液态食品冷冻浓缩冰晶生长机制研究
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摘要
冷冻浓缩产生的冰晶夹带率比较高,且难以分离,从而限制了它的推广与使用。长期以来,为解决冰晶夹带问题,国内外学者大多把目光停留在单位冰晶体积的层面上,主要凭经验或以实测资料为依据来控制冰晶的生长过程。本文从冷冻浓缩冰晶夹带率影响因素入手,先从宏观上分析冰晶生长的机制,再借鉴国内外金属微观结构研究领域非常热门的相场模型,微观上探索冰晶组织的形成规律和控制方法,较为系统地展开对冷冻浓缩的研究。具体的研究工作和主要结论如下:
     1.以荔枝汁为原料,讨论分析冰晶纯度影响因素。主要探讨冷冻温度、冷冻时间、冰晶形态、溶液粘度、冰晶分离工艺等方面对冰晶夹带率的影响。选择初始冷冻温度、把握冷冻时间、控制冰晶形态和采取合适的冰晶分离工艺,从而一定程度上降低冰晶的夹带率。
     2.通过对冷冻时间与浓缩液、冰晶中可溶性固形物含量的关系以及冷冻时间与浓缩液和冰晶质量关系进行研究,并根据Fick扩散方程式建立冰晶增长动力学模型,模型显示冰晶增长速率与冰晶质量成正比,同时也受到最大冰晶量的抑制。通过该模型,从宏观方面分析冰晶质量增长和热量传递之间的平衡,为建立冰晶增长的质量、热量传递之间的平衡提供了一定的理论依据和试验参考,从而把握较为合理的冰晶生长时间。
     3.冰晶是典型的凝固组织,因其非平衡组织结构涉及到热量、质量和动量传输以及界面动力学和毛细作用效应相耦合的自由边界问题。相场模型将组织转变过程界面演化的尖锐界面问题转变为弥散界面模型,故引入相场模型,用于模拟冷冻浓缩冰晶生长过程中微观组织的演化过程。探讨了相场模型建立的基本原理、其数值求解的离散处理、稳定性条件、初始条件和边界条件。
     4.利用相场模型对过冷纯水的冰晶生长过程进行数值模拟,模拟不同过冷时间、不同过冷度下的冰晶形貌的演化过程,并解释了Ostwald效应的竞争机制。同时与实际拍摄的冰晶进行比较,进一步证实相场法从微观上模拟冰晶生长的可行性。
     5.利用相场模型对液态食品冷冻浓缩过程的冰晶生长进行数值模拟。把液态简化为糖水二元物质,在近似等温的条件下耦合相场和溶质场进行模拟,探讨了冷冻时间、过冷度对冰晶形貌及溶质场的影响。验证控制冷冻时间、冷冻温度对减少冰晶夹带率的作用。
The entrainment rate of ice crystals was relatively high in the process of freeze concentration and difficult separation, and the seperation of ice crystles and soluble solid content is difficult, thereby it was limited to promote and use. Since a long time, in order to address the issue of entrainment of ice crystals, the unit size of ice crystals was concerned by domestic and foreign experts and scholars who con- trolled the growth of ice crystals based on the measured datas or main experience. In this paper, the growth mechanism of ice crystals was analyzed at the micro-macro level in the process of freeze concentration. Through domestic and international field of metal micro-structure of the phase-field model, the law of formation of ice crystals and methods of controlling were explored. Specific research work and the main con- clusions were as follows:
     1、The influencing factors of ice crystal purity were discussed and analyzed with litchi juices as raw materials. It was focused on the effects of the freeze temperature, freezing time, ice crystals form, the solution viscosity and separation process on the entrainment rate of ice crystals. To some extent, the entrainment rate of ice crystals could be reduced by controlling freezing temperature, freezing time, ice crystal form and separation process.
     2、The relationship among freezing time, concentrated liquid and soluble solid content was studied, and the relationship among freezing time, concentrated liquid and ice crystal quality was also studied. According to Fick diffusion equation, The kinetic model of ice crystals growth was developed, ,max,which showed that growth rate of ice was proportional to the mass of ice and was inhibited by the maximal mass of ice. The balance between the quality of ice crystal growth and heat transfer was analyzed at the macro level through the establishment of dynamic model of freeze concentration. Thus, a theoretical basis was provided for the establishment of the balance between the quality of ice crystal growth and heat transfer,and a more reasonable time for ice crystal growth was obtained.
     3、Ice crystal was a typical kind of solidfication structure. The phase-field model was introduced because of its non-equilibrium from its typical structure, involving energy, quality and momentum transfer, as well as the interface kinetics and the problem caused by capillarity effects coupled with the free boundary. Taken advantages of phase-field model which could change the sharp interface from the course of interface evolution into the diffuse interface, it was used to simulate the process of evolution of microstructure in the process of ice crystal growing of freeze concentration. The basic principles of phase-field,the discrete numerical solution, stability conditions, initial conditions and boundary conditions were discussed.
     4、The growth process of ice crystals of supercooling water was numerically simulated by phase-field model, which including the course of evolution of ice crystal morphology at different cooling time, different degrees of supercooling. And the competitive mechanism of Ostwald effect was explained. At the same time, compared with the actual filming ice crystals, it was confirmed further that to simulate ice crystal growth by phase-field model at the micro level was feasible.
     5、The growth of ice crystals was numerically simulated in the process of freeze concentration of liquid food. Liquid food were simplified as the dual material. Then it was simulated by coupling phase field with solute field under the isothermal condition. the effects of ice crystal morphology and solute field on freezing time and degrees of supercooling were studied. As a result, the control of freezing time and freezing tem- perature played an important role in reducing the entrainment of ice crystals.
引文
[1]袁惠新,陆振曦,吕季章.食品加工与保藏技术[M].北京:化学工业出版社,2000.1.
    [2]田恒增.我国农产品加工业的现状[J].粮油加工与食品械,2000,(4):1-71.
    [3] Huige NJJ,Thijssen H A C.Production of large crystals bycontinuous ripening in a stirred tank[J].Crystal Growth,1972(13/14):483-487.
    [4]邵长富.软饮料工艺学[M].化学轻工业出版社,1987.35-45.
    [5]高福成.现代食品工程高新技术[M].北京:中国轻工业出版社,1997.
    [6]Muller MI.Sekoulov Waste. Water reuse by freeze concentration with failing film reactor. Water Sci. Tech.1992,26(7&8):1475~1482.
    [7]李勇.食品冷冻加工技术[M].化学工业出版社24-28.
    [8]詹晓北.冷冻浓缩技术在啤酒工业中的应用[J].冷饮与速冻食品工业.1996,(1):14-16.
    [9]张春娅,张军,王树生,等.葡萄酒冷冻浓缩技术的研究及应用[J].酿酒科技,2007,(2):55-57.
    [10]孙卉卉,马会勤,陈尚武.冷冻浓缩对低糖葡萄汁及葡萄酒品质的影响的影响[J].食品科学,2007,28(5):86-89.
    [11]Atsuko Kobayashi, Yoshihito Shirai. A Method for Making Large Agglomerated Ice Crystals for Freeze Concentration [J].Journal of Food Engineering,1996(27):1-15.
    [12] Marino,Susana Luque, et al. A comparative study of reverse osmosis and freeze concentration for the removal of valeric acid from waste waters[J]. Desalination, 2000 (127): 1-11.
    [13]于涛,马军,崔崇威.高浓度尿素废水冷冻浓缩极限[J].化工学报,2006,57(12):2943-2947.
    [14]于涛.制冷在废水处理与再生领域中的应用研究[J].制冷学报,2008(4):47-50.
    [15]高锋,孙洁心,张永忠.冷冻浓缩法处理大豆乳清废水的研究初探[J].食品研究与开发, 2005,26(4):25-27.
    [16] Ramos F A., Delgado J L., Bautista E., Morales A L.,et al.Changes in volatiles with the application of progressive freeze-con-centration to Andes berry[J].Journal of Food Engi- neering,69(2005):291-297.
    [17] Durward Smith,Carol Ringenberg,Erik Olson.Freezecncentration of Fruit juice(R). Food&Nutrition Safety,2006.
    [18] Milind V. Rane,Siddharth K.Jabad.Freeze concentration of sugarcane juice in a jaggery making process[J].Applied Thermal Engineering 2005,(2):2122-2137.
    [19]袁林峰,闵华,黄霞萍.甘蔗汁冷冻浓缩特性研究初报[J].江西农业学报.2002,14(1):61-64.
    [20]冯毅,史森直,宁方芹.中药水提取液冷冻浓缩的研究[J].制冷.2005,24(1):5-8.
    [21]冯毅,唐伟强,宁方芹.冷冻浓缩提取新鲜茶浓缩液工艺的研究[J].农业机械学报.2006, 37(8):66-72.
    [22]江华,余世袁.低聚木糖溶液冷冻浓缩时冰晶生长动力学研究[J].林产化学与工业2007,. 27(3):53-56.
    [23]何松,胡卓炎,孙福在,赵延昌,钟士清.果汁冷冻浓缩中生物冰核的成冰作用及初步应用[J].食品工业科技.2001,22(02):15-17.
    [24] Kumeno K, Kurimoto K, Nakahama N.Biosci Biotechna1[J]. Biochem.1994,(58):447-450.
    [25] Minjung L,Kyung B S.Foods and Biotechnology.1995,4(3):164-168.
    [26] Watanabe M,Watanabe J,Kumeno K et a1.Agric.Biol,Chem.1989,5(3):2731-2735.
    [27] Jingkun L,Tungching[J].Journal of Food Science.1998,63(3):375-381.
    [28] Zasypkin D V.Tungching L[J].Journal of Food Science.1999,64(3):473-478.
    [29]范进填,黎伟文,孙过超.果汁冷冻浓缩过程中冰晶形成规律的研究[J].食品与发酵工业,1991,17(2):12~16.
    [30] Yano T. et al.Develop in Food Eng.,London. Blackie Academic and Professional.1994,391~393.
    [31] Yano T. et al.Develop in Food Eng[M].London.Blackie Academic and Professional. 1994, 391-393.
    [32]刘凌等.液体食品的渐进冷冻浓缩[J].食品与发酵工业,1999,25(4):31-34.
    [33] Zhang Z L,Hartel R W.[J] Journal of Food Engineering,1996;29:23-28.
    [34] Zhonglai Zhang and R.W.Hartel.A multilayer freezer for freeze concentration of liquid milk[J]. Food Eng.1996(29):23~28.
    [35] Levent Bayindirli, Mustafa Ozilgen & Suat Ungan. Mathematical Analysis of Freeze Concentration of Apple Juice[J]. Journal of Food Engineering 19(1993)95-107.
    [36]高福成等.现代食品工程高新技术[M].北京:中国轻工业出版社1997.
    [37]冯毅,谭展机.冷冻浓缩的原理、现状及实验研究[J].广州食品工业科技,Vol.18 No.4 63-65.
    [38]宋纪蓉.分离过程[M].化学工业出版社,346.
    [39] Wankat P C.Rate-Controlled Separations. New York:Elsevier Applied Science, 1990. 84-92,95-98,103-122,162
    [40]中国食品发酵工业研究院等.食品工程全书[M].中国轻工业出版社,2003 ,291-294.
    [41]张光跃,荆涛,柳百成.相场法原理及在微观组织模拟中的应用[[J].机械工程学报,2003, 39(5):6-9.
    [42] Yu Y M,Yang G C,Zhao D W,et al. Research Progress on the Solidification Microstru- cture[J].Special Casting and Nonferrous Alloys,2002(3):30.
    [43]Langer J S ,Lectures In The Theory of Pattern Formation.J. Souletie, J. Vannenimus, R.Stora Chance and Matter, Les Houches Session XLVI,Singapore, 1987, North Holland, Amsterdam.
    [44] G Caginalp. an Analysis of a Phase Field Model of a Free-Boundary[J].Archive for Rational Mechanics and Analysis.1986,92(3):205-245.
    [45]Caginalp G , Fife P.Higher-Order Phase Field Models and Detailed Anisotropy[J]. Phys Rev B,1986,34(7):4940-4943.
    [46]Caginalp G, Fife P. Phase-Field Methods for Interfacial Boundaries[J]. Phys Rev B.1986, 33(11):7792-7794.
    [47] Glick S M,Lupule S C. Dendritic Crystal Growth in Pure Materials[J].Journal of Crystal Growth, 2004,264:541.
    [48] Brittan N A, Wheeler A. A Phase-field Modeling of Multi-phase Solidificatiion[J]. Computer PhysicsCommunications,2002.147-230.
    [49]于艳梅.过冷熔体中枝晶生长的相场法数值模拟[D].西安:西北工业大学,2002.
    [50]田学雷.纯金属凝固过程枝晶生长的相场法研究[D].济南:山东大学,2007.
    [51] Karma A, Rappel W J.Quantitative Phase-Field Modeling of Dendritic Growth in Two and Three Dimensions[J].Phys Rev E.1998,57(4):4323-4349.
    [52] Nestl B er,Wheele A A , Ratke L. et al.Solidification of a Monotectic Ahoy with Phase-Field Model for Convection.141(1-2):133-154. Physica D,2000.
    [53] Fried E, Gurtin ME.A Phase-Field Theory for Solidification Based on a General Anisotro- pic Sharp-Interface Theory with Interfacial Energy and Entronv. Phvsica D. 1996. 91(1-2): 143-181
    [54] Karma A,Rappel W J.Phase-Field Method for Computationally Efficient Modeling of Solidification with Arbitrary Interface Kinetics[J].Phys Rev E.1996,53(4): 83017-83020.
    [55] Przylecka M,The Modeling of Structure and Properties of Carburized Low- Chromium Hypereutectoid Steels[J]. Mater Eng Perf.1996,5(2):165-191.
    [56] Wang S L,Sekerka.R F, Algorithms for Phase Field Computation of the Dendritic Operating State at Large Supercoolings[J].Comp.Phys 1996,127(1):110-117.
    [57] Wang S L, Sekerka R. F.Computation Large Supercoolings by the Phase Field of the Dendritic Operating State at Model[J].Phys Rev E.1996,53(4):3760-3776.
    [58] Conti M ,Planar Isothermal Solidification from an Undercooled Melt: Unsteady Solute Segregation Studied with the Phase-Field Model[J].Phys Rev E.1997, 55(1):701-707.
    [59] Conti M,Solidification of Binary Alloys:Thermal Effects Studied with the Phase-Field Model[J].Phys Rev E.1997,55(1):765-771.
    [60] Conti M,Solute One-DimensionalTrapping in Directional Solidification at High Speed: A Study with the Phase-Field Model[J].Phys Rev E.1997,56(3):3717-3720.
    [61] Pavlik S G , Sekerka R F.Fluctuations in the Phase-Field Model of Solidification[J]. Physica A. 2000,277(3-4):415-431.
    [62] Chen L Q, Khachaturyan A G.Computer-Simulation of Structural Transformations during Precipitation of an Ordered Intermetallic Phase[J]. Acta Metall Mater. 1991,39(11):2533-2551.
    [63] Y S Li,Z Chen,Y L Lu,et al.Computer Simulation for the Precipitation Process of Ni75A 17.5V 17.5 alloy[J].Prog Nat Sci.2004,14(12):1099-1106.
    [64] Shen C,Chen Q,Wen Y H.et al.Increasing Length Scale of Quantitative Phase Field Modeling of Concurrent Growth and Coarsening Processes[J].Scr Mater.2004,50(7): 1029-1034.
    [65] Zhu J Z, Wang T ,A Ardell J.et al.Three-Dimensional Phase-Field Simulations of CoarseningKinetics of Gamma' Particles in Binary Ni-Al Alloys[J]. Acta Mater.2004,52(9): 2837-2845.
    [66] Li Y S, Z.Chen Y Wang X.et al.Computer Simulation of Gamma and Theta Phase Precipitation of Ni-Al-V Alloy Using Microscopic Phase-Field Method[J].Trans Non Metals Soc China.2005,15(1):57-63.
    [67] Cahn J W ,P Fife, enrose O P.A Phase-Field Model for Diffusion-Induced Grain-Boundary Motion[J].Acta Mater.1997,45(10):4397-4413.
    [68] GurtinM.E.,Lusk.M.T. Sharp-Interface Recrystallization in the Plane.Physica D.1999,and Phase-Field Theories of 130(1-2):133-154.
    [69] Kazaryan A, Wang Y S, Dregia A.et al. Generalized Phase-Field Model for Computer Simulation of Grain Growth in Anisotropic Systems[J].Phys Rev B.2000,61(21):14275-14278.
    [70] Warren J A, Kobayashi R, Carter WC. Modeling Grain Boundaries Using a Phase-Field Technique[J]. Cryst Growth.2000,11(1-4):18-20.
    [71] Lobkovsky A E , Warren J A.Phase-Field Model of Crystl Grains[J]. Cryst Growth. 2001, 225(2-4):282-288.
    [72] Ramanarayan H ,Abinandanan T A.Phase Field Study of Grain Boundary Effects on Spinodal Decomposition[J].Acta Mater.2003,51(16):4761-4772.
    [73] Granasy L,Pusztai T,Warren J.A.Modelling Polycrystalline Solidification Using Phase Field Theory[J]. Phys.2004,16(41):R1205-R1235.
    [74] R Kobayashi,J A Warren.Modeling the Formation and Dynamics of Polycrystals in 3D. Physica A.2005,356(1):127-132.
    [75] Artemev A, Khachaturyan A G.The Phase Field Model and Computer Simulation of Trans- formation under Applied Stresses[J].Shape Mem Mater. 2000, 327-3:347-350.
    [76] Artemev .Wang A Y, Khachaturyan A G. Three-Dimensional Phase Field Model and Simulation of Martensitic Transformation in Multilayer Systems under Applied Stresses[J].Acta Mater.2000,48(10):2503-2518.
    [77] Artemev A, Jin Y, Khachaturyan A,G. Three-Dimensional Phase Field Model of Proper Mar- tensitic Transformation[J].Acta Mater.2001,49(7):1165-1177.
    [78] Jin Y M , Artemev A,Khachaturyan A G .Three-Dimensional Phase Field Model of Low- Symmetry Martensitic Transformation in Polycrystal:Simulation of Zeta'(2) Martensite in AuCd alloys[J]. Acta Mater.2001,49(12):2309-2320.
    [79] Hsu T .Y,Theoretical Models of Martensitic Transformations[J]. De Phys Iv.2003, 112:29-36.
    [80] Wang Y U , Jin Y M, Khachaturyan A G.The Effects of Free Surfaces on Martensite Microstructures: 3D Phase Field Microelasticity Simulation Study[J].Acta Mater. 2004, 52(4): 1039-1050.
    [81]李方方,刘静.细胞尺度冰晶生长行为的相场数值模拟[J].低温物理学报, 2008, 30(2): 171-175.
    [82] Udaykumar H S,Mao L,International of Heat and Mass Transfer, 45(2002), 4793.
    [83]贾伟建,凝固微观组织相场法模拟[D].兰州理工大学硕士学位论文(2005) .
    [84] Simmons J P, Youhai Wen, Shen C,et al.Microstructural development involving nucleation and growth phenomena simulated with the phase field method[J].Material Science Engineering. 2003,A365:136-143
    [85] Fan D. Computer simulation of microstructural evolution in multiphase materials using a diffuse-interface field model. The Pennsylvania state university Doctor thesis.1996
    [86] Lu Y, Beckermanm C,J. Ramirez C.Three-dimensional phase field simulation of the effect of convection on free dendritic growth[J]. Journal of Crystal Growth 2005,280:320-334.
    [87] Chen L Q, Yang W.Computer simulation of the domain dynamics of a quenched system with a large number of nonconserved order parameters:The grain-growth kinetics[J].Phys.Rev.1994, 50:15752-15756.
    [88] Boertinger W J,Warrgenja,Beckermann C,et al.,Phase-field simulation of solidification [J].Annual Review of Materials Research, 2002, 32:163-194.
    [89] Ramirez JC,Beckermann C,Karma A,et al.Phase-field modeling of binary alloy solidification with coupled heat and solute diffusion[J].Physical Review E,2004, 69: 051607-051622.
    [90] Mullis AM.An extension to the Wheeler phase-field model to allow decoupling of the capillary and kinetic anisotropies [J].The European Physical Journal B,2004,41(3):377-382.
    [91] Mullis A M.Quantification of mesh induced anisotropy effects in the phase-field method[J].Computational Materials Science 2006,36(3):345-353.
    [92] A Karma,W J Rappel. Numerical simulation of three-dimensional dendritic growth. Phys. Rev.Lett.,1996,77(10):4050-4053.
    [93] Kobayashi R.Modeling and numerical simulations of dendritic crystal growth[J].Physica D.1993,63:410-423.
    [94] Rappaz M, Karma A. Multiscale Finite- Difference-Diffusion- Monte-Carlo Method for Simulating Dendritic Solidification.Preprint.
    [95] Kim S G, Kim W T.Phase field modeling of rapid solidification[J].Mater. Sci.Enging.A, 2001,304-306:281-286.
    [96] Caginalp C,Xie W.Phase-field and sharp-interface alloy models[J].Phys.Rev. E,1993,48(3):1897-1909.
    [97]Rowlinson J S.Translation of J.D.vander walls“The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density”[J]. Journal of Statistical Physics, 1979,20(2):197-200.
    [98] Allensm,Cahn J W. A microscopic theory for anti-phase boundary motion and its application to anti-phase domain coarsening [J].Acta metal.,1979,27:1085-1092.
    [99] Cahn J W ,Hilliard J E. Free energy of a non-uniform system.Interfacial free energy [J]. Chem.Phys,1958,28:258-267.
    [100] Ginzburg VL,Landau L D.On the theory of superconductivity[J].Exptl.Theol. Phys.(USSR),1950,20:1064-1082.
    [101] Langer J S. Directions in Condensed Matter (World Scientific, Singapore, 1986),p.164.
    [102] Caginalp,G.Stefan and Hele-Shaw type models as asymptotic limits of the phase-field equations[J].Phys.Rev.A,1989,39(11):5887-5896.
    [103]Kpbayashi R.Modeling and numerical simulations of dendritic crystal growth [J].Physica D,1993,63(3-4):410-423.
    [104] Wheeler A A, Boettinger W J,Mcfadden G B.Phase-field model for isothermal phase transitions in binary alloys[J].Phys.Rev.A,1992,45(10):7424-7439.
    [105] Warren J A, Boettinger W J. Prediction of dendritic growth and microsegregation patterns in a binary alloy using the phase-field method[J]. Acta mater, 1995,43(2): 689-703.
    [106] Wang S L,Sekerka R. F.Computation of the dendritic operating state at large supercoolings by the phase field model[J].Phys.Rev.E,1996,53(4):3760-3776.
    [107] Karma A,Rappel W J.Phase-field method for computationally efficient modeling of solidification with arbitrary interface kinetics[J].Phys. Rev.E, 1996, 53(4):3017-3020.
    [108] Karma A ,Rappel W J.Quantitative phase-field modeling of dendritic growth in two and three dimensions [J]. Phys. Rev. E,1998,57(4):4323-4349.
    [109] Kim S G,Kim W T,Suzuki T.Interfacial compositions of solid and liquid in a phase-field model with finite interface thickness for isothermal solidification in binary alloys[J]. Phys. Rev. E,1998, 58(3):3316-3323.
    [110] Kim S G,Kim W T,Suzuki T.Phase-field model for binary alloys[J]. Phys.Rev. E, 1999, 60(6):7186-7197.
    [111] Lee B J,Oh K H. Numerical treatment of the moving interface in diffusional reactions[J]. Z.Metallkd.,1996,87(3):195-204.
    [112] Cha P R,Peon D H,Yoon J K. A phase field model for isothermal solidification of multicomponent alloys[J].Acta mater.2001,49(16):3295-3307.
    [113] Crusius S,Inden,Knoop U,et al.On the numerical treatment of moving boundary problems[J].Z.Metallkd.,1992,83(99):673-678.
    [114] Warren J A,Kobayashi R,Lobkovsky A E,et al.Extending phase field models of solidification to polycrystalline materials [J].Acta Materialia,2003,51(20): 6035-6058.
    [115] Hecht U,Granasy L, Pusztai T,et al.Multiphase solidification in multi-component alloys[J]. Mat Sci Eng R, 2004, 46(1-2):1-49.
    [116] Cha P R,Yeon D H,Yoon J K. Phase-field model for multi-component alloy solidification[J]. Cryst Growth,2005,274(1-2):281-293.
    [117]Cha P R,Yeon D H,Yoon J K.A phase field model for isothermal solidification of multi- component alloys.Acta Mater,2001,49(16):3295-3307.
    [118] Danilov D,Nestler B.Dendritic to globular morphology transition in ternary alloys solidification[J].Phys Rev Lett, 2004,93(21):215501-215501.
    [119] Danilov D,estler B.Phase field simulations of solidification in binary and ternary systems using a finite element method[J]. Cryst Growth, 2005,275(1-2): 177-182.
    [120] Nestler B, Garcke H, Stinner B. Mufti-component alloy solidification: Phase-field modeling and simulations[J].Phys Rev E,2005,71(4):041609-041609.
    [121] Kobayashi H,Ode M,Kim S G,et al.Phase-field model for solidifcation of ternary alloys coupled with thermodynamic database[J].Scripta Mater,2003,48(6):689-694.
    [122] Ode M, Lee J S, Kim S G, et al. Phase-field model for solidification of ternary alloys[J].ISIJInt,2000,40(9):870-876.
    [123] Zhang R,Jing T,Jie W,et al.Phase field simulation of solidifcation in multi-component alloys coupled with thermodynamic and diffusion mobolity databvases[J].Acta Mater,2006,54(8): 2235-2239.
    [124] Bottger B, Eiken J,Steinbach I.Multi phase-field approach for alloy solidification[J]. Phys Rev E, 2006,73(6):066122-1-066122-9.
    [125]刘健康.冰晶长大过程的相场模拟[J].西安工业大学学报,2008,28(4):361-365.
    [126]王锦程.多元合金枝晶生长形态转变及显微偏析的相场法研究[J].中国科学, 2007. 38(41):1921-1929.
    [127] Wheeler A A, Murray B T,Schaefer R J. Computation of dendrites using a phase field model[J].Physica D,1993,66(1-2):243-262.
    [128] Karma A, Sarkissian A. Interface dynamics and banding in rapid solidification [J].Physical Review E,1993,47(1):513-533.
    [129] Murray B T, Wheeler A, Glicksman M E. Simulations of experimentally observed dendritic growth behavior using a phase-field model [J].Journal of Crystal Growth, 1995, 154(3-4):386-400.
    [130] Mccarthy J F. One-dimensional phase field models with adaptive grids [J].Trans. of the ASME, 1998,120: 956-964.
    [131] Wang S L, Sekerka R F. Computation of the dendritic operating state at large supercooling by the phase field model [J].Phys. Rev. E, 1996, 53(7): 3760-3776.
    [132] D I Popov, I I Regel, W R Wilcox. Fourier collocation and Fourier Galerkin methods applied to the phase-field model of two-dimensional phase-transition problem [J].Journal of Physics D: Applied Physics, 1998, 31:2603-2611.
    [133] Provatas N, Goldenfeld N. Efficient computation of dendritic microstructures using adaptive mesh refinement [J].Comp. phys,1999, 148:268.
    [134] S Kim G, Kim W T, Lee J S. et al. Large scale simulation of dendritic growth in pure undercooled melt by phase field model.[ISI] International, 1999, 39(4): 335-340.
    [135] Muller, J G.Freeze concentration of food liquids,theory,practice andeconomics. Food Technol, 1967(21),49-61.
    [136] Omran,A M,King,C J.Kinetics of ice crystallization in sugar solutions and fruit juices. 1974,22(1),131-40.
    [137] Saal,H.Freezing can cut whey concentration costs 45%. Food Process [J].1980,41,62-3.
    [138] Stocking J H,King C.Secondary nucleation of ice in sugar solution and fruit juices. [J].AICHEJ1976, 22(1),131-40.
    [139] Van Pelt.Economics of Multistage Freeze Concentration Process.Grenco Special Appli- cations[J].1981,pp.1-31.
    [140] Akyurt M,Zakig,Habeebull H B.Freezing phenomena in ice-water systems[J]. Energy Conversion and Management,2002,43(14):l773-1789.
    [141] Carpenter J F , Crowe J H.Cryobiology[M].1988,25,244-255.
    [142] Martel G J.Influence of dissolved solids On the mechanism of freeze-thaw conditioning[J]. Water Research,2000,34(2):657-662.
    [143] Akyurt M,Zaki G,Hhbeebullah B.Freezing phenomena in ice-water systems[J]. Energy Conversion and Management,2002,43(14):1773-1789.
    [144] Edmond,E.,and Ogston,A. G. Biochem[M].1968 ,109,569.
    [145]小林登史夫.冷冻浓缩的现状和食品开发[J].食品开发(日)1987,22(12):34-37.
    [146] Stocking J H,King C j.Secondary nucleation of ice in sugar solution and fruit juices[J].Aichej, 1976,22(1),131-40.
    [147] Arakawa T, Timasheff S N. Biochemistry[M].1985,6756.
    [148] Arakawa T ,Kita Y,Carpenter J.F.Pharm.Res[M].1991,285-291.
    [149] Levent Bayindirli.Mathematical Analysis of Freeze Concentration of Apple Juice[J].Journal of Food Engineering,1993(19):95-107.
    [150]肖旭霖,李慧.苹果汁冷冻浓缩工艺的研究[J].农业工程学报,2006,22(1):192-194.
    [151] Steve H.The role of freeze concentration in waste water disposal[J].Filtration and Separation,1999,36(10):34-35.
    [152] Khusnatidinov N, Petrenko V F. Fast-growth technique for ice ingle crystals[J].Journal of Crystal Growth,1996,163(4):420-425.
    [153] MARTEL G J.Influence of dissolved solids on the mechanism of freeze-thaw Water Research,2000,34(2):657-662.
    [154]江华,余世援.低聚木糖溶液冷冻浓缩时冰晶生长动力学研究[J].林产化学与工业, 2007,23(3):53-56.第四章
    [155] Kurz W, Fisher D. Fundamentals of solidification [M].Trans Tech Publications Ltd. 1985.
    [156] Porter D A,Easterling K E.Phase Transformations in Metals and Alloys[M]. Chapman&Hall, 1992, 2nd edition.
    [157] Sinha A. Physical Metallurgy Handbook (McGraw-Hill. 2003).
    [158] Davis S. Theory of soldification, Cambridge Mongraphs on Mechanics (Cambridge University Press, 2001).
    [159] Fermi E. Thermodynamics (Dover Publications Inc., 1956).
    [160] Zemansky M, Dittman R. Heat and Thermodynamics (McGraw-Hill,1981).
    [161] Landaul L, Lifshitz E. Statistical Physics (Pergamon, NY, 1980).
    [162] Hurle D. editor, Fundamentals. Thermodynamics and Kinetics, volume 1a of Handbook of Crystal Growth(North-Holland, 1993).
    [163] Hurle D. editor, Fundamentals. Transport and Stability, volume 1b of Handbook of Crystal Growth(North-Holland, 1993).
    [164] J S Langer. in Directions in Condensed Physics,eds.Grinstein G and Maxenko G(World Science,1986):164-168.
    [165] Wang S. L. , Sekerka R. F. , Wheeler A. A. et al , Physics D,69 1993 , 189.
    [166] Lifshitz I M, Slyozov V V. J Phys Chem Solids, 1961; 19:35.
    [167] Wagner V C.Z Elektrochem, 1961; 65: 581.
    [168] Ardell A J.Phys Rev, 1990; 41B: 2554.
    [169] Rogere T M,Desai R C.Phys Rev,1989,39B:11956.
    [170]张清光,陈民,过增元.过冷熔体中枝晶生长的相场法模拟[[J].工程热物理学报,2004, 25(3):487-489.

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