聚苯乙烯微孔发泡中气泡长大及冷却定型模拟
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摘要
本文以聚苯乙烯(PS)-超临界CO_2系统为例,提出了一种基于细胞模型,结合动量方程、质量方程、扩散方程及本构方程建立气泡长大及冷却定型问题的数学模型。用MATLAB编制了基于以上数学模型的仿真模拟程序。在模拟过程中,通过引入材料性质与温度、压力、CO_2浓度的关系式,确定了工艺参数和微孔形态之间的量化关系。结果表明,三个工艺参数对PS-CO_2气泡长大的影响:CO_2浓度>压力>温度。由正交模拟实验可知,不同加工条件下得到的气泡半径最大为49.5μm,最小为1.27μm,其中适于微孔发泡的气泡半径则处于10~25μm之间。另外通过对气泡冷却定型的研究得到,快速冷却可以使气泡密度增加、气泡尺寸减小。
In this paper,apolystyrene(PS)-supercritical CO_2 system was used herein as a case example to simulate bubble growth behavior and cooling and solidification.The mathematical model based on the cell model was established to solve momentum equation,mass equation and diffusion equation.The software program of system simulation based on the above mathematical model was compiled with MATLAB language.In the process of simulation,the quantitative relationship between process parameters and microcellular morphology was determined by introducing the relationship between the material properties and the temperature,pressure and CO_2 concentration.The results show that CO_2 concentration has the greatest effect on bubble growth,and the effect of temperature is the least for the PS-CO_2 system.According to the simulation of orthogonal,under different processing conditions,the maximum value of bubble radius is 49.5μm,the minimum value is 1.27μm,and the suitable bubble radius for microcellular foaming is between 10μm and 25μm.In addition,the study of the bubble cooling shows that the increase of cooling rate will increase the bubble density and reduce the bubble size.
In this paper,apolystyrene(PS)-supercritical CO_2 system was used herein as a case example to simulate bubble growth behavior and cooling and solidification.The mathematical model based on the cell model was established to solve momentum equation,mass equation and diffusion equation.The software program of system simulation based on the above mathematical model was compiled with MATLAB language.In the process of simulation,the quantitative relationship between process parameters and microcellular morphology was determined by introducing the relationship between the material properties and the temperature,pressure and CO_2 concentration.The results show that CO_2 concentration has the greatest effect on bubble growth,and the effect of temperature is the least for the PS-CO_2 system.According to the simulation of orthogonal,under different processing conditions,the maximum value of bubble radius is 49.5μm,the minimum value is 1.27μm,and the suitable bubble radius for microcellular foaming is between 10μm and 25μm.In addition,the study of the bubble cooling shows that the increase of cooling rate will increase the bubble density and reduce the bubble size.
引文
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[17]SATO Y,TAKIKAWA T,TAKISHIMA S,et al.Solubility and diffusion coefficients of carbon dioxide in poly(vinyl acetate)and polystyrene[J].Journal of Supercritical Fluids,2001,19:187-198.
[18]LEE M,PARK C B,TZOGANAKIS C.Measurements and modeling of PS/supercritical CO2solution viscosities[J].Polymer Engineering and Science,1999,39(1):99-109.
[19]PARK H,THOMPSON R B,LANSON N,et al.Effect of temperature and pressure on surface tension of polystyrene in supercritical carbon dioxide[J].Journal of Physical Chemistry B,2007,111(15):3859-3868.
[20]VENERUS D C,ZHU S H,OTTINGER H C.Stress and birefringence measurements during the uniaxial elongation of polystyrene melts[J].Journal of Rheology,1999,43(3):795-813.
[21]LEUNG S N,PARK C B,XU D,et al.Computer simulation of bubble-growth phenomena in foaming[J].Industrial&Engineering Chemistry Research,2006,45(23):7823-7831.
[22]KUMAR V,VANDERWEL M,WELLER J,et al.Experimental characterization of the tensile behavior of microcellular polycarbonate foams[J].Journal of Engineering Materials and Technology,1994,116(4):439-445.
[2]JACOBS L J M,KEMMERE M F,KEURENTJES J T F.Sustainable polymer foaming using high pressure carbon dioxide:A review on fundamentals,processes and applications[J].Green Chemistry,2008,10(7):731-738.
[3]SUH N P.Impact of microcellular plastics on industrial practice and academic research[J].Macromolecular Symposia,2003,201(1):187-201.
[4]余坚,何嘉松.超临界CO2技术制备微孔聚合物中的基本问题[J].中国科学:化学,2010,40(1):1-15.YU J,HE J S.Fundamental issues for micro foaming polymers with supercritical CO2technology[J].Scientia Sinica Chimica,2010,40(1):1-15(in Chinese).
[5]STREET J R,FRICKE A L,REISS L P.Dynamics of phase growth in viscous,non-newtonian liquids.Initial stages of growth[J].Industrial and Engineering Chemistry Fundamentals,1971,10(1):54-64.
[6]VENERUS D C,YALA N,BERNSTEIN B.Analysis of diffusion-induced bubble growth in viscoelastic liquids[J].Journal of Non-Newtonian Fluid Mechanics,1998,75(1):55-75.
[7]AMON M,DENSON C D.A Study of the dynamics of foam growth:Analysis of the growth of closely spaced spherical bubbles[J].Polymer Engineering and Science,1984,24(13):1028-1034.
[8]LI Y,YAO Z,CHEN Z H,et al.Numerical simulation of polypropylene foaming process assisted by carbon dioxide:Bubble growth dynamics and stability[J].Chemical Engineering Science,2011,66(16):3656-3665.
[9]OTSUKI Y,KANAI T.Numerical simulation of bubble growth in viscoelastic fluid with diffusion of dissolved foaming agent[J].Polymer Engineering and Science,2005,45(9):1277-1287.
[10]许星明,赵国群,李辉平.气泡在聚合物内长大过程的等温有限元模拟[J].高分子材料科学与工程,2010,26(10):171-174.XU X M,ZHAO G Q,LI H P.Finite element simulation of bubble growth in isothermal liquid[J].Polymer Materials Science and Engineering,2010,26(10):171-174(in Chinese).
[11]AREFMANESH A,ADVANI S G.Diffusion-induced growth of a gas bubble in a viscoelastic fluid[J].Rheologica Acta,1991,30(3):274-283.
[12]POLING B E,PRAUSNITZ J M,O’CONNELL J P.The properties of gases and liquids[M].McGraw-Hill Education,2001.
[13]FAVELUKIS M.Dynamics of foam growth:Bubble growth in a limited amount of liquid[J].Polymer Engineering and Science,2004,44(10):1900-1906.
[14]TAKI K.Experimental and numerical studies on the effects of pressure release rate on number density of bubbles and bubble growth in a polymeric foaming process[J].Chemical Engineering Science,2008,63(14):3643-3653.
[15]WELTY J R,WICKS C E,WILSON R E.Fundamentals of momentum,heat,and mass transfer[M].Wiley,2001.
[16]OSORIO A,TURNG L S.Mathematical modeling and numerical simulation of cell growth in injection molding of microcellular plastics[J].Polymer Engineering&Science,2004,44(12):2274-2287.
[17]SATO Y,TAKIKAWA T,TAKISHIMA S,et al.Solubility and diffusion coefficients of carbon dioxide in poly(vinyl acetate)and polystyrene[J].Journal of Supercritical Fluids,2001,19:187-198.
[18]LEE M,PARK C B,TZOGANAKIS C.Measurements and modeling of PS/supercritical CO2solution viscosities[J].Polymer Engineering and Science,1999,39(1):99-109.
[19]PARK H,THOMPSON R B,LANSON N,et al.Effect of temperature and pressure on surface tension of polystyrene in supercritical carbon dioxide[J].Journal of Physical Chemistry B,2007,111(15):3859-3868.
[20]VENERUS D C,ZHU S H,OTTINGER H C.Stress and birefringence measurements during the uniaxial elongation of polystyrene melts[J].Journal of Rheology,1999,43(3):795-813.
[21]LEUNG S N,PARK C B,XU D,et al.Computer simulation of bubble-growth phenomena in foaming[J].Industrial&Engineering Chemistry Research,2006,45(23):7823-7831.
[22]KUMAR V,VANDERWEL M,WELLER J,et al.Experimental characterization of the tensile behavior of microcellular polycarbonate foams[J].Journal of Engineering Materials and Technology,1994,116(4):439-445.