高聚物熔体在微流道内流变行为的研究
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摘要
随着微机电系统的快速发展,微注塑成型制品广泛应用于生产生活的各个领域,因此急需开发出适用于微注塑成型过程的数值模拟软件,而确定高聚物熔体在微尺度下的流变行为对于模拟结果的准确性至关重要。研究表明,高聚物熔体在微尺度下的流变行为与在宏观尺度下有很大不同,一些在宏观尺度下被忽略的因素,如壁面滑移、表面张力、微观粘度等,在微尺度下可能会有显著的影响。本文引入壁面滑移模型和微观粘度模型对高聚物熔体在微流道内的等温稳态和非等温非稳态流动过程进行数值模拟,主要工作及结论如下：
1.借鉴宏观尺度下的壁面滑移理论,探讨了壁面滑移产生的机理、壁面滑移速率的测定方法和壁面滑移模型的建立,分析了高聚物熔体在微尺度下易发生壁面滑移现象的原因。
2.基于粘性流体力学基本方程,结合高聚物熔体在微流道内的流动特点,经过合理的假设和简化,建立了高聚物熔体在微流道内流动过程的数学模型。
3.对高聚物熔体在微流道内的等温稳态流动进行数值模拟,分别考虑了微观粘度、壁面滑移以及两者共同作用时的影响。模拟结果表明,微观粘度效应使壁面剪切应力升高,而壁面滑移效应使壁面剪切应力降低。在较高表观剪切速率下,以壁面滑移的影响为主,在较低的表观剪切速率下,受到两者共同作用的影响。
4.利用混合有限元／有限差分／控制体积方法实现高聚物熔体在微流道内非等温非稳态流动过程的数值模拟。分析了不同温度场和压力场下,壁面滑移和微观粘度对流动过程的影响。模拟结果表明,在一定压力范围内,壁面剪切应力随着流道内压力的增加而增大。当微流道尺寸小于10μm时,可看作是在壁面温度下的等温流动过程,因此壁面温度必须高于高聚物的熔融温度。同时发现,提高表观剪切速率有助于高聚物熔体在微流道内的流动。
With the rapid development of MEMS, micro-injection molding is widely used in many fields. It becomes more and more important to develop suitable simulation software for micro-injection molding. Determination of the rheological behavior of the polymer melt within micro-channels is vital for the accurate simulation modeling of micro-injection molding. There are evidences indicating that polymeric flows in micro-channels differ significantly from those in macro-channels. Some factors that ignored in macro-scale may have significant effect in micro-scale, such as wall slip, surface tension, micro-viscosity etc. In the paper, slip models and micro-viscosity model were introduced to simulate the flow behavior of polymer melt in micro-channels under the isothermal-steady-state and non-isothermal-unsteady-state situations. The major work and main conclusions are as following:
1. On the base of macro-scale wall slip theories, the wall slip mechanisms, slip determination techniques and wall slip models were investigated. And analyzed the reasons why wall slip would easily occur in micro-channels.
2. Based on the viscous fluid mechanics and flow characteristics of polymer melt in micro-channels, the reasonable simplification and hypothesis were introduced, and the mathematical model of polymer flow behavior in micro-channels was established.
3. The isothermal-steady-state flow of polymer melt in micro-channels was analyzed. The micro-viscosity effect, the wall slip effect and the combined effect of two factors on isothermal-steady-state flow were investigated. The results showed that both factors were important to the flow behaviors in micro-channels, Micro-viscosity effect increased the wall shear stress and wall slip effect released the wall shear stress. When the apparent wall shear rate is high, wall slip plays a main role in the flow behavior. When the apparent shear rate is low, the flow behavior is determined by the combined effect of wall slip and micro-viscosity.
4. Numerical simulation of non-isothermal and unsteady-state flow was implemented using Finite Element/Finite Difference/Control Volume method. The effects of wall slip and micro-viscosity on the flow behaviors were investigated in different temperature and pressure fields. The simulation results show that, due to the influence of pressure on wall slip velocity, the apparent wall shear stress increased with the increase of pressure within a certain range. When micro-channel is smaller than 10μm, it can be seen as isothermal flow at the wall temperature, so the wall temperature must be higher than the melt temperature. Also found that the flow became easier when apparent shear rate was increased.
1.借鉴宏观尺度下的壁面滑移理论,探讨了壁面滑移产生的机理、壁面滑移速率的测定方法和壁面滑移模型的建立,分析了高聚物熔体在微尺度下易发生壁面滑移现象的原因。
2.基于粘性流体力学基本方程,结合高聚物熔体在微流道内的流动特点,经过合理的假设和简化,建立了高聚物熔体在微流道内流动过程的数学模型。
3.对高聚物熔体在微流道内的等温稳态流动进行数值模拟,分别考虑了微观粘度、壁面滑移以及两者共同作用时的影响。模拟结果表明,微观粘度效应使壁面剪切应力升高,而壁面滑移效应使壁面剪切应力降低。在较高表观剪切速率下,以壁面滑移的影响为主,在较低的表观剪切速率下,受到两者共同作用的影响。
4.利用混合有限元／有限差分／控制体积方法实现高聚物熔体在微流道内非等温非稳态流动过程的数值模拟。分析了不同温度场和压力场下,壁面滑移和微观粘度对流动过程的影响。模拟结果表明,在一定压力范围内,壁面剪切应力随着流道内压力的增加而增大。当微流道尺寸小于10μm时,可看作是在壁面温度下的等温流动过程,因此壁面温度必须高于高聚物的熔融温度。同时发现,提高表观剪切速率有助于高聚物熔体在微流道内的流动。
With the rapid development of MEMS, micro-injection molding is widely used in many fields. It becomes more and more important to develop suitable simulation software for micro-injection molding. Determination of the rheological behavior of the polymer melt within micro-channels is vital for the accurate simulation modeling of micro-injection molding. There are evidences indicating that polymeric flows in micro-channels differ significantly from those in macro-channels. Some factors that ignored in macro-scale may have significant effect in micro-scale, such as wall slip, surface tension, micro-viscosity etc. In the paper, slip models and micro-viscosity model were introduced to simulate the flow behavior of polymer melt in micro-channels under the isothermal-steady-state and non-isothermal-unsteady-state situations. The major work and main conclusions are as following:
1. On the base of macro-scale wall slip theories, the wall slip mechanisms, slip determination techniques and wall slip models were investigated. And analyzed the reasons why wall slip would easily occur in micro-channels.
2. Based on the viscous fluid mechanics and flow characteristics of polymer melt in micro-channels, the reasonable simplification and hypothesis were introduced, and the mathematical model of polymer flow behavior in micro-channels was established.
3. The isothermal-steady-state flow of polymer melt in micro-channels was analyzed. The micro-viscosity effect, the wall slip effect and the combined effect of two factors on isothermal-steady-state flow were investigated. The results showed that both factors were important to the flow behaviors in micro-channels, Micro-viscosity effect increased the wall shear stress and wall slip effect released the wall shear stress. When the apparent wall shear rate is high, wall slip plays a main role in the flow behavior. When the apparent shear rate is low, the flow behavior is determined by the combined effect of wall slip and micro-viscosity.
4. Numerical simulation of non-isothermal and unsteady-state flow was implemented using Finite Element/Finite Difference/Control Volume method. The effects of wall slip and micro-viscosity on the flow behaviors were investigated in different temperature and pressure fields. The simulation results show that, due to the influence of pressure on wall slip velocity, the apparent wall shear stress increased with the increase of pressure within a certain range. When micro-channel is smaller than 10μm, it can be seen as isothermal flow at the wall temperature, so the wall temperature must be higher than the melt temperature. Also found that the flow became easier when apparent shear rate was increased.
引文
[1]Julien Giboz, Thierry Copponnex, Patrice Mele.Microinjection molding of thermoplastic polymers:a review. J. Micromech. Microeng,2007,17:96～109
[2]M Heckele,W K Schomburg.Review on micro molding of thermoplastic polymers. J.Micromech. Microeng,2004,14:1～14
[3]Whiteside B R, Martyn M T, Coates P D, et al. Micromoulding:process characteristics and product properties. Plast. Rubber Compos,2003,32:231～239
[4]Ruprecht R,Gietzelt T,Mueller K,et al.Injection molding of microstructured components from plastics,metals and ceramics.Microsyst.Technol,2002,8:351～358
[5]蒋炳炎,谢磊,杜雪.微注射成型机发展现状与展望.中国塑料,2004,Vol.18(9)6-11
[6]蒋炳炎,沈龙江,彭华建.注射成型中的变模温控制技术.中国塑料,2006,Vol.20(3)99-102
[7]王雷刚,倪雪峰,黄瑶等.微注射成型技术的发展与展望.现代塑料加工应用,2007,19(1)：55-58
[8]Takanori Katoh, Ryuichi Tokuno, Yanping Zhang, et al.Micro injection molding for mass production using LIGA mold inserts. Microsyst Technol (2008) 14:1507～1514
[9]Piotter V,Hanemann T,Ruprecht R, et al.Injection molding and related techniques for fabrication of microstructures. Microsys. Tech,1997,3(3):129～133
[10]Zhao J, Mayes R H, Chen G, et al. Effects of process parameters on the micro molding process. Poly.Eng.Sci,2003,43 (9):1542～1554
[11]Kukla C.Micro injection molding. Proceeding of The 20d ESAFORM. Conference on Material Forming, Liege,2001:81～84
[12]卢振,张凯峰.微注射成型聚丙烯微阵列充填与形态结构.纳米技术与精密工程,2007,Vol.5(4)：239～242
[13]庄俭,吴大鸣,赵中里等.微注射成型工艺的实验研究.化工学报,2009,Vol.60(4)：1040-1045
[14]卢振,张开峰.微注射成形制品质量影响因素分析.机械工程学报,2009, Vol.45(12)：295～299
[15]ShenY K, Wu W Y, An analysis of the three-dimensional micro-injection molding. Int.Comm. Heat Mass Transfer,2002,29(3):423～431
[16]Shen Y K,, Yeh S L, Chen S H. Three-dimension non-newtonian computations of micro-injection molding with the Finite Element Method. Int Comm. Heat Mass Transfer, 2002,29(5):643～652
[17]Donggang Yao, Byung Kim. Simulation of the filling process in micro channels for polymeric materials. J. Micromech Microeng,2002,12:604～616
[18]Yu L, Kuo C G, Lee L J, Keolling K W, et al.Experimental investigation and numerical simulation of injection molding with micro-features. Polym. Eng. Sci,2002,42:871～86
[19]Juang Y J, Lee L, Koelling K W. Hot embossing in microfabrication. Part Ⅱ:Rheological characterization and process analysis. Polym. Eng. Sci,2002,42:551～66
[20]H. L. Zhang, N. S. Ong, Y. C. Lam. Mold surface routhness effects on cavity filling of polymer melt in micro injection molding. Int J Adv Manuf Technol,2008,37:1105～1112
[21]Chen. S. C.,Tsai. R. J.,Chien. R. D. Study on the rheological behavior of polymer melt for micro molding. Annual Technical Conference,2005,2:230～234
[22]Wei Cao, Ole Hassager, Yanwei Zhang. Surface tension effect on micro injection molding. Proceeding of the Polymer Processing Society 24th Annual Meeting PPS.2008(7)
[23]W. B. Yong, Simulation of the filling process in molding components with micro channels, Microsystem Technologies,11 (2005)410-415.
[24]Eringen A C and Okada 1995 A lubrication theory for fluids with microstructure int.J.Eng.sci.332297-308.
[25]Cohen Y, Metzner A B.Apparent slip flow of polymer solution. J. Rheo,1985,29:67～ 102
[26]Lau H C.A model for adhesive failure of viscoelastic fluids during flow. J.Rheol,1986,30: 193-206
[27]Ramamurthy A V. Wall slip in viscous fluids and influence of material construction. J.Rheol. 1986,30:337～357
[28]Hatzikiriakos S G, Dealy J M. Wall slip of molten high density polyethylene:I. Sliding plate rheometer studies. J.Rheol,1991,35:497～523
[29]Rosenbaum E E, Hatzikiriakos S G. Wall slip in the capillary flow of molten polymers subject to viscous heating.AlChE J,1997,43:598～608
[30]Henson D J,Mackay M E.Effect of gap on the viscosity of monodisperse polystyrene melts: slip effects.J.Rheol,1995,39:359～373
[31]Awati K M,Park Y,Weisser E,Mackay M E.Wall slip and shear stresses of polymer melts at high shear rates without pressure and viscous heating effects J.Non-Newton.Fluid Mech, 2000,89:117～131
[32]Chun-Sheng Chen.Rheological behavior of low/high density polyethylene melt flowing through micro-channels.e-Polymers,2008,39:1～14
[33]Chun-Sheng Chen,Shia-Chung Chen,Wei-Liang Liaw,et al.Rheological behavior of POM polymer melt flowing through micro-channels.European Polymer Journal,2008,44:1891-1898
[34]徐佩弦.高聚物加工流变学及其应用.北京:化学工业出版社,2003.105～123
[35]王克俭,周持兴.考虑壁面滑移的Z-W流变模型及其应用.高分子通报,2003,2:8-17
[36]Monney M.,Explicit Formulas for Slip and Fluidity.J.Rheol.1931,2,210～223
[37]Wang S Q,Drda P A.Superfluid-like stick-slip transition in capillary flow of linear polyethylene melts:1.general features[J].Macromolecules,1996,29(6):2627-2632.
[38]Shi-Qing Wang,Patrick A.Drda.Stick-Slip Transition in Capillary Flow of Polyethylene.2. Molecular Weight Dependence and Low-Temperature Anomaly.Macromolecules,1996, 29:4115-4119
[39]Shi-Qing Wang,Patrick A.Drda.Stick-slip transition in capillary flow of linear polyethylene: 3.Surface condition.Rheol Acta,1997,36:128-134
[40]Kalika,D.S.,M.M.Denn.Wall Slip and Extrudate Distortion in Linear Low-Density Polyethylene.J.Rheol,1987,31:815-834
[41]Hill,D.A.,T.Hasegawa,M.M.Denn.On the Apparent Relation Between Adhesive Failure and Melt Fracture.J.Rheol,1990,34:891-918
[42]Vinogradov,G. V., L.I.Ivanova.Viscous Properties of Polymer Melts and Elastomers Exemplified by Ethylene-Propylene Copolymer.Rheol.Acta,1967,6:209-222
[43]Vinogradov,G. V.,L.I.Ivanova,Wall Slippage and Elastic Turbulence of Polymers in the Rubbery State,Rheol.Acta,7,1968,243-254
[44]White,.L.,M.H.Han,N.Nakajima,et a1.The Influence of Materials of Construction on Biconical Rotor and Capillary Measurements of Shear Viscosity of Rubber and its Compounds and Considerations of Slippage.J. Rheol,1991,35:167～189
[45]Savvas GHatzikiriakos, John M.Dealy. Wall slip of molten high density polyethylenes.Ⅱ.Capillary rheometer studies.J.Rheol,1992,36(4):703～741
[46]庄俭,王敏杰,于同敏.微注塑成型中壁面滑移对熔体充模流动影响的研究.中国机械工程,2007,Vol18(16)：1995-1999
[47]徐斌,王敏杰,于同敏,赵丹阳.微尺度效应对聚合物熔体壁面壁面滑移影响的研究.材料工程,2008,Vol10：16-24
[48]唐俊,于同敏,徐斌.考虑熔体弹性的壁面滑移对微尺度流动的影响.中国机械工程,2009,Vol11(20)：1361～1364
[49]Navier,C. L. M. H.:Sur les lois du movement des fluids. Mem.Acad. R. Sci. Inst. Fr.,1827, 6:368-440
[50]申长雨等.塑料模具计算机辅助工程.郑州：河南科学技术出版社.1998.9-24
[2]M Heckele,W K Schomburg.Review on micro molding of thermoplastic polymers. J.Micromech. Microeng,2004,14:1～14
[3]Whiteside B R, Martyn M T, Coates P D, et al. Micromoulding:process characteristics and product properties. Plast. Rubber Compos,2003,32:231～239
[4]Ruprecht R,Gietzelt T,Mueller K,et al.Injection molding of microstructured components from plastics,metals and ceramics.Microsyst.Technol,2002,8:351～358
[5]蒋炳炎,谢磊,杜雪.微注射成型机发展现状与展望.中国塑料,2004,Vol.18(9)6-11
[6]蒋炳炎,沈龙江,彭华建.注射成型中的变模温控制技术.中国塑料,2006,Vol.20(3)99-102
[7]王雷刚,倪雪峰,黄瑶等.微注射成型技术的发展与展望.现代塑料加工应用,2007,19(1)：55-58
[8]Takanori Katoh, Ryuichi Tokuno, Yanping Zhang, et al.Micro injection molding for mass production using LIGA mold inserts. Microsyst Technol (2008) 14:1507～1514
[9]Piotter V,Hanemann T,Ruprecht R, et al.Injection molding and related techniques for fabrication of microstructures. Microsys. Tech,1997,3(3):129～133
[10]Zhao J, Mayes R H, Chen G, et al. Effects of process parameters on the micro molding process. Poly.Eng.Sci,2003,43 (9):1542～1554
[11]Kukla C.Micro injection molding. Proceeding of The 20d ESAFORM. Conference on Material Forming, Liege,2001:81～84
[12]卢振,张凯峰.微注射成型聚丙烯微阵列充填与形态结构.纳米技术与精密工程,2007,Vol.5(4)：239～242
[13]庄俭,吴大鸣,赵中里等.微注射成型工艺的实验研究.化工学报,2009,Vol.60(4)：1040-1045
[14]卢振,张开峰.微注射成形制品质量影响因素分析.机械工程学报,2009, Vol.45(12)：295～299
[15]ShenY K, Wu W Y, An analysis of the three-dimensional micro-injection molding. Int.Comm. Heat Mass Transfer,2002,29(3):423～431
[16]Shen Y K,, Yeh S L, Chen S H. Three-dimension non-newtonian computations of micro-injection molding with the Finite Element Method. Int Comm. Heat Mass Transfer, 2002,29(5):643～652
[17]Donggang Yao, Byung Kim. Simulation of the filling process in micro channels for polymeric materials. J. Micromech Microeng,2002,12:604～616
[18]Yu L, Kuo C G, Lee L J, Keolling K W, et al.Experimental investigation and numerical simulation of injection molding with micro-features. Polym. Eng. Sci,2002,42:871～86
[19]Juang Y J, Lee L, Koelling K W. Hot embossing in microfabrication. Part Ⅱ:Rheological characterization and process analysis. Polym. Eng. Sci,2002,42:551～66
[20]H. L. Zhang, N. S. Ong, Y. C. Lam. Mold surface routhness effects on cavity filling of polymer melt in micro injection molding. Int J Adv Manuf Technol,2008,37:1105～1112
[21]Chen. S. C.,Tsai. R. J.,Chien. R. D. Study on the rheological behavior of polymer melt for micro molding. Annual Technical Conference,2005,2:230～234
[22]Wei Cao, Ole Hassager, Yanwei Zhang. Surface tension effect on micro injection molding. Proceeding of the Polymer Processing Society 24th Annual Meeting PPS.2008(7)
[23]W. B. Yong, Simulation of the filling process in molding components with micro channels, Microsystem Technologies,11 (2005)410-415.
[24]Eringen A C and Okada 1995 A lubrication theory for fluids with microstructure int.J.Eng.sci.332297-308.
[25]Cohen Y, Metzner A B.Apparent slip flow of polymer solution. J. Rheo,1985,29:67～ 102
[26]Lau H C.A model for adhesive failure of viscoelastic fluids during flow. J.Rheol,1986,30: 193-206
[27]Ramamurthy A V. Wall slip in viscous fluids and influence of material construction. J.Rheol. 1986,30:337～357
[28]Hatzikiriakos S G, Dealy J M. Wall slip of molten high density polyethylene:I. Sliding plate rheometer studies. J.Rheol,1991,35:497～523
[29]Rosenbaum E E, Hatzikiriakos S G. Wall slip in the capillary flow of molten polymers subject to viscous heating.AlChE J,1997,43:598～608
[30]Henson D J,Mackay M E.Effect of gap on the viscosity of monodisperse polystyrene melts: slip effects.J.Rheol,1995,39:359～373
[31]Awati K M,Park Y,Weisser E,Mackay M E.Wall slip and shear stresses of polymer melts at high shear rates without pressure and viscous heating effects J.Non-Newton.Fluid Mech, 2000,89:117～131
[32]Chun-Sheng Chen.Rheological behavior of low/high density polyethylene melt flowing through micro-channels.e-Polymers,2008,39:1～14
[33]Chun-Sheng Chen,Shia-Chung Chen,Wei-Liang Liaw,et al.Rheological behavior of POM polymer melt flowing through micro-channels.European Polymer Journal,2008,44:1891-1898
[34]徐佩弦.高聚物加工流变学及其应用.北京:化学工业出版社,2003.105～123
[35]王克俭,周持兴.考虑壁面滑移的Z-W流变模型及其应用.高分子通报,2003,2:8-17
[36]Monney M.,Explicit Formulas for Slip and Fluidity.J.Rheol.1931,2,210～223
[37]Wang S Q,Drda P A.Superfluid-like stick-slip transition in capillary flow of linear polyethylene melts:1.general features[J].Macromolecules,1996,29(6):2627-2632.
[38]Shi-Qing Wang,Patrick A.Drda.Stick-Slip Transition in Capillary Flow of Polyethylene.2. Molecular Weight Dependence and Low-Temperature Anomaly.Macromolecules,1996, 29:4115-4119
[39]Shi-Qing Wang,Patrick A.Drda.Stick-slip transition in capillary flow of linear polyethylene: 3.Surface condition.Rheol Acta,1997,36:128-134
[40]Kalika,D.S.,M.M.Denn.Wall Slip and Extrudate Distortion in Linear Low-Density Polyethylene.J.Rheol,1987,31:815-834
[41]Hill,D.A.,T.Hasegawa,M.M.Denn.On the Apparent Relation Between Adhesive Failure and Melt Fracture.J.Rheol,1990,34:891-918
[42]Vinogradov,G. V., L.I.Ivanova.Viscous Properties of Polymer Melts and Elastomers Exemplified by Ethylene-Propylene Copolymer.Rheol.Acta,1967,6:209-222
[43]Vinogradov,G. V.,L.I.Ivanova,Wall Slippage and Elastic Turbulence of Polymers in the Rubbery State,Rheol.Acta,7,1968,243-254
[44]White,.L.,M.H.Han,N.Nakajima,et a1.The Influence of Materials of Construction on Biconical Rotor and Capillary Measurements of Shear Viscosity of Rubber and its Compounds and Considerations of Slippage.J. Rheol,1991,35:167～189
[45]Savvas GHatzikiriakos, John M.Dealy. Wall slip of molten high density polyethylenes.Ⅱ.Capillary rheometer studies.J.Rheol,1992,36(4):703～741
[46]庄俭,王敏杰,于同敏.微注塑成型中壁面滑移对熔体充模流动影响的研究.中国机械工程,2007,Vol18(16)：1995-1999
[47]徐斌,王敏杰,于同敏,赵丹阳.微尺度效应对聚合物熔体壁面壁面滑移影响的研究.材料工程,2008,Vol10：16-24
[48]唐俊,于同敏,徐斌.考虑熔体弹性的壁面滑移对微尺度流动的影响.中国机械工程,2009,Vol11(20)：1361～1364
[49]Navier,C. L. M. H.:Sur les lois du movement des fluids. Mem.Acad. R. Sci. Inst. Fr.,1827, 6:368-440
[50]申长雨等.塑料模具计算机辅助工程.郑州：河南科学技术出版社.1998.9-24