 76.
[16]Tambo N,Wang X C.Control of coagulation condition for treatment of highturbidity water by fluidized pellet - bed operation[J]J War SRTAqua,1993,42(4):212-222.
[17]Tambo N,Wang X C.Application of fluidized pellet - bed technique in the treatment of highly colored and turbid water[J].J Wat SRT -Aqua,1993,42(5):301-309.
[18]Thomas D N,J udd S J,Fawceet N.Flocculation modeling:A review[J].Wat Res,1999,33(7):1579-1592.
[19]Ernest A N et al.Determination of particle collision efficiencies for flocculent transport models[J].J.Environmental Engineering,1995,121(4):320-329
[20]Meakin P.Fractal aggregates[J].Advances in Colloid Interface Science,1988,28:249-331.
[21]Li Dh,Ganczarczyk J.Fractal geometry of particle aggregates generated in waste and wastewater treatment processes.Environ Science & Technology,1989,23:1385-1389.
[22]Logan B E,Wilkinson DB.Fractal dimensions and porosities of Zoogloea ramigera and Saccharomyces cerevisae aggregates.Biotechnol Bioengin 1991,38(4):389-396.
[23]Kim J W and Kramer T A..Improved models for fractal colloidal agglomeration:computationally efficient algorithms.Colloids and Surfaces A:Physicochem.Eng.Aspects,2005,253:330-349.
[24]Li X & Logan B E.Collision frequencies between fractal aggregates and small particles in a turbulently sheared fluid[J].Environmental Science & Technology,1997,31(4):1237-1242.
[25]Lee DG,Bonner JS,Garton LS et al.Modeling coagulation kinetics incorporating fractal theories:a fractal rectilinear model[J].Water Research,2000,34(7):1987-2000.
[26]Lee D G,Bonner J S,Garton L S et al.Modeling Coagulation kinetics incorporating fractal theories:comparison with observed data[J].Water Research,2002,36(4):1056-1066.
[27]Lattuada M,Wu H,and Morbidelli M.A simple model for the structure of fractal aggregates[J].Journal of Colloid and Interface Science,2003,268:106-120.
[28]赵海波,郑楚光,徐明厚.求解考虑颗粒凝聚的通用动力学方程的多重MonteCarlo算法[J].应用数学和力学.2005,7(26):875-882.
[29]Wu R M,Lee D.J.,Waite T.D.et al.Multilevel structure of sludge flocs[J].J.Colloid and Interface Science,2002,252:383-392.
[30]Wang X C,Jin P K and Gregory J.Structure of Al-humic flocs and their removal at slightly acidic and neutral pH.Water Science & Technology:Water Supply,2002,2(2):99-106.
[31]T.A.Witten,L.M.Sander,Phys.Rev.Lett.47(1981)1400.
[32]黄昀.百科知识,1992,6-54
[33]Meakin P.远离平衡态的分形动力学,1987
[34]P Meakin.A historical introduction to computer models for fractal aggregates[J].J Sol-Gel Sci Tech,1999,15:97-117
[35]Meakin P.Fractal aggregates.Advances in Colloid and interface science,1988,28:249-331
[36]刘华杰,分形的艺术,1997
[37]H.Choi,G.Gervais,K.Yawata,T.M.Haard,Superfluid He in Aerogel.National Science Foundation DMR-0244099
[38]A.S.Kim,K.D.Stolzenbach,J.Colloid Interface Sci.253(2002)315.
[39]Rafael Salazar,Lev D.Gelb,Molecular Phyics,10-20 May 2004,Vol.102,Nos.9-10,1015-1030.
[40]蒋新,Matlab平台上的DLCA过程模拟,计算机仿真,2003.
[41]M.Kolb,R.Botet,R.Jullien,Phys.Rev.Lett.51(1983)1123.
[42]R.Jullien and R.botet,Aggregation and Fractal Aggregates,World Scientific,1987.
[43]Remi Jullien and Anwar Hasmy,Fluctuating Bond Aggregation:a Model for Chemical Gel Formation,2004.
[44]S.Kiez Orrite,S.Stoll and P.Schurtenberger.Study of the Structure of Fractal Aggregates:Off-lattice Monte Carlo Simulation,2001.
[45]S.Kim,Dynamics of Particle Accumulation at Engineered and Natural Interfaces,Ph.D.thesis,University of Califonia,Los Angeles,2000
[46]P.C.Hiemenz,Principles of Colloid and Surface Chemistry,Dekker,New York,1986.
[47]F.Family and D.P.Landau,Kinetics of Aggregation and Gelation,North-Holland,1984.
[48]M Kostoglou and A G Konstandopolulos.Evolution of aggregate size and fractal dimension during Brownian coagulation[J].J Aerosol Sci,2001,32:1399-1460
[49]A Rzepiela,J H Opheusden and T Vliet.Brownian Dynamics simula-tion of aggregation kinetics of hard spheres with flexible bonds[j].J Colloid Interface Sci,2001,244:43-50.
[50]A M Brasil,T L Farias and M G Carvalho.Numerical characterization of the morphology of aggregated particles[J].Aerosol Sci,2001.
[51]Jiang Q,Logan B E.Fractal dimensions of aggregates determined from steadystate size distributions[J].Environ Sci Tech,1991,25:2031-2038.
[52]Clifford P J,Li X Y,Logan B E.Settling velocities of fractal aggregates[J].Environ Sci Tech,1996,30:1911-1981.
[53]Matlab7.0从入门到精通.人民邮电出版社.2006.