微孔塑料注射成型数值模拟
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摘要
微孔塑料是指泡孔直径为1～50微米、泡孔密度为10~9～10~(12)个／cm~3、泡孔分布非常均匀的泡沫塑料，其设计思想即在高分子材料内部产生比原有缺陷更小的气泡，使泡孔的存在不仅不会降低材料的强度，反而会使材料中原有的裂纹尖端钝化，阻止裂纹在应力作用下扩展，从而提高其力学性能。由麻省理工学院(MIT)与Trexel公司共同研发的制备微孔塑料的微孔发泡技术(Mucell)已经商业化，其原理是将超临界状态的大气(N_2或CO_2)通过安装在注射机机筒上的注射器注射入聚合物熔体中，形成单一均相的聚合物／气体体系，随后，熔体被快速注射入模具型腔，随着压力骤降，超临界气体便会逸出，形成大量的微孔，然后微孔与模腔内熔体一起冷却定型而得到泡孔大小均匀、分布均匀的微孔塑料制品。
微孔制品不仅力学性能优异，而且与传统注射工艺相比，微泡注射工艺还具有以下优点：减少耗能36％左右；成型周期缩短20～50％；原材料消耗减少5～30％。微泡注射成型提供了传统注塑工艺所不具有的巨大能力，为开发新型塑料产品、优化注射工艺和降低产品成本开拓了广阔的空间。微孔塑料制品正被应用于许多工业领域，如航空航天、汽车、医药、电子、食品包装等行业，越来越多的塑料加工企业投入资金对现有的注射机进行改造，利用微孔注射工艺进行生产，提高企业的竞争力。
本文研究了微泡注射成型加工的基本原理和工艺过程，剖析了成型过程中微泡的成核、生长以及冷却定型机理；引入合理的假设，并进行必要的简化，建立了微泡生长和熔体流动的数学模型，并构造了有效算法，实现对微泡注射成型过程的数值模拟。主要内容包括：
1、探讨了超临界流体在聚合物中混合、扩散、完全溶解进入聚合物形成物理性质均一体系的过程；探讨了气泡成核机理，分析了气泡长大理论模型的发展，以及气泡的稳定与固化过程。
2、基于流体动力学和热力学理论，运用连续性方程、动量方程、菲克扩散定律以及亨利定律，描述微泡的流体动力学生长和扩散生长，建立微泡生长过程的数学模型。
3、计入微泡生长对熔体流动的驱动作用以及微泡对熔体粘度的影响，宏观上将成型过程视为单相流。基于粘性流体力学基本理论，考虑模具冷却效应，用连续性方程、动量方程和能量方程来描述成型过程中熔体的流动和传热，并与微泡生长方程耦合，建立微泡注射成型过程的数学模型。
4、微泡注射成型过程数学模型的数值求解。利用伽辽金加权余量法建立型腔内压力场求解的有限元方程，沿厚度和时间域差分建立温度场求解的差分方程，并对微泡生长方程进行差分离散。构造有效算法对这些方程进行求解，实现微泡注射成型过程的数值模拟。
Microcellular foams, characterized by cell size about 1μm～50μm and cell density about 10~9 cells/cm~3～10~(12) cells/cm~3, are drawing increased attention. This concept was based on the theory if a cellular structure could be develop where the bubble size was smaller than the flaws inherent in the polymer structure, the cell could not affect the mechanical properties, however, the cell will reduce the effect of the flaws inherent and stop the further development of the flaws under stress factor. Microcellular injection molding (also commercially known as the Mucell process) was invented by Massachusetts Institute of Technology (M.I.T.) and commercialized by Trexel. The first stage of the MuCell process is to inject supercritical carbon dioxide (CO_2) or nitrogen (N_2) into the barrel, create and maintain a single-phase solution in molten polymer. The second stage is to inject the single-phase into the mold quickly and then a large number of nucleation sites are formed by the sudden pressure drop. The third stage is bubble growth take place during the injection and solidification and the final shape of the part with uniform cell size and density is provided by the mold through solidification.
Microcellular plastic has many excellent performances. Compared to conventional injection molding, microcellular injection molding has many benefits as following: Power cost saving 36%; Significant cycle timer reductions 20-50%; Material reductions 5-30%. Microcellular injection molding will enlarge the field of developing new plastic product, optimizing the injection molding process and saving the cost. Microcellular plastic has been widely used in many fields such as avigation and spaceflight, motorcar, medicine, electron, packaging and so on. To improve the efficiency of manufacture and reduce the cost, more and more enterprises have took interest and attention to modify the injection machine for Mucell process.
This study presents the theory and process of microcellular injection molding and investigates the process of cell nucleation, cell growth and shaping. We introduce reasonable assumption and present a simulation model for microcellular injection molding based on the numerical algorithms. The main work of this paper include following parts:
1. Discuss the process of forming polymer/gas single-phase with supercritical fluid (SCF) mixing, dissolving and diffusing in polymer. Discuss and analyze the theory of bubble nucleation, the development of the model of bubble growth and solidification with the final shape.
2. Based on Hydrokinetics and Thermodynamics, a mathematic model was introduced that includes the energy equation, the continuity equation, momentum equation, and a group of equations that describe the mass diffusion of dissolved gas and growth of micro-cells in the microcellular injection molding.
3. Taking account of the effect of cell growth on melt flow and viscosity, we treat the microscopic multiphase fluid as a macroscopic single-phase fluid. The equations of continuity and momentum, as well as energy equation are employed to describe the flow and heat transfer in the simulation. The microscopic model of the cell is coupled with the macroscopic flow model to describe the microcellular injection molding.
4. Galerkin weighted residual method is employed to discretize the governing equation of pressure field and finite difference method is adopted to discretize the energy equations and the cell growth model. Numerical scheme is configured to solve those discrete equations to simulate the microcellular injection molding.
微孔制品不仅力学性能优异，而且与传统注射工艺相比，微泡注射工艺还具有以下优点：减少耗能36％左右；成型周期缩短20～50％；原材料消耗减少5～30％。微泡注射成型提供了传统注塑工艺所不具有的巨大能力，为开发新型塑料产品、优化注射工艺和降低产品成本开拓了广阔的空间。微孔塑料制品正被应用于许多工业领域，如航空航天、汽车、医药、电子、食品包装等行业，越来越多的塑料加工企业投入资金对现有的注射机进行改造，利用微孔注射工艺进行生产，提高企业的竞争力。
本文研究了微泡注射成型加工的基本原理和工艺过程，剖析了成型过程中微泡的成核、生长以及冷却定型机理；引入合理的假设，并进行必要的简化，建立了微泡生长和熔体流动的数学模型，并构造了有效算法，实现对微泡注射成型过程的数值模拟。主要内容包括：
1、探讨了超临界流体在聚合物中混合、扩散、完全溶解进入聚合物形成物理性质均一体系的过程；探讨了气泡成核机理，分析了气泡长大理论模型的发展，以及气泡的稳定与固化过程。
2、基于流体动力学和热力学理论，运用连续性方程、动量方程、菲克扩散定律以及亨利定律，描述微泡的流体动力学生长和扩散生长，建立微泡生长过程的数学模型。
3、计入微泡生长对熔体流动的驱动作用以及微泡对熔体粘度的影响，宏观上将成型过程视为单相流。基于粘性流体力学基本理论，考虑模具冷却效应，用连续性方程、动量方程和能量方程来描述成型过程中熔体的流动和传热，并与微泡生长方程耦合，建立微泡注射成型过程的数学模型。
4、微泡注射成型过程数学模型的数值求解。利用伽辽金加权余量法建立型腔内压力场求解的有限元方程，沿厚度和时间域差分建立温度场求解的差分方程，并对微泡生长方程进行差分离散。构造有效算法对这些方程进行求解，实现微泡注射成型过程的数值模拟。
Microcellular foams, characterized by cell size about 1μm～50μm and cell density about 10~9 cells/cm~3～10~(12) cells/cm~3, are drawing increased attention. This concept was based on the theory if a cellular structure could be develop where the bubble size was smaller than the flaws inherent in the polymer structure, the cell could not affect the mechanical properties, however, the cell will reduce the effect of the flaws inherent and stop the further development of the flaws under stress factor. Microcellular injection molding (also commercially known as the Mucell process) was invented by Massachusetts Institute of Technology (M.I.T.) and commercialized by Trexel. The first stage of the MuCell process is to inject supercritical carbon dioxide (CO_2) or nitrogen (N_2) into the barrel, create and maintain a single-phase solution in molten polymer. The second stage is to inject the single-phase into the mold quickly and then a large number of nucleation sites are formed by the sudden pressure drop. The third stage is bubble growth take place during the injection and solidification and the final shape of the part with uniform cell size and density is provided by the mold through solidification.
Microcellular plastic has many excellent performances. Compared to conventional injection molding, microcellular injection molding has many benefits as following: Power cost saving 36%; Significant cycle timer reductions 20-50%; Material reductions 5-30%. Microcellular injection molding will enlarge the field of developing new plastic product, optimizing the injection molding process and saving the cost. Microcellular plastic has been widely used in many fields such as avigation and spaceflight, motorcar, medicine, electron, packaging and so on. To improve the efficiency of manufacture and reduce the cost, more and more enterprises have took interest and attention to modify the injection machine for Mucell process.
This study presents the theory and process of microcellular injection molding and investigates the process of cell nucleation, cell growth and shaping. We introduce reasonable assumption and present a simulation model for microcellular injection molding based on the numerical algorithms. The main work of this paper include following parts:
1. Discuss the process of forming polymer/gas single-phase with supercritical fluid (SCF) mixing, dissolving and diffusing in polymer. Discuss and analyze the theory of bubble nucleation, the development of the model of bubble growth and solidification with the final shape.
2. Based on Hydrokinetics and Thermodynamics, a mathematic model was introduced that includes the energy equation, the continuity equation, momentum equation, and a group of equations that describe the mass diffusion of dissolved gas and growth of micro-cells in the microcellular injection molding.
3. Taking account of the effect of cell growth on melt flow and viscosity, we treat the microscopic multiphase fluid as a macroscopic single-phase fluid. The equations of continuity and momentum, as well as energy equation are employed to describe the flow and heat transfer in the simulation. The microscopic model of the cell is coupled with the macroscopic flow model to describe the microcellular injection molding.
4. Galerkin weighted residual method is employed to discretize the governing equation of pressure field and finite difference method is adopted to discretize the energy equations and the cell growth model. Numerical scheme is configured to solve those discrete equations to simulate the microcellular injection molding.
引文
[1] 吴舜英，徐敬一．泡沫塑料成型．北京：化学工业出版社，1999．
[2] J.E Martini, N.P Sun and FA Waldman. Microcelluar closed cell foamand their method of manufacture[P].US Patent. 4473 665,1984.
[3] J. W. Falconter, W Nazarow, M J Baker, et al. Lower Density Disc Shape Microcellular Polymeric Foams[J]. Journal Cellular Plastics, 1997, 33 : 12～19
[4] L.M. Matuana, C.B. Park, J. J. Babtinecz. Structures and Mechanical Properties of Microcellular Foamed Polyvinyl Chloride[J]. Cellular Polymers, 1998, 17(1):1～16.
[5] M. Shibao, D. F. Baldwin. The Viscoelastic Behavior of Microcellular Plastics with Varying Cell Size[J]. Ploym Eng Sic, 1995, 35:1387～1395
[6] J.D. Gaspari. Microcellular Foams[J]. Plastics Technology, 1993, (2): 63～65.
[7] J.H Aubert, R.L Clough. Low-density, Microcellular Polystyrene Foams[J]. Polymer, 1985,26(13):2047
[8] S.K Goel , E.J Beckman. Generation of Microcellular Polymeric Foams Using Supercritical Carbon-Dioxide 2 . Cell-Growth and Skin Formation . Polymer Engineering and Science, 1994 Vol.34, No. 14, 1148-1156,
[9] W.E.P Raj, M. Sasthav, H.M. Cheung. Microcellular Polymeric Materials from Micro-emulsions: Control of Microstructure and Morphology, J.appl. Polym. Sci., 1993,47:499.
[10] D.J Dixon, G. Lunabarcenas, K.P Johnston. Microcellular Microspheres and Microballoons by Precipitation with a Vapor-Liquid Compressed Fluid Antisolvent. Polymer, 1994 Vol.35, No. 18, 3998-4005,
[11] Baldwin D F et al. Polym Eng Sci, 1996, 36(11):1473
[12] Michaeli, W. and Habibi-Naini, S. Saving Time by Foam Injection Molding. ANTEC. 2004, vol. 1: 812-816
[13] Michaeli, W. and Habibi-Naini, S. Injection Moulding of Microcellular Foams: The Designs behind the Methods. Kunststoffe, Plast Europe 2002, vol. 92, 16-18
[14] Mapleston, R, Modern Plastics, 2002, 11, p. 31
[15] www.Trexel.com
[16] Durrill, P.L., Griskey, R.G., Diffusion and solution of gases in thermally softened or molten polymers . Am Inst Chem Eng J. 1966, p. 1147
[17] Park, C. B. , Ph. D. Dissertation, Massachusetts Institute of Technology, Cambridge, MA (1993)
[18] Handa Y P, Zhang Z Y. Sorption, diffusion, and dilation in linear and branched polycarbonate-CO2 systems in relation to solid state processing of microcellular foams. Cell Polym, 2002, 21 (4): 221-235
[19] Cardona, Juan.;,M.S.Eng.Short Screw Designs for the MuCell Process.University of Massachusetts Lowell. 2004.AAI1419234
[20] Juan P .Hernandez, Alexander Chandra , Andreas Winardi, Lih -sheng Turng andTim Osswald. Moldeling cell nucleation during microcellular injection molding. ANTER 2003,2210-2214.
[21] Amon, M. and C.D. Denson, A Study of the Dynamics of Foam Growth: Analysis of the Growth of Closely Spaced Spherical Bubbles. Polymer Engineering and Science, 1984. 24(13): p. 1026-1034.
[22]Amon, M. and C.D. Denson, A Study of the Dynamics of FoamGrowth:Simplified Analysis and Experimental Results for Bulk Density in StructureFoam Molding. Polymer Engineering and Science, 1986. 26(3): p. 255-67.
[23] J.L. Katz and H. Wiedersich. Effect of Insoluble Gas Molecules on Nucleation of Voids in Materials Supersaturated with Both Vacancies and Interstitials. Journal of Nuclear Materials. 1973, 46(1):41～45
[24] M. Blander and J. L Katz. Bubble Nucleation in Liquids. AICHE Journal. 1975, 21(5):833～848
[25] M. A. Shafi , K. Joshi and R. W. Flumerfelt. Bubble Size Distributions in Freely Expanded Polymer Foams. Chemical Engineering Science. Vol. 52. No. 4, pp 635-644, 1997
[26] E. F Abraham. Homogeneous Nucleation. New York : Academic Press, 1974
[27] Hold P. Mixing of Polymers-an Overview, Part I , Adv Polym Techn, 1983,2(2):114
[28] Park C B, Sub N P. Rapid Polymer/Gas Solution Formation for Continuous Production of Microcellular Plastics. Journal of Manufacturing Science and Engineering, 1996, 118:639
[29]李开林，彭玉成，颜家华．微孔发泡塑料挤出成型中聚合物—气体均相体系形成研究。中国塑料，1998．12(6)：63～67
[30] 高长云，周南桥，彭响方．微孔发泡过程中聚合物／超临界CO2均相体系形成的研究。工程塑料应用，2004，31(10)：32～34
[31] Handa Y P, Wong B, Zhang Z. Some Thermodynamic and Kinetic Properties of the System PETG-CO2, and Morphological Characteristics of the CO2-Blown PETG Foams, Polymer Engineering and Science, 1999, 39 (1):55～61
[32] P G Hall and H. F Stoeckli. Adsorption of Nitrogen, N-butane and Neo-Pentane on Chlorohydrocarbon Polymers, Trans Faraday, 1969, 65 (564):3334-3340
[33] H. B Hopfenberg, R. H Holley. Effect of Pemetrant Activity and Temperature on Anomalous Diffusion of Hydrocardons and Solvent Crazing in Polystyrene, Polymer Engineering and Science, 1969, 9 (4):242-249
[34] R. H Hansen. Production of Fine Cells in the Extrusion of Foams, Journal of SPE, 1962, 18 (1):77～82
[35] R. H Hansen and W. M Martin. Novel Methods for the Production of Foamed Polymer Ⅱ Nucleation of Dissolved Gas by Finely Divided Metals. Journal of Polymer Science, Part B : Polymer letters. 1965, 3:325～330
[36] N.S Deshpande and M. Barigou. Performance Characteristics of Novel Mechanical Foam Breakers in a Stirred Tank Reactor, Journal of Chemical Technology and Biotechnology, 1999,74(10):979～987
[37] G. Djelveh, J. B Gros and J. F Cornet, Foaming Process Analysis for a Stirred Column with a Narrow Annular Region, Chemical Engineering Science, 1998,53(17):3157～3160
[38] J. E Martini, N. P Suh. Nucleation of Microcellular Foam: Theory and Practice. Polymer Engineering and Science, 1987,27(7):485
[39] Epstein PS and Plesset MS, On the Stability of Gas Bubble in Liquid-Gas Solution, J. Chem. Phys, 1950, 18:1505-1513
[40] Gent AN and Tompkins DA, Nucleation and Growth of Gas Bubbles in Elastomers, J. Appl. Phys., 1969, 40:2520-2525
[41] Vilamizar CA and Han CD, Studies on Structural Foam Processing II. Bubble Dynamics in Foam Injection Molding, Poly. Eng. Sci., 1978, 18(9):699～710
[42] Barlow EJ and Langlois WE., Diffusion of Gas from a Liquid into an Expanding Bubble, IBM J. Res. Develop., 1962, 7:329-337
[43] Han CD and Yoo HJ, Studies on structural Foam Processing IV. Bubble Growth During Mold Filling, Poly. Eng. Sci., 1981, 21(9):518-533
[44] Szekely J and Martins GP, Non-Equilibrium Effects in the Growth of SphericalGas Bubbles Due to Solute Diffusion, Chem. Eng. Sci., 1971, 26(1):147-154
[45] Patel RD, Bubble Growth in a Viscous Newtonian Liquid, Chem. Eng. Sci., 1980, 35(11):2352～2358
[46] Han CD and Ma C-Y, Foam Extrusion Characteristics of Thermoplastic Resin with Fluoracarbon Blowing Agent I :Low-Density Polyethylene Foam Extrusion, J.Appl. Poly. Sci, 1983, 28(9):2961～2982
[47] Papanastasiou AC, Scriven LE and Macosko CW, Bubble Growth and Collapse in Viscoelastic Liquids Analyzed, J. Non-Newtonian Fluid Mechanics, 1984,16:53-57
[49] Arefmanesh A, Advani SG and Michaelides EF, A Numerical Study of Bubble Growth During Low Pressure Structural Foam Molding Process, oly. Eng. Sci., 1990, 30(20):1330～1337
[50] Arefmanesh A and Advani SG, Diffusion-Induced Growth of Gas Bubble in a Vicoelastic Fluid, Rheol. Acta, 1991, 30(3):274～283
[51] Goel SK and Beckman EJ, Generation of Microcellular Polymeric Foams Using Supercritical Carbon Dioxide. II :Cell Growth and Skin Formation, Poly. Eng. Sci., 1944, 34(14):1148～1156
[52] Goel SK and Beckman EJ, Nucleation and Growth in Microcellular Materials: Supercritical CO_2 as Foaming Agent, AIChe Journal, 1995, 41(2):357～367
[53] Collias DI and Baird DG, Tensile Toughness of Microcellular Foams of Polystyrene, Styrene-Acrylonitrile Copolymer, and Polycarbonate, and the Effect of Dissolved Gas on the Tensile Toughness of the Same Polymer Matrices and Microcellular Foams, Poly. Eng. Sci., 1995, 35(14):1167～1177
[54] 田森平，吴舜英．气泡长大过程中的数学模型及简化，合成材料老化与应用，1999，(1)：1～4
[55] S. Han and R Kennedy, Numerical Analysis of Microcellular Injection Molding, Journal of Cellular Plastics, 2003 (39):475～485
[56] Street, J. R., Arthur, L.F. and Reiss, L.P Dynamics of Phase Growth in Viscous, Non-Newtonian Liquids. Ind. Eng. Chem. 1971, 10:54-64
[57] Hobbs, S.Y. The Application of Structure Property Studies to Structural Foams. Poly. Eng. Sci. 1975, 15, 854-862
[58] Hobbs, S.Y. Bubble Growth in Thermoplastic Structural Foams. Poly. Eng. Sci. 1976, 16, 854-862
[59] Saeed Doroudiani, Chul B. Park, Mark T. Kortschot. Effect of the Crystallinity and Morphology on the Microcellular Foam Structure of Semicrystalline Polymers, Poly. Eng. Sci. 1996, vol36, 22:2645-2662
[60] 章梓雄，董曾男．粘性流体力学[M]．北京：清华大学出版社，1999．
[61] C.A Hieber, S.F Shen. A Finite-Element/finite-Difference Simulation of the Injection-molding Filling Process[J]. Journal of Non-Newtonian Fluid Mechanics, 7(1980): 1-32
[62] Kennedy P. Flow Analysis of Injection Molds. New York: Hanser Publisher, 1995
[63] 王勖成，邵敏．有限单元法基本原理和数值方法[M]．北京：清华大学出版社，1996．
[2] J.E Martini, N.P Sun and FA Waldman. Microcelluar closed cell foamand their method of manufacture[P].US Patent. 4473 665,1984.
[3] J. W. Falconter, W Nazarow, M J Baker, et al. Lower Density Disc Shape Microcellular Polymeric Foams[J]. Journal Cellular Plastics, 1997, 33 : 12～19
[4] L.M. Matuana, C.B. Park, J. J. Babtinecz. Structures and Mechanical Properties of Microcellular Foamed Polyvinyl Chloride[J]. Cellular Polymers, 1998, 17(1):1～16.
[5] M. Shibao, D. F. Baldwin. The Viscoelastic Behavior of Microcellular Plastics with Varying Cell Size[J]. Ploym Eng Sic, 1995, 35:1387～1395
[6] J.D. Gaspari. Microcellular Foams[J]. Plastics Technology, 1993, (2): 63～65.
[7] J.H Aubert, R.L Clough. Low-density, Microcellular Polystyrene Foams[J]. Polymer, 1985,26(13):2047
[8] S.K Goel , E.J Beckman. Generation of Microcellular Polymeric Foams Using Supercritical Carbon-Dioxide 2 . Cell-Growth and Skin Formation . Polymer Engineering and Science, 1994 Vol.34, No. 14, 1148-1156,
[9] W.E.P Raj, M. Sasthav, H.M. Cheung. Microcellular Polymeric Materials from Micro-emulsions: Control of Microstructure and Morphology, J.appl. Polym. Sci., 1993,47:499.
[10] D.J Dixon, G. Lunabarcenas, K.P Johnston. Microcellular Microspheres and Microballoons by Precipitation with a Vapor-Liquid Compressed Fluid Antisolvent. Polymer, 1994 Vol.35, No. 18, 3998-4005,
[11] Baldwin D F et al. Polym Eng Sci, 1996, 36(11):1473
[12] Michaeli, W. and Habibi-Naini, S. Saving Time by Foam Injection Molding. ANTEC. 2004, vol. 1: 812-816
[13] Michaeli, W. and Habibi-Naini, S. Injection Moulding of Microcellular Foams: The Designs behind the Methods. Kunststoffe, Plast Europe 2002, vol. 92, 16-18
[14] Mapleston, R, Modern Plastics, 2002, 11, p. 31
[15] www.Trexel.com
[16] Durrill, P.L., Griskey, R.G., Diffusion and solution of gases in thermally softened or molten polymers . Am Inst Chem Eng J. 1966, p. 1147
[17] Park, C. B. , Ph. D. Dissertation, Massachusetts Institute of Technology, Cambridge, MA (1993)
[18] Handa Y P, Zhang Z Y. Sorption, diffusion, and dilation in linear and branched polycarbonate-CO2 systems in relation to solid state processing of microcellular foams. Cell Polym, 2002, 21 (4): 221-235
[19] Cardona, Juan.;,M.S.Eng.Short Screw Designs for the MuCell Process.University of Massachusetts Lowell. 2004.AAI1419234
[20] Juan P .Hernandez, Alexander Chandra , Andreas Winardi, Lih -sheng Turng andTim Osswald. Moldeling cell nucleation during microcellular injection molding. ANTER 2003,2210-2214.
[21] Amon, M. and C.D. Denson, A Study of the Dynamics of Foam Growth: Analysis of the Growth of Closely Spaced Spherical Bubbles. Polymer Engineering and Science, 1984. 24(13): p. 1026-1034.
[22]Amon, M. and C.D. Denson, A Study of the Dynamics of FoamGrowth:Simplified Analysis and Experimental Results for Bulk Density in StructureFoam Molding. Polymer Engineering and Science, 1986. 26(3): p. 255-67.
[23] J.L. Katz and H. Wiedersich. Effect of Insoluble Gas Molecules on Nucleation of Voids in Materials Supersaturated with Both Vacancies and Interstitials. Journal of Nuclear Materials. 1973, 46(1):41～45
[24] M. Blander and J. L Katz. Bubble Nucleation in Liquids. AICHE Journal. 1975, 21(5):833～848
[25] M. A. Shafi , K. Joshi and R. W. Flumerfelt. Bubble Size Distributions in Freely Expanded Polymer Foams. Chemical Engineering Science. Vol. 52. No. 4, pp 635-644, 1997
[26] E. F Abraham. Homogeneous Nucleation. New York : Academic Press, 1974
[27] Hold P. Mixing of Polymers-an Overview, Part I , Adv Polym Techn, 1983,2(2):114
[28] Park C B, Sub N P. Rapid Polymer/Gas Solution Formation for Continuous Production of Microcellular Plastics. Journal of Manufacturing Science and Engineering, 1996, 118:639
[29]李开林，彭玉成，颜家华．微孔发泡塑料挤出成型中聚合物—气体均相体系形成研究。中国塑料，1998．12(6)：63～67
[30] 高长云，周南桥，彭响方．微孔发泡过程中聚合物／超临界CO2均相体系形成的研究。工程塑料应用，2004，31(10)：32～34
[31] Handa Y P, Wong B, Zhang Z. Some Thermodynamic and Kinetic Properties of the System PETG-CO2, and Morphological Characteristics of the CO2-Blown PETG Foams, Polymer Engineering and Science, 1999, 39 (1):55～61
[32] P G Hall and H. F Stoeckli. Adsorption of Nitrogen, N-butane and Neo-Pentane on Chlorohydrocarbon Polymers, Trans Faraday, 1969, 65 (564):3334-3340
[33] H. B Hopfenberg, R. H Holley. Effect of Pemetrant Activity and Temperature on Anomalous Diffusion of Hydrocardons and Solvent Crazing in Polystyrene, Polymer Engineering and Science, 1969, 9 (4):242-249
[34] R. H Hansen. Production of Fine Cells in the Extrusion of Foams, Journal of SPE, 1962, 18 (1):77～82
[35] R. H Hansen and W. M Martin. Novel Methods for the Production of Foamed Polymer Ⅱ Nucleation of Dissolved Gas by Finely Divided Metals. Journal of Polymer Science, Part B : Polymer letters. 1965, 3:325～330
[36] N.S Deshpande and M. Barigou. Performance Characteristics of Novel Mechanical Foam Breakers in a Stirred Tank Reactor, Journal of Chemical Technology and Biotechnology, 1999,74(10):979～987
[37] G. Djelveh, J. B Gros and J. F Cornet, Foaming Process Analysis for a Stirred Column with a Narrow Annular Region, Chemical Engineering Science, 1998,53(17):3157～3160
[38] J. E Martini, N. P Suh. Nucleation of Microcellular Foam: Theory and Practice. Polymer Engineering and Science, 1987,27(7):485
[39] Epstein PS and Plesset MS, On the Stability of Gas Bubble in Liquid-Gas Solution, J. Chem. Phys, 1950, 18:1505-1513
[40] Gent AN and Tompkins DA, Nucleation and Growth of Gas Bubbles in Elastomers, J. Appl. Phys., 1969, 40:2520-2525
[41] Vilamizar CA and Han CD, Studies on Structural Foam Processing II. Bubble Dynamics in Foam Injection Molding, Poly. Eng. Sci., 1978, 18(9):699～710
[42] Barlow EJ and Langlois WE., Diffusion of Gas from a Liquid into an Expanding Bubble, IBM J. Res. Develop., 1962, 7:329-337
[43] Han CD and Yoo HJ, Studies on structural Foam Processing IV. Bubble Growth During Mold Filling, Poly. Eng. Sci., 1981, 21(9):518-533
[44] Szekely J and Martins GP, Non-Equilibrium Effects in the Growth of SphericalGas Bubbles Due to Solute Diffusion, Chem. Eng. Sci., 1971, 26(1):147-154
[45] Patel RD, Bubble Growth in a Viscous Newtonian Liquid, Chem. Eng. Sci., 1980, 35(11):2352～2358
[46] Han CD and Ma C-Y, Foam Extrusion Characteristics of Thermoplastic Resin with Fluoracarbon Blowing Agent I :Low-Density Polyethylene Foam Extrusion, J.Appl. Poly. Sci, 1983, 28(9):2961～2982
[47] Papanastasiou AC, Scriven LE and Macosko CW, Bubble Growth and Collapse in Viscoelastic Liquids Analyzed, J. Non-Newtonian Fluid Mechanics, 1984,16:53-57
[49] Arefmanesh A, Advani SG and Michaelides EF, A Numerical Study of Bubble Growth During Low Pressure Structural Foam Molding Process, oly. Eng. Sci., 1990, 30(20):1330～1337
[50] Arefmanesh A and Advani SG, Diffusion-Induced Growth of Gas Bubble in a Vicoelastic Fluid, Rheol. Acta, 1991, 30(3):274～283
[51] Goel SK and Beckman EJ, Generation of Microcellular Polymeric Foams Using Supercritical Carbon Dioxide. II :Cell Growth and Skin Formation, Poly. Eng. Sci., 1944, 34(14):1148～1156
[52] Goel SK and Beckman EJ, Nucleation and Growth in Microcellular Materials: Supercritical CO_2 as Foaming Agent, AIChe Journal, 1995, 41(2):357～367
[53] Collias DI and Baird DG, Tensile Toughness of Microcellular Foams of Polystyrene, Styrene-Acrylonitrile Copolymer, and Polycarbonate, and the Effect of Dissolved Gas on the Tensile Toughness of the Same Polymer Matrices and Microcellular Foams, Poly. Eng. Sci., 1995, 35(14):1167～1177
[54] 田森平，吴舜英．气泡长大过程中的数学模型及简化，合成材料老化与应用，1999，(1)：1～4
[55] S. Han and R Kennedy, Numerical Analysis of Microcellular Injection Molding, Journal of Cellular Plastics, 2003 (39):475～485
[56] Street, J. R., Arthur, L.F. and Reiss, L.P Dynamics of Phase Growth in Viscous, Non-Newtonian Liquids. Ind. Eng. Chem. 1971, 10:54-64
[57] Hobbs, S.Y. The Application of Structure Property Studies to Structural Foams. Poly. Eng. Sci. 1975, 15, 854-862
[58] Hobbs, S.Y. Bubble Growth in Thermoplastic Structural Foams. Poly. Eng. Sci. 1976, 16, 854-862
[59] Saeed Doroudiani, Chul B. Park, Mark T. Kortschot. Effect of the Crystallinity and Morphology on the Microcellular Foam Structure of Semicrystalline Polymers, Poly. Eng. Sci. 1996, vol36, 22:2645-2662
[60] 章梓雄，董曾男．粘性流体力学[M]．北京：清华大学出版社，1999．
[61] C.A Hieber, S.F Shen. A Finite-Element/finite-Difference Simulation of the Injection-molding Filling Process[J]. Journal of Non-Newtonian Fluid Mechanics, 7(1980): 1-32
[62] Kennedy P. Flow Analysis of Injection Molds. New York: Hanser Publisher, 1995
[63] 王勖成，邵敏．有限单元法基本原理和数值方法[M]．北京：清华大学出版社，1996．