泡沫金属发泡过程的泡沫演化动力学研究
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摘要
闭孔泡沫金属是一种内部结构含有大量孔隙的新型功能材料,以其独特的结构和优异的物理性能、机械性能、声学性能和热性能,以及可回收利用性等,成为一种极具开发前途的工程材料。在众多制备泡沫金属的方法中,吹气发泡法因为设备简单、成本低、可以连续生产等特点,更适用于规模化生产。生产过程中,如何控制气泡的尺寸大小及与分布、以及其拓扑结构是该项工艺的核心问题。从发泡到凝固成型,从湿泡沫到干泡沫再到泡沫金属成品过程中,影响泡沫尺寸及其分布的因素众多,单纯通过传统的以小规模实验为主的经验方法,不仅工作量大,周期长,成本高,而且很难全面了解各种参数的影响,更无法掌握其机理与规律。本文以相关实验研究为依据,采用数值模拟方法对金属泡沫从液态到固态的演化过程动力学行为进行系统分析,从深层次上揭示液态金属演化过程的动力学机制,为吹气法制备泡沫金属提供准确而可靠的科学依据和理论预测模型。主要研究内容和成果包括以下几个方面:
对泡沫析液现象从二个方面进行了研究。一是宏观方面,即研究泡沫群的整体行为;二是微观方面,即对单条Plateau边界、节点、液膜等的研究。宏观方面,初步尝试了泡沫金属析液过程的二维数值计算,计算结果与实验结果进行了定性比较,研究了在不同工况参数下金属泡沫铝的孔隙率的变化规律。结果表明:泡沫最终的孔隙率受到泡沫初始孔隙率、泡沫层的高度、泡沫的直径、重力加速度和熔体粘度等因素的影响。其中泡沫的孔径对最终的孔隙率有较大的影响,而粘度对最终的孔隙率影响较小,只是对析液速率有较大的影响。微观方面,研究了单条Plateau边界及节点处的析液现象。对单条泡沫体Plateau边界内部的速度场的研究表明:泡沫体内部Plateau边界内的速度要小于同等条件下的容器壁面处Plateau边界内的速度,间接解释了宏观析液过程中析液速率与不同容器条件的关系。分析了Plateau边界中界面流变特性对析液过程的影响,进而将单条Plateau边界内液体流动的分析结果应用于泡沫体析液过程的宏观研究,建立了一个析液模型,计算结果与实验结果的比较显示:在泡沫层上部、中部吻合较好,在底部存在一定误差。
建立了描述了吹气法制备泡沫铝过程中泡沫孔隙率随空间的变化的数学模型。计算结果表明,在不考虑气泡的合并的情况下,熔液粘度、表面张力、重力加速度、气体的流量对泡沫孔隙率,即Plateau边界的横截面积,有显著的影响。重力加速度和表面张力在析液过程中起着关键的作用。通过理论建模和数值计算预测了发泡层高度随时间,气体流速等的关系,模型能较好的解释泡沫层高度的变化。利用相场(Phase field)方法对界面演化过程进行了数值模拟,较为直观合理的解释了液膜破裂现象。
通过析液方程和由于气体扩散造成的气泡长大的方程的耦合,建立了铝合金熔体泡沫中气泡尺寸分布发展的数学模型。通过数值计算,得出了不同工况下泡沫尺寸分布的发展过程,讨论了表面张力、亨利常数、扩散率等因素对泡沫尺寸分布发展的影响。计算结果表明:表面张力越大、亨利常数越大,泡沫尺寸演化过程越剧烈;含液率较小的泡沫体析液量很小,所以,泡沫尺寸分布变化主要由气体扩散引起。
利用Surface Evolver软件及MacPherson等人的最新理论成果,对金属泡沫多面体气泡的演化过程中的泡沫尺寸和拓扑结构进行了数值计算研究,数值模拟结果与试验研究结果进行了定性的比较,一些特征非常相似。利用Potts模型对液态金属泡沫胞元结构进行了随机模拟,得到了二维泡沫的胞元尺寸、拓扑参数以及分布等定量特征信息。计算结果与实验结果完全吻合,表明Potts模型应用于熔体泡沫演化过程研究的可行性、可靠性。
建立了一个简化的泡沫铝合金凝固过程数学模型,通过对模型的求解,获得不同时刻泡沫铝合金的温度场、凝固界面的位置以及形状。通过求解液体体积分数分布,间接得到孔隙率的分布。在凝固过程中,考虑了粘度、比热容等物性参数随温度的变化现象。整个凝固过程与液态泡沫析液现象有着密切的关系;重力和表面张力在析液过程中起着关键作用,在微重力条件下凝固的泡沫铝产品比较理想,即孔隙率分布比较均匀。
As a representative of metal foam material,foamed aluminum,which has been used widely in the fields of spaceflight,architectural structure and automobile,is a promising functional and structural material.Because of its outstanding thermal,acoustical and mechanical performances,foamed aluminum has become a hotspot of research and development in the material science and technology.There are many approaches to manufacture cellular metallic materials.From which the gas injection method has special advantages in the respect that metallic foams can be produced continuously and their size is little limited.In this technique,a major issue is how to control the size and uniformity of the cells during the foaming process of molten aluminum.In order to explore approaches through which one can effectively control the manufacture process and the performance of aluminum foams,it is necessary to investigate and understand deeply factors affecting the foaming process.In this thesis,hydrodynamic behaviors of metallic foam flow and bubble moving and distribution characteristics in the melt were systematically studied by numerical simulation, and on this basis some insights into effects of relevant parameters on the foam structure have been gained.The main works and conclusions are summarized as follows:
Firstly,microscopical and macroscopical numerical studies are performed on the drainage process in fabricating foamed aluminum.The former studied the liquid flowing in a single Plateau border(PB) of aluminum foam during drainage process and a structural model of a single node with different liquid holdup is presented.Then the CFD software FLUENT is used to compute the velocity field in a single node.The latter proposes,based on the results from the microscopical model,a new macroscopical drainage model for aluminum foams. Furthermore,the liquid/gas interface mobility is taken into account,which is characterized by the Newtonian surface viscosity.Computational results indicate that at the same liquid/gas interfacial mobility(M) and same radius of curvature,the max velocity inside an exterior Plateau border is about 6～8 times as large as that inside an interior Plateau border.It is indicated that drier forms have smaller drainage rate and show rapider coarsening,implying that gas diffusion between bubbles is the predominate factor for coarsening of foams.Besides, surface tension,and fluid properties(Henry constant,diffusion rate etc) have also remarkable effects on the evolution of bubble size distribution.The holdup of foams is gained by a mathematic model based on the gas injection method.The results suggested that gravity, viscosity,surface tension and the velocity of gas injection affected the holdup of foams greatly.The theory of phase field is applied to studying the evolution of the liquicuid/gas interface.The results explain the coalescence of neighboring bubbles.
For any foams,gas diffusion through the film between bubbles in foams is inevitable.A mathematical model for predicting the evolution of bubble size distribution in aluminum foams is presented,which takes into account effects of both the coarsening due to gas diffusion between bubbles and the liquid drainage.A bubble size distribution equation and a one-dimensional drainage equation are solved coupled by a finite difference approach. Comparison with experimental results from the literature shows a reasonable agreement.The model predictions indicate that the bubble size increases exponentially with time that is in good agreement with MacPherson's theory.Furthermore,computational results reveal that bubble size distributions are dependent strongly on the drainage behavior,the Henry constant, gas diffusivity and surface tension of the aluminum foam in liquid state.Furthermore,a method for geometrical and topological modeling the evolution of close-cell metallic foams based on the Voronoi tessellation in three-dimensional space is presented.Numerical computations were carried out to examine the evolution of bubble size distribution and topological and geometric properties of aluminum foams in liquid state,which were implemented by using McPherson's new theory on coarsening of microstructures as well as the topological transition rules(T1 and T2 processes) in 3D foams,accounting for remarkable effects of both the gas diffusion and surface tension.Computational results show that the bubble size distributions of metallic foams are strongly coupled to the evolution of the cellular structure and dependent on the gas diffusivity and surface tension.Gas diffusion between bubbles dominates the evolution of bubble sizes and foam structures.
Additionally,the cell structure of foamed aluminum is predicted by using a Monte Carlo Potts model,which takes into account effects of surface tension between gas and liquid.The statistical results of numerical simulation and experiment were compared,which indicate that the Potts model can be used in predicting the cell structure of foamed aluminum in liquid.The results show that the cell size distribution of foamed aluminum can be fitted by the Weibull function approximately.
Finally,a mathematical model for the coupling process between drainage and solidification of aluminum foams is presented based on the coupling of the foam drainage equation and the energy equation.The time evolution and spatial distribution of the aluminum volume fraction and temperature during the solidification process are numerically predicted. Effects of relevant parameters e.g.gravity,viscosity and surface tension are discussed. Computational results show that foam drainage and solidification are two closely coupled and interactive processes and that the melt properties have significant influences on the solidification time and foam porosity.
对泡沫析液现象从二个方面进行了研究。一是宏观方面,即研究泡沫群的整体行为;二是微观方面,即对单条Plateau边界、节点、液膜等的研究。宏观方面,初步尝试了泡沫金属析液过程的二维数值计算,计算结果与实验结果进行了定性比较,研究了在不同工况参数下金属泡沫铝的孔隙率的变化规律。结果表明:泡沫最终的孔隙率受到泡沫初始孔隙率、泡沫层的高度、泡沫的直径、重力加速度和熔体粘度等因素的影响。其中泡沫的孔径对最终的孔隙率有较大的影响,而粘度对最终的孔隙率影响较小,只是对析液速率有较大的影响。微观方面,研究了单条Plateau边界及节点处的析液现象。对单条泡沫体Plateau边界内部的速度场的研究表明:泡沫体内部Plateau边界内的速度要小于同等条件下的容器壁面处Plateau边界内的速度,间接解释了宏观析液过程中析液速率与不同容器条件的关系。分析了Plateau边界中界面流变特性对析液过程的影响,进而将单条Plateau边界内液体流动的分析结果应用于泡沫体析液过程的宏观研究,建立了一个析液模型,计算结果与实验结果的比较显示:在泡沫层上部、中部吻合较好,在底部存在一定误差。
建立了描述了吹气法制备泡沫铝过程中泡沫孔隙率随空间的变化的数学模型。计算结果表明,在不考虑气泡的合并的情况下,熔液粘度、表面张力、重力加速度、气体的流量对泡沫孔隙率,即Plateau边界的横截面积,有显著的影响。重力加速度和表面张力在析液过程中起着关键的作用。通过理论建模和数值计算预测了发泡层高度随时间,气体流速等的关系,模型能较好的解释泡沫层高度的变化。利用相场(Phase field)方法对界面演化过程进行了数值模拟,较为直观合理的解释了液膜破裂现象。
通过析液方程和由于气体扩散造成的气泡长大的方程的耦合,建立了铝合金熔体泡沫中气泡尺寸分布发展的数学模型。通过数值计算,得出了不同工况下泡沫尺寸分布的发展过程,讨论了表面张力、亨利常数、扩散率等因素对泡沫尺寸分布发展的影响。计算结果表明:表面张力越大、亨利常数越大,泡沫尺寸演化过程越剧烈;含液率较小的泡沫体析液量很小,所以,泡沫尺寸分布变化主要由气体扩散引起。
利用Surface Evolver软件及MacPherson等人的最新理论成果,对金属泡沫多面体气泡的演化过程中的泡沫尺寸和拓扑结构进行了数值计算研究,数值模拟结果与试验研究结果进行了定性的比较,一些特征非常相似。利用Potts模型对液态金属泡沫胞元结构进行了随机模拟,得到了二维泡沫的胞元尺寸、拓扑参数以及分布等定量特征信息。计算结果与实验结果完全吻合,表明Potts模型应用于熔体泡沫演化过程研究的可行性、可靠性。
建立了一个简化的泡沫铝合金凝固过程数学模型,通过对模型的求解,获得不同时刻泡沫铝合金的温度场、凝固界面的位置以及形状。通过求解液体体积分数分布,间接得到孔隙率的分布。在凝固过程中,考虑了粘度、比热容等物性参数随温度的变化现象。整个凝固过程与液态泡沫析液现象有着密切的关系;重力和表面张力在析液过程中起着关键作用,在微重力条件下凝固的泡沫铝产品比较理想,即孔隙率分布比较均匀。
As a representative of metal foam material,foamed aluminum,which has been used widely in the fields of spaceflight,architectural structure and automobile,is a promising functional and structural material.Because of its outstanding thermal,acoustical and mechanical performances,foamed aluminum has become a hotspot of research and development in the material science and technology.There are many approaches to manufacture cellular metallic materials.From which the gas injection method has special advantages in the respect that metallic foams can be produced continuously and their size is little limited.In this technique,a major issue is how to control the size and uniformity of the cells during the foaming process of molten aluminum.In order to explore approaches through which one can effectively control the manufacture process and the performance of aluminum foams,it is necessary to investigate and understand deeply factors affecting the foaming process.In this thesis,hydrodynamic behaviors of metallic foam flow and bubble moving and distribution characteristics in the melt were systematically studied by numerical simulation, and on this basis some insights into effects of relevant parameters on the foam structure have been gained.The main works and conclusions are summarized as follows:
Firstly,microscopical and macroscopical numerical studies are performed on the drainage process in fabricating foamed aluminum.The former studied the liquid flowing in a single Plateau border(PB) of aluminum foam during drainage process and a structural model of a single node with different liquid holdup is presented.Then the CFD software FLUENT is used to compute the velocity field in a single node.The latter proposes,based on the results from the microscopical model,a new macroscopical drainage model for aluminum foams. Furthermore,the liquid/gas interface mobility is taken into account,which is characterized by the Newtonian surface viscosity.Computational results indicate that at the same liquid/gas interfacial mobility(M) and same radius of curvature,the max velocity inside an exterior Plateau border is about 6～8 times as large as that inside an interior Plateau border.It is indicated that drier forms have smaller drainage rate and show rapider coarsening,implying that gas diffusion between bubbles is the predominate factor for coarsening of foams.Besides, surface tension,and fluid properties(Henry constant,diffusion rate etc) have also remarkable effects on the evolution of bubble size distribution.The holdup of foams is gained by a mathematic model based on the gas injection method.The results suggested that gravity, viscosity,surface tension and the velocity of gas injection affected the holdup of foams greatly.The theory of phase field is applied to studying the evolution of the liquicuid/gas interface.The results explain the coalescence of neighboring bubbles.
For any foams,gas diffusion through the film between bubbles in foams is inevitable.A mathematical model for predicting the evolution of bubble size distribution in aluminum foams is presented,which takes into account effects of both the coarsening due to gas diffusion between bubbles and the liquid drainage.A bubble size distribution equation and a one-dimensional drainage equation are solved coupled by a finite difference approach. Comparison with experimental results from the literature shows a reasonable agreement.The model predictions indicate that the bubble size increases exponentially with time that is in good agreement with MacPherson's theory.Furthermore,computational results reveal that bubble size distributions are dependent strongly on the drainage behavior,the Henry constant, gas diffusivity and surface tension of the aluminum foam in liquid state.Furthermore,a method for geometrical and topological modeling the evolution of close-cell metallic foams based on the Voronoi tessellation in three-dimensional space is presented.Numerical computations were carried out to examine the evolution of bubble size distribution and topological and geometric properties of aluminum foams in liquid state,which were implemented by using McPherson's new theory on coarsening of microstructures as well as the topological transition rules(T1 and T2 processes) in 3D foams,accounting for remarkable effects of both the gas diffusion and surface tension.Computational results show that the bubble size distributions of metallic foams are strongly coupled to the evolution of the cellular structure and dependent on the gas diffusivity and surface tension.Gas diffusion between bubbles dominates the evolution of bubble sizes and foam structures.
Additionally,the cell structure of foamed aluminum is predicted by using a Monte Carlo Potts model,which takes into account effects of surface tension between gas and liquid.The statistical results of numerical simulation and experiment were compared,which indicate that the Potts model can be used in predicting the cell structure of foamed aluminum in liquid.The results show that the cell size distribution of foamed aluminum can be fitted by the Weibull function approximately.
Finally,a mathematical model for the coupling process between drainage and solidification of aluminum foams is presented based on the coupling of the foam drainage equation and the energy equation.The time evolution and spatial distribution of the aluminum volume fraction and temperature during the solidification process are numerically predicted. Effects of relevant parameters e.g.gravity,viscosity and surface tension are discussed. Computational results show that foam drainage and solidification are two closely coupled and interactive processes and that the melt properties have significant influences on the solidification time and foam porosity.
引文
[1]http://www.metalfoam.net
[2]http://www.tcd.ie/Phvsics/Foams/
[3]http://www.mnfgmbh.de/cmap/contrib-list.htm
[4]http://www.npl.co.uk/materials/metal_foams/index.html
[5]宋振纶,马立群,吴照金,何德坪,舒光冀,铝熔体泡沫化过程体积变化与胞状组织的演变,材料科学与工艺[J],Vol.8,No.1,2000
[6]Bastawros A F,Bart-Smith H,Evans A G.Experimental Analysis of Deformation Mechanisms in a Closed-Cell Aluminum Alloy Foam[J].Journal of the Mechanics and Physics of Solids,2000,48(2):301-322
[7]储少军,吴铿,牛强,等.冶金熔体泡沫分类的研究[J].北京科技大学学报,1998,20(1):20-26.
[8]陈策,王永进,何德坪.高比强多孔铝合金的压缩变形性能[J].材料研究学报,2003,17(3):230-234
[9]Shim V P W,Tay B Y,Stronge W J.Dynamic Crushing of Strain-Softening Cellular Structures.A One-Dimensional Analysis[J].Journal of Engineering Materials and Technology,Transactions of the ASME,1990,112(4):398-405
[10]Hall R L.Late B.Ammonites from the Fernie Formation[J],Canadian Rocky Mountains.Journal of Paleontology,1999,62(4):575
[11]McRae J.,Kelkar A.,Grace C.et al.Impact Damage Resistance of Aluminum Alloy Foams.American Society of Mechanical Engineers[J],Pressure Vessels and Piping Division(Publication) PVP,1998,381:71-77
[12]Mukai T.,Kanahashi H.,Yamada Y.et al.Dynamic Compressive Behavior of an Ultra-Lightweight Magnesium Foam[J].Scripta Materialia,1999,41(4):365-371
[13]Nieh T.G.,Kinney J.H.,Wadsworth J.et al.Morphology and Elastic Properties of Aluminum Foams Produced by a Casting Technique[J].Scripta Materialia,1998,38(10):1487-1494
[14]Andrews E.,Sanders W.,Gibson L.J..Compressive and.Tensile Behaviour of Aluminum Foams[J].Materials Science and Engineering A,1999,270(2):113-124
[15]Lorenzi L.,Fuganti A.,Todaro E.et al.Aluminum Foam Applications for Impact Energy Absorbing Structures[J].SAE Special Publications,1997,1226:1-10
[16]Gui M.C.,Wang D.B.,Wu J.J.et al.Deformation and Damping Behaviors of Foamed Al-Si-Sicp Composite[J].Materials Science and Engineering A,2000,286(2):282-288
[17]John B.,Manufacture,characterization and application of cellular metals and metal foams[J],Progress in Materials Science,46(2001) 559-632
[18]Koehler S.A.,Hilgenfeldt S.,Stone H.A.,A generalized view of foam drainage:experiment and theory[J].Langmuir 2000;16:6327-41
[19]Gergely V.,Clyne T.W..Drainage in standing liquid metal foams:modeling and experimental observations[J],Acta Material,2004,52(10),3047-3058
[20]Cox S.J.,Weaire D.,Hutzler S.,Murphy J.,Phelan R.,Verbist G..Applications and generalizations of the foam drainage equation[J],Proc R Soc Lond A 2000:2441-64
[21]Saint J.A.,Physical chemistry in foam drainage and coarsening[J],Soft Matter,2006,2,836-849
[22]Koehler S.A.,Stone H.A.,Brenner M.P.et al,Dynamics of foam drainage[J],Physical Review E,1998,58:2097-2106
[23]马立群,何德坪.新型泡沫铝的制备及其孔结构的控制[J].材料研究学报,1994,8(1):11-17.
[24]梁晓军,朱勇刚,陈锋,等.泡沫铝芯三明治板的粉末冶金制备及其板/芯界面研究[J].材料科学与工程学报,2005,23(1):077-080.
[25]刘士魁.泡沫铝粉末冶金复合加热法制备技术的试验研究:(硕士学位论文).大连:大连理工大学,2005.
[26]罗洪杰.熔体发泡法制各泡沫铝材工[J].轻金属,2003,C9:51-53.
[27]王录才,陈新,柴跃生.熔模铸造法通孔泡沫铝制备工艺研究[J].铸造,1999,1:9-11.
[28]薛涛.多孔金属材料泡沫铝的发展[J].机械工程材料,1992 2:4-5.
[29]Wang D.Q.,Lopez H.F.,Effect of Thermal Gradients on the Nucleation of Primary Phase in Al-4%Si Composite[J].Mater.Sci.Tech.,1998,16(1):29.
[30]许庆彦,陈玉勇,李庆春.多孔泡沫金属的研究现状[J].铸造设备研究,1997,1:18-24.
[31]Fusheng H.,Jianning W.,Hefa C.et al.Effects of Process Parameters and Alloy Compositions on the Pore Sructure of Foamed Aluminum[J].Journal of Materials Processing Technology,2003,138:505-507.
[32]王茗.泡沫金属发泡基础理论研究:(硕士学位论文).昆明:昆明理工大学,2004.
[33]李晶.泡沫铝的制备研究:(硕士学位论文)广西大学,2005.
[34]den Engelsen C.W.,Isarin J.C.,Gooijer H.,M.,Warmoeskerken M.C.G.,Groot Wassink J.,Bubble size distribution of foam[J],AUTEX research journal,2002,12(1)
[35]Laakkonen M.,Alopaeus V.,Aittamaa J.,Validation of bubble breakage,coalescence and mass transfer models for gas-liquid dispersion in agitated vessel[J],Chemical engineering science,61,2006,218-228
[36]Shen H.,Oppenheimer S.M.,Dunand D.C.,Brinson L.C.,Numerical Modeling of Pore Size and Distribution in Foamed Titanium[J],Mechanics of Materials,2005
[37]komer C.,Thies M.I.,Singer R.F.,Modeking of metal foaming with lattice boltzmann automata[J],advanced engineering materials,2002,4(10):765-769
[38]朱勇刚,陈锋,梁晓军,何德坪 粉末冶金发泡时泡沫铝孔结构及泡壁的微观组织演变,中国有色金属学报[J],2004,14(7):1106-1111
[39]Oak S.M.,Kim B.J.,Kim W.T.et al.Physical Modeling of Bubble Generation in Foamed-Aluminum [J].Journal of Materials Processing Technology,2002,130-131:304-309
[40]Fusheng H.,Jianning W.,Hera C.et al,Effects of Process Parameters and Alloy Compositions on the Pore Sructure of Foamed Aluminum[J].Journal of Materials Processing Technology,2003,138:505-507
[41]Wang D.Q.,Shi Z.Y..Effect of Ceramic Particles on Cell Size and Wall Thickness of Aluminum Foam[J].Mater.Sci.Eng.,2003,361:45-49
[42]吴新光,刘荣佩,熔体吹气发泡法制备泡沫铝合金研究[J].云南冶金,2003,32(1):50-53
[43]Koerner C.,Ties M.,Singe R.F.Modeling of Metal Foaming with Lattice Boltzmann Automata[J]. Adv.Eng.Mater,2002,4(10):765- 769.
[44]Pilon D.,Panneton R.,Sgard F.et al.Influence of Micro-Structural Properties on the Acoustic Performances of Novel Metallic Foams.Canadian Acoustics-Acoustique Canadienne,2004,32(3):24-25.
[45]Cox S.J.,Bradley G.,Weaire D..Metallic Foam Processing from the Liquid State:The Competition between Solidification and Drainage[J].EPJ Applied Physics,2001,14(2):87-96
[46]Thomas B.G.,Mathematical modeling of fluid flow in continuous casting[J],ISIJ international,Vol.41(2001),No.10,1181-1193
[47]Lane G.L.,Schwarz M.P.,Evans G.M..Predicting Gas-Liquid Flow in a Mechanically Stirred Tank [J].Applied Mathematical Modelling,2002,26(2):223-235
[48]Guo D.C.,Gu L.,Irons G.A..,Developments in Modelling of Gas Injection and Slag Foaming[J].Applied Mathematical Modelling,2002,26(2):263-280.
[49]Cross M.,Croft T.N.et al,Developments in modeling of gas injection and slag foaming[J],Applied mathematical modeling 26,(2006) 1145-1458
[50]赵连刚,张慧,连铸结晶器过程综合冶金行为的数值模拟[J],钢铁研究学报,2007,19,30-34
[51]詹树华,欧俭平,赖朝彬.两种浸入式侧吹模式下的熔池搅拌现象[J].中南大学学报(自然科学版),2005,36(1):49-54
[52]Sommerfield m.,Decker S.,state of the art and future trends in CFD simulation of stirred vessel hydrodynamics[J],Chem.Eng.Technol.,2004,27,215-224
[53]Jakobsen H.A..Phase Distribution Phenomena in Two-Phase Bubble Column Reactors[J].Chemical Engineering Science,2001,56(3):1049-1056.
[54]Luo J.V.,Issa R.I.,Gosman A.D..Prediction of impeller induced flows in mixing vessels using multiple frames of reference[J].IChemE Symp Ser 136,1994.549-556.
[55]Avinash R.,Khopkar,Vivek V.,CFD simulation of gas-liquid stirred vessel:VC,S33 and L33flow regimes[J],AICHE journal,2006,52,1654-1673
[56]Mazumdar D.,Kim H.B.,Guthrie R.I.J.,Modelling criteria for flow simulation in gas stirred ladles:experimental study[J],ironmaing and steelmaking,2000,27,302-309
[57]Taniguchi S.,Kawaguchi S.,Kikuch A.,Fluid flow and gas-liquid mass transfer in gas-injection vessels[J],Applied Mathematical Modelling,26(2002)249-262
[58]Pan Y.H.,Bjorkman B.,Numerical analysis on the similarity between steel ladels and hot water models regarding natural convection phnomena[J],ISIJ international,2002,42,53-62
[59]Leonard R.,Lemlich R.,A study of interstitial liquid flow in foam[J],AIChE 11(1)(1965)18-25.A.M.
[60]Kraynik,Sandia Report SAND 83-0844(1983)
[61]Bhakta A.,Ruckenstein E..Decay of standing foams:drainage,coalescence and collapse[J].Adv Colloid Interface Sci 1997;70:1-124
[62]Koehler S.A.,Hilgenfeldt S.,Stone H.A..Foam drainage on the microscale I.Modeling flow through single Plateau borders[J],Journal of Colloid and Interface Science 276(2004) 420-438
[63]Cox S.J.,Graner F.,Three-dimensional bubble clusters:Shape,packing,and growth rate[J],PHYSICAL REVIEW E 69,031409(2004)
[64]Neethling S.J,,Lee H.T.,The growth,drainage and breakdown of foams[J].Colloids and Surfaces A:Physicochem.Eng.Aspects 263(2005) 184-196
[65]Wubben,Stanzick H.,Banhart J.et al,Stability of metallic foams studied under microgravity[J].J.Phys.Condens.Matter 15(2003),S427-S433
[66]Brunke O.,Odenbach S.,In situ observation and numerical calculations of the evolution of metallic foams[J],J.Phys.:Condens.Matter 18(2006) 6493-6506
[67]Neethling S.J.,Cilliers J.J.,A visual kinematic model of flowing foams incorporating coalescence[J],Powder Technology,101(1998),249-256
[68]Cox S.J.,Weaire D.,Glazier J.A.,The rheology of two-dimensional foams[J],Rheol Acta(2004) 43:442-448
[69]Cox S.J.,Weaire D.,Hutzler S.,Murphy J.,Phelan R.,Verbist G.,Applications and generalizations of the foam drainage equation[J].Proc R Soc Lond A 2000:2441-2464
[70]Briant A.J.,Wagner A.J.,Yeomans J.M.,Lattice Boltzmann simulations of contact line motion.I.Liquid-gas systems[J],Physical Review E 69,031602(2004)
[71]Kern N.,Weaire D.,Martin A.,Hutzler S.,and Cox S.J.,Two-dimensional viscous froth model for foam dynamics[J],PHYSICAL REVIEW E70,041411(2004)
[72]Neethling S.J.,Cilliers J.J.,Woodburn E.T.,Prediction of the water distribution in a flowing foam[J],Chemical Engineering Science 55(2000) 4021-4028
[73]Shen H.,Oppenheimer S.M.,Dunand D.C.,Brinson L.C.,Numerical Modeling of Pore Size and Distribution in Foamed Titanium[J],Mechanics of Materials,2005
[74]戴戈,何德坪,尚金堂 铝合金熔体泡沫化过程中粘度的变化[J],材料研究学报,2005,19(1):33-41
[75]尚金堂,何德坪 铝合金熔体中球形泡沫的生长[J],中国科学,B辑,2005,35(3):212-219
[76]朱勇刚,陈锋,梁晓军,何德坪 粉末冶金发泡时泡沫铝孔结构及泡壁的微观组织演变[J],中国有色金属学报,2004,14(7):1106-1111
[77]解茂昭,韩薇,刘红,王德庆,液态金属熔体中气泡运动特性数值模拟[J],大连理工大学学报,46:340-345,2006
[78]刘红,解茂昭,李科等,泡沫金属湍流射流发泡过程数值模拟研究[J],材料科学与工艺,2007,15,178-182
[79]刘红,解茂昭,李科等,机械搅拌流场中制备闭孔泡沫铝过程的数值模拟研究[J],过程工程学报。2007,890-895
[80]刘红,解茂昭,李科等,液态金属中气体射流过程数值模拟研究[J],大连理工大学学报,2007,47,652-656
[81]Weaire D.,Cox S.J.,Banhart J.,Methods and models of metallic foam fabrication Proc.8th Ann.Intl.Conf.Composites Eng,D.Hui(ed),977-978(2001)
[82]Gergely V.,Clyne T.W.,Drainage in standing liquid metal foams:modeling and experimental observations[J],Acta Materialia,(2004).52,453-463
[83].Garadiner B.S,Dlugogorsk B.Z.,Jameson G.J.,Coarsening of two-and three-dimensional wet polydisperse foams[J],Philosophical Magazine A,2000,VOL.80,NO.4,981-1000
[84]Glazier J.A.,Stavans J.,Nonideal effects in the two-dimensional soap froth[J],Physical Review A, 1989,40(12):7398-7401
[85]Robert D.MacPherson,Srolovitz D.J.,The von Neumann relation generalized to coarsening of three-dimensional microstructures[J],Nature,1053-1055(2007)
[86]Douglas A.Reinelt,Kraynik A.M.,Simple shearing flow of dry soap foams with tetrahedrally close-packed steucture[J],J.Rheol,(44)3,2000,453-471
[87]Weaire D.,Fortes M.S.,Stress and strain in liquid and solid foams[J],Advance in physics[J],1994,(43)6,685-738
[88]Weaire D.,Cox S.J.,Banhart J.,Methods and models of metallic foam fabrication Proc.8th Ann.Intl.Conf.Composites Eng,D.Hui(ed),977-978(2001)
[89]姜斌,赵乃勤,泡沫铝的制备方法及应用进展[J].《金属热处理》,2005,30(6),36-40
[90]Weaire D.,Kermode J.P.,Computer simulation of a two dimension soap forth,Philosophical Magazine B[J],Vol.48,No.3,(1983)245-259
[91]Lehmhus D.,Banhart J.,Properties of heat-treated aluminum foams[J],Materials Science and Engineering,A349(2003)98-110
[92]郑明军,何德坪,胞状铝(合金)的准静态压缩性能[J],功能材料,2005.4(36),536-542
[93]陈策,王永进,何德坪.高比强多孔铝合金的压缩变形性能[J].材料研究学报,2003,17(3):230-234
[94]Koehler S.A.,Stone H.A.,Brenner M.P.,Eggers J..Dynamics of foam drainage[J],Physical Review E,1998,58(2),2097-2106
[95]Bhakta A.,Ruckenstein E..Decay of standing foams:drainage,coalescence and collapse,Advanced Colloid Interface Science,1997,70:1-124
[96]Koehler S.A.,Hilgenfeldt S.,Stone H.A.,Foam drainage on the micro scale Ⅱ.Imaging flow through single Plateau borders[J],Journal of Colloid and Interface Science 276(2004) 420-438
[97]Koehler S.A.,Hilgenfeldt S.,Stone HA.A generalized view of foam drainage:experiment and theory[J],Langmuir 2000;16:6327-6341
[98]Verbist G.,Weaire D.,Kraynik A.M.,The foam drainage equation,Journal of Physics[J],Condensed Matter,8(1996),3715-3731
[99]Stephan A.K.,Hilgenfeldt S.,.Weeks E.R,Stone H.A.,Drainage of single Plateau borders:Direct observation of rigid and mobile interfaces[J],PHYSICAL REVIEW E 66,040601(R),2000
[100]Cox S.J.,Weaire D.,Hutzler S.,Murphy J.,Applications and generalizations of the foam drainage equation[J],The Royal Society,2000,2441-2464
[101]Pan C.,Hilpert M.,Miller C.T.,Lattice-Boltzmann simulation of two-phase flow in porous media[J],Water Resources Research,Vol.40,2004
[102]He X.Y.,Luo L.S.,Lattice Boltzmann Model for the incompressible Navier-Stokes Equation[J],Journal of Statistical Physics,Vol.88(1997),927-944
[103]Pan C.,Hilpert M.,Miller C.T.,Lattice-Boltzmann simulation of two-phase flow in porous media[J],Water Resources Research,Vol.40,2004
[104]K.Brakke,Surface Evolver(2.30),2008
[105]The Physics of foams,Denis Weaire,Stefan Hutzler,2001
[106]黄晋,孙其诚,一维液态泡沫渗流实验研究及表面能和粘性耗散分析[J],物理学报,Vol.56,No.10,2007
[107]Koehler S.A.,Stone H.A.,Brenner M.P.,Eggers J..Dynamics of foam drainage[J],Physical Review E,(1998) 58(2),2097-2106
[108]Bhakta A.,Eli ruckenstein,Decay of standing foams:drainage,coalescence and collapse[J],Advances in colloid and interface science,70(1997),1-124
[109]Sun Q.,Hutzler S.,Studying localized bubble rearrangements in 2D liquid foams using a hybrid lattice gas model[J],Colloids and Surfaces A:Physicochem.Eng.Aspects 263(2005) 27-32
[110]Hilgenfeldt S.,Kraynik A.M.,Koehler S.A.,Stone H.A.,An Accurate von Neumann's Law for Three-Dimensional Foams[J],Physical review letters,82001,6(12),2685-2688
[111]Hutzler S.,Cox S.J.,Wang G.,Foam drainage in two dimensions[J],Colloids and Surfaces A,263(2005),178-186
[112]Verbist G.,Weaire D.,Kraynik A.M.,The foam drainage equation[J],Journal of Physics:Condensed Matter,8(1996),3715-3731
[113]Neethling S.J.,Cilliers J.J.,A visual kinematic model of flowing foams incorporating coalescence[J],Powder Technology,101(1998),249-256
[114]Laurent P.,Andrei G.F.,Raymond V..Analysis of transient thickness of pneumatic foams[J],Chemical Engineering Science 57(2002) 977-990
[115]luo K.F.,Kuittu M.P.,Tong C.H.et al,Phase-field modeling of wetting on structured surfaces[J],the Journal of chemical physics 123,192702(1-12),2005
[116]Magrabi S.A.,Dlugogorski B.Z.,Jameson G.J.,Bubble size distribution and coarsening of aqueous foams[J],Chemical Engineering Science 54(1999) 4007-4022
[117]Magrabi S.A.,Dlugogorski B.Z.,Jameson G.J.,A comparative study of drainage characteristics in AFFF and FFFP compressed-air fire-fighting foams,Fire Safety Journal 37(2002) 21-52
[118]Wang Z.B.,Narsimhan G.,Modelfor Plateau border drainage of power-law fluid with mobile interface and its application to foam drainage[J],Journal of Colloid and Interface Science 300(2006) 327-337
[119]Grassia P.,Neethling S.J.,Quasi-one-dimensional and two-dimensional drainage of foam[J],Colloids and Surfaces A:Physicochem.Eng.Aspects 263(2004) 165-177
[120]Magrabi S.A.,Dlugogorski B.Z.,Jameson G.L.,Bubble size distribution and coarsening of aqueous foams[J],Chemical Engineering Science,54(1999)4007-4002
[121]Robert L.,Prediction of Changes in Bubble Size Distribution Due to Inter bubble Gas Diffusion in Foam[J],Ind.Eng.Chem.Fundam.,Vol.17,No.2,(1978),89-93
[122]陶东平,《液态合金和熔融炉渣的性质》,云南科技出版社,1997,昆明
[123]田荣璋,王祝堂,《铝合金及其加工手册》,中南大学出版社,2000,长沙
[124]左孝青,潘晓亮,高芝,铝合金泡沫长大动力学研究[J],中国有色金属学报,Vol.16 No.12,2006
[125]Hilgenfeldt S.,Stephan A.K.,Howard A.S.,Dynamics of Coarsening Foams:Accelerated and Self-Limiting Drainage[J],PHYSICAL REVIEW LETTERS,vol.86,(20),2001
[126]Robert D.MacPherson,David J.S.,Supplementary material for generalization of the Von Neumann relation to coarsening of cellular microstructures in 3-D[J],Nature,(2007),1-11
[127]Weaire D.,Kermode J.P.,Computer simulation of a 2-D soap froth[J],Philosophical Magazine B, 48(1983),245-259
[128]Durian D.J.,Weitz,D.A.Pine D.J.,Scaling behavior in shaving cream[J],Physical review letters A,1991,44(12),R7902-R7906
[129]Garadiner B.S.,Dlugogorsk B.Z.,Jameson G.J.,Coarsening of two-and three-dimensional wet polydisperse foams[J],Philosophical Magazine A,2000,VOL.80,NO.4,981-1000
[130]Monnereau C.,Vignes-Adler M.,Dynamics of 3D Real Foam Coarsening[J],Physical review letters,1998,80(23),5228-5231
[131]Florence R.,Sylvie C.A.,Miche'le Vignes-Adler,Reinhard Ho"hler,Dynamics of yielding observed in a three-dimensional aqueous dry foam[J],Physical review letters E,67,2003,021405-1-7
[132]Durian D.J.,Weitz D.A.,Pine D.J.,Scaling behavior in shaving cream[J],Physical review letters A,44(12),1991,R7902-R7906
[133]Neethling S.J.,Effect of simple shear on liquid drainage within foams[J],Physical review letters E,73,(2006),061408-1-061408-13
[134]Hilgenfeldt S.,Stephan A.K.r,Howard A.S.,Dynamics of Coarsening Foams:Accelerated and Self-Limiting Drainage[J],PHYSICAL REVIEW LETTERS,vol.86,(20),2001
[135]Glazier J.A.,Stavans J.,Nonideal effects in the two-dimensional soap froth[J],Physical Review A,1989,40(12):7398-7401
[136]Reinelt D.A.,Kraynik A.M.,Simple shearing floe of dry soap foams with tetrahedrally closed-packed structure[J],J.Rheol.2000,44(3),453-471
[137]Turner S.,Sherratt J.A.Intercellular adhesion and cancer invasion:A discrete simulation using the extended Potts model[J].J.Theo.Biol.,2002,216:85-100
[138]Hassold G.N.,Elizabeth A.H.,A fast serial algorithm for then finite temperature quenched Potts model[J],COMPUTERS IN PHYSICS,Vol.7,No.1,1993,97-107
[139]Sanyal S.,Glazier J,A,,Viscous instabilities in flowing foams:a Cellular Potts Model approach[J],Journal of Statistical Mechanics Theory andExperiment,doi:10.1088/1742-5468/2006/10/P10008,2006
[140]Turner S.,Sherratt J.A..Intercellular adhesion and cancer invasion:A discrete simulation using the extended Potts model[J].J.Theo.Biol.,2002,216:85-107
[141]朱鸣芳,于金,戴挺,金属凝固过程数值模拟的最新进展[J],铸造,Vol.54(2005),No.2,115-120
[142]王君卿,MCSP622004国际会议概况和铸造过程数值模拟技术发展动向[J],铸造Vol.54(2005),No.4,303-317
[143]Cox S.J.,Bradley G.,and Weaire D.,Metallic foam processing from the liquid state[J],Eur.Phys.J.AP 14(2001),87-97
[144]Orenckhan W.,PHD Thesis,Trinity College Dublin,University of Dublin,Dublin,2005
[145]李东辉,高云宝,辛启斌等,铸件凝固潜热的处理方法与应用研究[J],铸造,Vol.53(2004),No.12,1005-1007
[146]何德坪,何思渊,尚金堂,超轻多孔金属的进展与物理学[J],物理学进展,Vol.26(2006),No.3and 4,346-350
[2]http://www.tcd.ie/Phvsics/Foams/
[3]http://www.mnfgmbh.de/cmap/contrib-list.htm
[4]http://www.npl.co.uk/materials/metal_foams/index.html
[5]宋振纶,马立群,吴照金,何德坪,舒光冀,铝熔体泡沫化过程体积变化与胞状组织的演变,材料科学与工艺[J],Vol.8,No.1,2000
[6]Bastawros A F,Bart-Smith H,Evans A G.Experimental Analysis of Deformation Mechanisms in a Closed-Cell Aluminum Alloy Foam[J].Journal of the Mechanics and Physics of Solids,2000,48(2):301-322
[7]储少军,吴铿,牛强,等.冶金熔体泡沫分类的研究[J].北京科技大学学报,1998,20(1):20-26.
[8]陈策,王永进,何德坪.高比强多孔铝合金的压缩变形性能[J].材料研究学报,2003,17(3):230-234
[9]Shim V P W,Tay B Y,Stronge W J.Dynamic Crushing of Strain-Softening Cellular Structures.A One-Dimensional Analysis[J].Journal of Engineering Materials and Technology,Transactions of the ASME,1990,112(4):398-405
[10]Hall R L.Late B.Ammonites from the Fernie Formation[J],Canadian Rocky Mountains.Journal of Paleontology,1999,62(4):575
[11]McRae J.,Kelkar A.,Grace C.et al.Impact Damage Resistance of Aluminum Alloy Foams.American Society of Mechanical Engineers[J],Pressure Vessels and Piping Division(Publication) PVP,1998,381:71-77
[12]Mukai T.,Kanahashi H.,Yamada Y.et al.Dynamic Compressive Behavior of an Ultra-Lightweight Magnesium Foam[J].Scripta Materialia,1999,41(4):365-371
[13]Nieh T.G.,Kinney J.H.,Wadsworth J.et al.Morphology and Elastic Properties of Aluminum Foams Produced by a Casting Technique[J].Scripta Materialia,1998,38(10):1487-1494
[14]Andrews E.,Sanders W.,Gibson L.J..Compressive and.Tensile Behaviour of Aluminum Foams[J].Materials Science and Engineering A,1999,270(2):113-124
[15]Lorenzi L.,Fuganti A.,Todaro E.et al.Aluminum Foam Applications for Impact Energy Absorbing Structures[J].SAE Special Publications,1997,1226:1-10
[16]Gui M.C.,Wang D.B.,Wu J.J.et al.Deformation and Damping Behaviors of Foamed Al-Si-Sicp Composite[J].Materials Science and Engineering A,2000,286(2):282-288
[17]John B.,Manufacture,characterization and application of cellular metals and metal foams[J],Progress in Materials Science,46(2001) 559-632
[18]Koehler S.A.,Hilgenfeldt S.,Stone H.A.,A generalized view of foam drainage:experiment and theory[J].Langmuir 2000;16:6327-41
[19]Gergely V.,Clyne T.W..Drainage in standing liquid metal foams:modeling and experimental observations[J],Acta Material,2004,52(10),3047-3058
[20]Cox S.J.,Weaire D.,Hutzler S.,Murphy J.,Phelan R.,Verbist G..Applications and generalizations of the foam drainage equation[J],Proc R Soc Lond A 2000:2441-64
[21]Saint J.A.,Physical chemistry in foam drainage and coarsening[J],Soft Matter,2006,2,836-849
[22]Koehler S.A.,Stone H.A.,Brenner M.P.et al,Dynamics of foam drainage[J],Physical Review E,1998,58:2097-2106
[23]马立群,何德坪.新型泡沫铝的制备及其孔结构的控制[J].材料研究学报,1994,8(1):11-17.
[24]梁晓军,朱勇刚,陈锋,等.泡沫铝芯三明治板的粉末冶金制备及其板/芯界面研究[J].材料科学与工程学报,2005,23(1):077-080.
[25]刘士魁.泡沫铝粉末冶金复合加热法制备技术的试验研究:(硕士学位论文).大连:大连理工大学,2005.
[26]罗洪杰.熔体发泡法制各泡沫铝材工[J].轻金属,2003,C9:51-53.
[27]王录才,陈新,柴跃生.熔模铸造法通孔泡沫铝制备工艺研究[J].铸造,1999,1:9-11.
[28]薛涛.多孔金属材料泡沫铝的发展[J].机械工程材料,1992 2:4-5.
[29]Wang D.Q.,Lopez H.F.,Effect of Thermal Gradients on the Nucleation of Primary Phase in Al-4%Si Composite[J].Mater.Sci.Tech.,1998,16(1):29.
[30]许庆彦,陈玉勇,李庆春.多孔泡沫金属的研究现状[J].铸造设备研究,1997,1:18-24.
[31]Fusheng H.,Jianning W.,Hefa C.et al.Effects of Process Parameters and Alloy Compositions on the Pore Sructure of Foamed Aluminum[J].Journal of Materials Processing Technology,2003,138:505-507.
[32]王茗.泡沫金属发泡基础理论研究:(硕士学位论文).昆明:昆明理工大学,2004.
[33]李晶.泡沫铝的制备研究:(硕士学位论文)广西大学,2005.
[34]den Engelsen C.W.,Isarin J.C.,Gooijer H.,M.,Warmoeskerken M.C.G.,Groot Wassink J.,Bubble size distribution of foam[J],AUTEX research journal,2002,12(1)
[35]Laakkonen M.,Alopaeus V.,Aittamaa J.,Validation of bubble breakage,coalescence and mass transfer models for gas-liquid dispersion in agitated vessel[J],Chemical engineering science,61,2006,218-228
[36]Shen H.,Oppenheimer S.M.,Dunand D.C.,Brinson L.C.,Numerical Modeling of Pore Size and Distribution in Foamed Titanium[J],Mechanics of Materials,2005
[37]komer C.,Thies M.I.,Singer R.F.,Modeking of metal foaming with lattice boltzmann automata[J],advanced engineering materials,2002,4(10):765-769
[38]朱勇刚,陈锋,梁晓军,何德坪 粉末冶金发泡时泡沫铝孔结构及泡壁的微观组织演变,中国有色金属学报[J],2004,14(7):1106-1111
[39]Oak S.M.,Kim B.J.,Kim W.T.et al.Physical Modeling of Bubble Generation in Foamed-Aluminum [J].Journal of Materials Processing Technology,2002,130-131:304-309
[40]Fusheng H.,Jianning W.,Hera C.et al,Effects of Process Parameters and Alloy Compositions on the Pore Sructure of Foamed Aluminum[J].Journal of Materials Processing Technology,2003,138:505-507
[41]Wang D.Q.,Shi Z.Y..Effect of Ceramic Particles on Cell Size and Wall Thickness of Aluminum Foam[J].Mater.Sci.Eng.,2003,361:45-49
[42]吴新光,刘荣佩,熔体吹气发泡法制备泡沫铝合金研究[J].云南冶金,2003,32(1):50-53
[43]Koerner C.,Ties M.,Singe R.F.Modeling of Metal Foaming with Lattice Boltzmann Automata[J]. Adv.Eng.Mater,2002,4(10):765- 769.
[44]Pilon D.,Panneton R.,Sgard F.et al.Influence of Micro-Structural Properties on the Acoustic Performances of Novel Metallic Foams.Canadian Acoustics-Acoustique Canadienne,2004,32(3):24-25.
[45]Cox S.J.,Bradley G.,Weaire D..Metallic Foam Processing from the Liquid State:The Competition between Solidification and Drainage[J].EPJ Applied Physics,2001,14(2):87-96
[46]Thomas B.G.,Mathematical modeling of fluid flow in continuous casting[J],ISIJ international,Vol.41(2001),No.10,1181-1193
[47]Lane G.L.,Schwarz M.P.,Evans G.M..Predicting Gas-Liquid Flow in a Mechanically Stirred Tank [J].Applied Mathematical Modelling,2002,26(2):223-235
[48]Guo D.C.,Gu L.,Irons G.A..,Developments in Modelling of Gas Injection and Slag Foaming[J].Applied Mathematical Modelling,2002,26(2):263-280.
[49]Cross M.,Croft T.N.et al,Developments in modeling of gas injection and slag foaming[J],Applied mathematical modeling 26,(2006) 1145-1458
[50]赵连刚,张慧,连铸结晶器过程综合冶金行为的数值模拟[J],钢铁研究学报,2007,19,30-34
[51]詹树华,欧俭平,赖朝彬.两种浸入式侧吹模式下的熔池搅拌现象[J].中南大学学报(自然科学版),2005,36(1):49-54
[52]Sommerfield m.,Decker S.,state of the art and future trends in CFD simulation of stirred vessel hydrodynamics[J],Chem.Eng.Technol.,2004,27,215-224
[53]Jakobsen H.A..Phase Distribution Phenomena in Two-Phase Bubble Column Reactors[J].Chemical Engineering Science,2001,56(3):1049-1056.
[54]Luo J.V.,Issa R.I.,Gosman A.D..Prediction of impeller induced flows in mixing vessels using multiple frames of reference[J].IChemE Symp Ser 136,1994.549-556.
[55]Avinash R.,Khopkar,Vivek V.,CFD simulation of gas-liquid stirred vessel:VC,S33 and L33flow regimes[J],AICHE journal,2006,52,1654-1673
[56]Mazumdar D.,Kim H.B.,Guthrie R.I.J.,Modelling criteria for flow simulation in gas stirred ladles:experimental study[J],ironmaing and steelmaking,2000,27,302-309
[57]Taniguchi S.,Kawaguchi S.,Kikuch A.,Fluid flow and gas-liquid mass transfer in gas-injection vessels[J],Applied Mathematical Modelling,26(2002)249-262
[58]Pan Y.H.,Bjorkman B.,Numerical analysis on the similarity between steel ladels and hot water models regarding natural convection phnomena[J],ISIJ international,2002,42,53-62
[59]Leonard R.,Lemlich R.,A study of interstitial liquid flow in foam[J],AIChE 11(1)(1965)18-25.A.M.
[60]Kraynik,Sandia Report SAND 83-0844(1983)
[61]Bhakta A.,Ruckenstein E..Decay of standing foams:drainage,coalescence and collapse[J].Adv Colloid Interface Sci 1997;70:1-124
[62]Koehler S.A.,Hilgenfeldt S.,Stone H.A..Foam drainage on the microscale I.Modeling flow through single Plateau borders[J],Journal of Colloid and Interface Science 276(2004) 420-438
[63]Cox S.J.,Graner F.,Three-dimensional bubble clusters:Shape,packing,and growth rate[J],PHYSICAL REVIEW E 69,031409(2004)
[64]Neethling S.J,,Lee H.T.,The growth,drainage and breakdown of foams[J].Colloids and Surfaces A:Physicochem.Eng.Aspects 263(2005) 184-196
[65]Wubben,Stanzick H.,Banhart J.et al,Stability of metallic foams studied under microgravity[J].J.Phys.Condens.Matter 15(2003),S427-S433
[66]Brunke O.,Odenbach S.,In situ observation and numerical calculations of the evolution of metallic foams[J],J.Phys.:Condens.Matter 18(2006) 6493-6506
[67]Neethling S.J.,Cilliers J.J.,A visual kinematic model of flowing foams incorporating coalescence[J],Powder Technology,101(1998),249-256
[68]Cox S.J.,Weaire D.,Glazier J.A.,The rheology of two-dimensional foams[J],Rheol Acta(2004) 43:442-448
[69]Cox S.J.,Weaire D.,Hutzler S.,Murphy J.,Phelan R.,Verbist G.,Applications and generalizations of the foam drainage equation[J].Proc R Soc Lond A 2000:2441-2464
[70]Briant A.J.,Wagner A.J.,Yeomans J.M.,Lattice Boltzmann simulations of contact line motion.I.Liquid-gas systems[J],Physical Review E 69,031602(2004)
[71]Kern N.,Weaire D.,Martin A.,Hutzler S.,and Cox S.J.,Two-dimensional viscous froth model for foam dynamics[J],PHYSICAL REVIEW E70,041411(2004)
[72]Neethling S.J.,Cilliers J.J.,Woodburn E.T.,Prediction of the water distribution in a flowing foam[J],Chemical Engineering Science 55(2000) 4021-4028
[73]Shen H.,Oppenheimer S.M.,Dunand D.C.,Brinson L.C.,Numerical Modeling of Pore Size and Distribution in Foamed Titanium[J],Mechanics of Materials,2005
[74]戴戈,何德坪,尚金堂 铝合金熔体泡沫化过程中粘度的变化[J],材料研究学报,2005,19(1):33-41
[75]尚金堂,何德坪 铝合金熔体中球形泡沫的生长[J],中国科学,B辑,2005,35(3):212-219
[76]朱勇刚,陈锋,梁晓军,何德坪 粉末冶金发泡时泡沫铝孔结构及泡壁的微观组织演变[J],中国有色金属学报,2004,14(7):1106-1111
[77]解茂昭,韩薇,刘红,王德庆,液态金属熔体中气泡运动特性数值模拟[J],大连理工大学学报,46:340-345,2006
[78]刘红,解茂昭,李科等,泡沫金属湍流射流发泡过程数值模拟研究[J],材料科学与工艺,2007,15,178-182
[79]刘红,解茂昭,李科等,机械搅拌流场中制备闭孔泡沫铝过程的数值模拟研究[J],过程工程学报。2007,890-895
[80]刘红,解茂昭,李科等,液态金属中气体射流过程数值模拟研究[J],大连理工大学学报,2007,47,652-656
[81]Weaire D.,Cox S.J.,Banhart J.,Methods and models of metallic foam fabrication Proc.8th Ann.Intl.Conf.Composites Eng,D.Hui(ed),977-978(2001)
[82]Gergely V.,Clyne T.W.,Drainage in standing liquid metal foams:modeling and experimental observations[J],Acta Materialia,(2004).52,453-463
[83].Garadiner B.S,Dlugogorsk B.Z.,Jameson G.J.,Coarsening of two-and three-dimensional wet polydisperse foams[J],Philosophical Magazine A,2000,VOL.80,NO.4,981-1000
[84]Glazier J.A.,Stavans J.,Nonideal effects in the two-dimensional soap froth[J],Physical Review A, 1989,40(12):7398-7401
[85]Robert D.MacPherson,Srolovitz D.J.,The von Neumann relation generalized to coarsening of three-dimensional microstructures[J],Nature,1053-1055(2007)
[86]Douglas A.Reinelt,Kraynik A.M.,Simple shearing flow of dry soap foams with tetrahedrally close-packed steucture[J],J.Rheol,(44)3,2000,453-471
[87]Weaire D.,Fortes M.S.,Stress and strain in liquid and solid foams[J],Advance in physics[J],1994,(43)6,685-738
[88]Weaire D.,Cox S.J.,Banhart J.,Methods and models of metallic foam fabrication Proc.8th Ann.Intl.Conf.Composites Eng,D.Hui(ed),977-978(2001)
[89]姜斌,赵乃勤,泡沫铝的制备方法及应用进展[J].《金属热处理》,2005,30(6),36-40
[90]Weaire D.,Kermode J.P.,Computer simulation of a two dimension soap forth,Philosophical Magazine B[J],Vol.48,No.3,(1983)245-259
[91]Lehmhus D.,Banhart J.,Properties of heat-treated aluminum foams[J],Materials Science and Engineering,A349(2003)98-110
[92]郑明军,何德坪,胞状铝(合金)的准静态压缩性能[J],功能材料,2005.4(36),536-542
[93]陈策,王永进,何德坪.高比强多孔铝合金的压缩变形性能[J].材料研究学报,2003,17(3):230-234
[94]Koehler S.A.,Stone H.A.,Brenner M.P.,Eggers J..Dynamics of foam drainage[J],Physical Review E,1998,58(2),2097-2106
[95]Bhakta A.,Ruckenstein E..Decay of standing foams:drainage,coalescence and collapse,Advanced Colloid Interface Science,1997,70:1-124
[96]Koehler S.A.,Hilgenfeldt S.,Stone H.A.,Foam drainage on the micro scale Ⅱ.Imaging flow through single Plateau borders[J],Journal of Colloid and Interface Science 276(2004) 420-438
[97]Koehler S.A.,Hilgenfeldt S.,Stone HA.A generalized view of foam drainage:experiment and theory[J],Langmuir 2000;16:6327-6341
[98]Verbist G.,Weaire D.,Kraynik A.M.,The foam drainage equation,Journal of Physics[J],Condensed Matter,8(1996),3715-3731
[99]Stephan A.K.,Hilgenfeldt S.,.Weeks E.R,Stone H.A.,Drainage of single Plateau borders:Direct observation of rigid and mobile interfaces[J],PHYSICAL REVIEW E 66,040601(R),2000
[100]Cox S.J.,Weaire D.,Hutzler S.,Murphy J.,Applications and generalizations of the foam drainage equation[J],The Royal Society,2000,2441-2464
[101]Pan C.,Hilpert M.,Miller C.T.,Lattice-Boltzmann simulation of two-phase flow in porous media[J],Water Resources Research,Vol.40,2004
[102]He X.Y.,Luo L.S.,Lattice Boltzmann Model for the incompressible Navier-Stokes Equation[J],Journal of Statistical Physics,Vol.88(1997),927-944
[103]Pan C.,Hilpert M.,Miller C.T.,Lattice-Boltzmann simulation of two-phase flow in porous media[J],Water Resources Research,Vol.40,2004
[104]K.Brakke,Surface Evolver(2.30),2008
[105]The Physics of foams,Denis Weaire,Stefan Hutzler,2001
[106]黄晋,孙其诚,一维液态泡沫渗流实验研究及表面能和粘性耗散分析[J],物理学报,Vol.56,No.10,2007
[107]Koehler S.A.,Stone H.A.,Brenner M.P.,Eggers J..Dynamics of foam drainage[J],Physical Review E,(1998) 58(2),2097-2106
[108]Bhakta A.,Eli ruckenstein,Decay of standing foams:drainage,coalescence and collapse[J],Advances in colloid and interface science,70(1997),1-124
[109]Sun Q.,Hutzler S.,Studying localized bubble rearrangements in 2D liquid foams using a hybrid lattice gas model[J],Colloids and Surfaces A:Physicochem.Eng.Aspects 263(2005) 27-32
[110]Hilgenfeldt S.,Kraynik A.M.,Koehler S.A.,Stone H.A.,An Accurate von Neumann's Law for Three-Dimensional Foams[J],Physical review letters,82001,6(12),2685-2688
[111]Hutzler S.,Cox S.J.,Wang G.,Foam drainage in two dimensions[J],Colloids and Surfaces A,263(2005),178-186
[112]Verbist G.,Weaire D.,Kraynik A.M.,The foam drainage equation[J],Journal of Physics:Condensed Matter,8(1996),3715-3731
[113]Neethling S.J.,Cilliers J.J.,A visual kinematic model of flowing foams incorporating coalescence[J],Powder Technology,101(1998),249-256
[114]Laurent P.,Andrei G.F.,Raymond V..Analysis of transient thickness of pneumatic foams[J],Chemical Engineering Science 57(2002) 977-990
[115]luo K.F.,Kuittu M.P.,Tong C.H.et al,Phase-field modeling of wetting on structured surfaces[J],the Journal of chemical physics 123,192702(1-12),2005
[116]Magrabi S.A.,Dlugogorski B.Z.,Jameson G.J.,Bubble size distribution and coarsening of aqueous foams[J],Chemical Engineering Science 54(1999) 4007-4022
[117]Magrabi S.A.,Dlugogorski B.Z.,Jameson G.J.,A comparative study of drainage characteristics in AFFF and FFFP compressed-air fire-fighting foams,Fire Safety Journal 37(2002) 21-52
[118]Wang Z.B.,Narsimhan G.,Modelfor Plateau border drainage of power-law fluid with mobile interface and its application to foam drainage[J],Journal of Colloid and Interface Science 300(2006) 327-337
[119]Grassia P.,Neethling S.J.,Quasi-one-dimensional and two-dimensional drainage of foam[J],Colloids and Surfaces A:Physicochem.Eng.Aspects 263(2004) 165-177
[120]Magrabi S.A.,Dlugogorski B.Z.,Jameson G.L.,Bubble size distribution and coarsening of aqueous foams[J],Chemical Engineering Science,54(1999)4007-4002
[121]Robert L.,Prediction of Changes in Bubble Size Distribution Due to Inter bubble Gas Diffusion in Foam[J],Ind.Eng.Chem.Fundam.,Vol.17,No.2,(1978),89-93
[122]陶东平,《液态合金和熔融炉渣的性质》,云南科技出版社,1997,昆明
[123]田荣璋,王祝堂,《铝合金及其加工手册》,中南大学出版社,2000,长沙
[124]左孝青,潘晓亮,高芝,铝合金泡沫长大动力学研究[J],中国有色金属学报,Vol.16 No.12,2006
[125]Hilgenfeldt S.,Stephan A.K.,Howard A.S.,Dynamics of Coarsening Foams:Accelerated and Self-Limiting Drainage[J],PHYSICAL REVIEW LETTERS,vol.86,(20),2001
[126]Robert D.MacPherson,David J.S.,Supplementary material for generalization of the Von Neumann relation to coarsening of cellular microstructures in 3-D[J],Nature,(2007),1-11
[127]Weaire D.,Kermode J.P.,Computer simulation of a 2-D soap froth[J],Philosophical Magazine B, 48(1983),245-259
[128]Durian D.J.,Weitz,D.A.Pine D.J.,Scaling behavior in shaving cream[J],Physical review letters A,1991,44(12),R7902-R7906
[129]Garadiner B.S.,Dlugogorsk B.Z.,Jameson G.J.,Coarsening of two-and three-dimensional wet polydisperse foams[J],Philosophical Magazine A,2000,VOL.80,NO.4,981-1000
[130]Monnereau C.,Vignes-Adler M.,Dynamics of 3D Real Foam Coarsening[J],Physical review letters,1998,80(23),5228-5231
[131]Florence R.,Sylvie C.A.,Miche'le Vignes-Adler,Reinhard Ho"hler,Dynamics of yielding observed in a three-dimensional aqueous dry foam[J],Physical review letters E,67,2003,021405-1-7
[132]Durian D.J.,Weitz D.A.,Pine D.J.,Scaling behavior in shaving cream[J],Physical review letters A,44(12),1991,R7902-R7906
[133]Neethling S.J.,Effect of simple shear on liquid drainage within foams[J],Physical review letters E,73,(2006),061408-1-061408-13
[134]Hilgenfeldt S.,Stephan A.K.r,Howard A.S.,Dynamics of Coarsening Foams:Accelerated and Self-Limiting Drainage[J],PHYSICAL REVIEW LETTERS,vol.86,(20),2001
[135]Glazier J.A.,Stavans J.,Nonideal effects in the two-dimensional soap froth[J],Physical Review A,1989,40(12):7398-7401
[136]Reinelt D.A.,Kraynik A.M.,Simple shearing floe of dry soap foams with tetrahedrally closed-packed structure[J],J.Rheol.2000,44(3),453-471
[137]Turner S.,Sherratt J.A.Intercellular adhesion and cancer invasion:A discrete simulation using the extended Potts model[J].J.Theo.Biol.,2002,216:85-100
[138]Hassold G.N.,Elizabeth A.H.,A fast serial algorithm for then finite temperature quenched Potts model[J],COMPUTERS IN PHYSICS,Vol.7,No.1,1993,97-107
[139]Sanyal S.,Glazier J,A,,Viscous instabilities in flowing foams:a Cellular Potts Model approach[J],Journal of Statistical Mechanics Theory andExperiment,doi:10.1088/1742-5468/2006/10/P10008,2006
[140]Turner S.,Sherratt J.A..Intercellular adhesion and cancer invasion:A discrete simulation using the extended Potts model[J].J.Theo.Biol.,2002,216:85-107
[141]朱鸣芳,于金,戴挺,金属凝固过程数值模拟的最新进展[J],铸造,Vol.54(2005),No.2,115-120
[142]王君卿,MCSP622004国际会议概况和铸造过程数值模拟技术发展动向[J],铸造Vol.54(2005),No.4,303-317
[143]Cox S.J.,Bradley G.,and Weaire D.,Metallic foam processing from the liquid state[J],Eur.Phys.J.AP 14(2001),87-97
[144]Orenckhan W.,PHD Thesis,Trinity College Dublin,University of Dublin,Dublin,2005
[145]李东辉,高云宝,辛启斌等,铸件凝固潜热的处理方法与应用研究[J],铸造,Vol.53(2004),No.12,1005-1007
[146]何德坪,何思渊,尚金堂,超轻多孔金属的进展与物理学[J],物理学进展,Vol.26(2006),No.3and 4,346-350
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