Progress on separation and purification for organic compounds by melt crystallization

doi:10.16085/j.issn.1000-6613.2022-0233

Abstract

Abstract:

Different components have different freezing points. Melt crystallization utilizes the difference of freezing point to separate and purify the target components from the melt mixture through crystallization, washing and sweating on the basis of management of the energy flow. Due to the advantages of no solvent, low energy consumption, compact equipment and high pure product, melt crystallization is widely used in the field of separation and purification of organic compounds. The classification of melt crystallization are introduced firstly. Then the patterns of melt crystallizers are sketched. Besides, the research progress on separation and purification of organic isomers, organic chemical materials, daily necessities, food and medicine by melt crystallization is reviewed systematically. Furthermore, the existing problems in separation and purification of organic compounds by melt crystallization are analyzed. Finally, the development trends of separation and purification of organic compounds by melt crystallization are discussed. With the development of melt crystallization, the separation and purification of organic compounds by hybrid melt crystallization technologies aiming at raising product quality, decreasing energy consumption, and saving money, has been the main trend. The system engineering which contains melt crystallizers, processes, nucleation kinetics, growth kinetics, sweating mechanisms, and heat and mass transfer model will be the research hotspot of separation and purification of organic compounds by melt crystallization.

Key words: melt crystallization, separation, purification, organic compounds

摘要：

熔融结晶技术是利用被分离物质各组分间凝固点的差异，通过控制热量的输入和移出，使被分离组分从熔融液中结晶析出，经洗涤、发汗等操作，实现目标组分分离纯化的一种结晶技术。熔融结晶分离纯化技术由于具有不需要使用溶剂、能耗低、设备体积小、能得到高纯产品等优点，在有机化合物的分离纯化领域得到了广泛应用。本文简述了熔融结晶的方式，介绍了熔融结晶器的类型，综述了熔融结晶技术分离纯化有机同分异构体、有机化工原料、日用品、食品和药品的研究进展，分析了熔融结晶技术分离纯化有机化合物过程中存在的问题，展望了熔融结晶技术分离纯化有机化合物的发展方向。文中指出：随着熔融结晶技术的发展，以提高产品质量，减小能耗和降低成本为目的的耦合熔融结晶技术已成为熔融结晶技术发展的方向。以包含熔融结晶设备、工艺、晶体成核和生长动力学、发汗机理以及传热传质模型的系统工程将会成为熔融结晶分离纯化有机化合物的研究热点。

关键词: 熔融结晶, 分离, 纯化, 有机化合物

CLC Number:

TQ028.6

QI Yabing, JIA Honglei. Progress on separation and purification for organic compounds by melt crystallization[J]. Chemical Industry and Engineering Progress, 2023, 42(1): 373-385.

齐亚兵, 贾宏磊. 熔融结晶技术分离纯化有机化合物的研究进展[J]. 化工进展, 2023, 42(1): 373-385.

Figures/Tables 18

熔融结晶方式	过程	优点	缺点	适用情况
层式熔融结晶	先结晶、再发汗、后熔化	生长速率快、装置简单、无结垢、固液分离容易、装置易放大	间歇操作、能耗高、处理能力小、效率低、固液相界面积小	不太关注能耗和效率时，为熔融结晶法制备精细化学品的首选
悬浮熔融结晶	结晶、洗涤、发汗和熔化同时进行	固液相界面积大、传热传质性能好、连续操作、处理能力大、效率高	固液分离难、易结垢、易堵塞、设备复杂、稳定运行周期短	固液分离和结垢问题能较好解决的情况下，采用此法
区域熔融结晶	熔区多次从材料棒一端移动到另一端，材料棒中间段为高纯产品	结晶设备体积小、操作简单、产品纯度高	处理量小、分离时间长、效率低	适合高附加值、高纯度精细化学品和药物的制备
层式熔融结晶与悬浮熔融结晶的耦合	原料经造粒、发汗、洗涤后得到纯度较高、粒度较大的结晶产品	能耗较低、产品纯度较高、粒度较大		适合对产品纯度和粒度要求较高的情况
精馏与熔融结晶的耦合	精馏塔顶串联降膜结晶器，精馏塔顶轻组分依次结晶、发汗、熔化	能耗较低、收率较高、产量较高、分离因子较高		适合混合液中轻重组分熔点差异大、沸点差异小，需获得高纯度轻组分的情况

结晶器类型	结晶器型号	特点	分离精制应用
层式熔融结晶器	MWB结晶器	结构简单、无运转件、开停车容易	苯甲酸、己内酰胺、苯酚、医药中间体
层式熔融结晶器	FFC结晶器	可随时开停车、操作灵活，能耗低、应用面广、配有计算机辅助控制系统	醚醛、萘、对二氯苯、对硝基氯苯
悬浮熔融结晶器	Brodie结晶器	投资少、操作费用低、处理量大、操作弹性大、产品纯度高、腐蚀小；设备结构复杂、维修要求高、操作难度大、回收率不高	萘、苯、对二氯苯、对二甲苯、对硝基氯苯
	Phillips结晶器	提纯塔轴向温差较大、能量消耗大、生产经济性较低、产品收率较低	二甲苯异构体
	TNO结晶器	结晶塔需要振动、工业放大困难、产品纯度高	二甲苯、苯并噻吩
	CCCC结晶器	运转件简单、容时生产能力较大、操作控制难度大、具有运转件	苯、对二甲苯、对二氯苯、萘
	KCP结晶器	子设备较多，提纯设备结构复杂并带有运转件，维修及控制要求较高	二氯苯、二甲苯、萘
	倾斜塔式结晶器	结晶塔处理能力大、稳定性好、产品纯度高	对二氯苯
区域熔融结晶器	箱式熔融结晶器	设备体积小、能耗低、产品纯度高、产量低、效率低	1, 2-二苯乙烷

分离方式	结晶器	原料	工艺参数	产品纯度、收率	文献
悬浮熔融结晶	倾斜塔式熔融结晶器	对二氯苯+邻二氯苯	C_对二氯苯=80%~93%（质量分数，本表下同）, θ=45°, n=15r/min, T_c=25~30℃, τ=48h	C_对二氯苯=99.997%	[29]
层式熔融结晶	降膜熔融结晶器	α-甲基萘+β-甲基萘	C_α_-甲基萘=5.69%, C_β-甲基萘=84.7%	C_β_-甲基萘=96%	[31]
层式熔融结晶	静态熔融结晶器	2,4’-MDI+4, 4’-MDI	C_4,4’-MDI=92.1%	C_4,4’-MDI>99% （四次熔融结晶）	[32]
层式熔融结晶	鼓泡降膜熔融结晶器	对甲酚+间甲酚	C_对甲酚=97%~98%, Q_氮气=90L/min, T_ci=40℃, t_c=40min, R_c=0.6~0.8℃/min, T_s=25~35℃, R_s=0.2~0.3℃/min, t_s=40min	C_对甲酚=99.42%	[33]
层式熔融结晶	降膜熔融结晶器	6-叔丁基间甲酚+ 2-叔丁基对甲酚	C_{6-叔丁基间甲酚}=95.8%	C_{6-叔丁基间甲酚}=99.9%,η=72.4%（两次结晶)	[34]
层式熔融结晶	降膜熔融结晶器	1,2,4,5-四甲基苯+ 1,2,3,4-四甲基苯+ 1,2,3,5-四甲基苯	C_{1,2,4,5-四甲基苯}=94.02%, T_c=73℃,R_c=0.03℃/min, T_s=77℃, t_s=30min	C_{1,2,4,5-四甲基苯}=99.06%,η=75.29%	[35]
悬浮结晶+区域熔融结晶	MSMPR结晶器+箱式区域熔融结晶器	2,4-TDI+2,6-TDI	悬浮结晶原料:C_2,4-TDI=80%, C_2,6-TDI=20%; 区域熔融结晶原料: C_2,4-TDI=90.1%	C_2,4-TDI=90.1%, η_悬浮结晶=12.61%（3次悬浮结晶）;C_2,4-TDI>98.5%, η_熔融结晶=60%（6次熔融结晶）	[36]
层式熔融结晶	降膜熔融结晶器	2,4-DNT+2,6-DNT	C_{2, 4-DNT}=76.2%, C_2,6-DNT=19.8%, R_c=0.12~0.2℃/min, T_c=25~30℃, R_s<0.1℃/min,T_s=66~68℃, τ=10~15h	C_2,4-DNT=98.5%,η=25%~35%	[37]
悬浮熔融结晶	塔式悬浮熔融结晶器	对二甲苯+间二甲苯	C_对二甲苯=93.8%	C_对二甲苯>99%	[38]
层式熔融结晶	降膜熔融结晶器	2,4-TDI+2,6-TDI	C_2,4-TDI=80%	C_2,4-TDI>95%（一级熔融结晶）,C_2,4-TDI>99%（二级熔融结晶）,η_总>40%	[39]
层式熔融结晶	静态熔融结晶器	对硝基氯苯+间硝基氯苯	C_{对硝基氯苯}=60%~68%	C_{对硝基氯苯}>99% （两级结晶）	[40]
层式熔融结晶	静态熔融结晶器	2,4-二硝基氯苯+ 2,6-二硝基氯苯	C_{2,4-二硝基氯苯}=84.77%, T_ci=49℃, T_cf=47℃, R_c=0.1℃/min, T_sf=49℃, R_s=0.05℃/min	C_{2,4-二硝基氯苯}=99.94% （三级熔融结晶）	[41]
层式熔融结晶	鼓泡降膜熔融结晶器	L-丙交酯+M-丙交酯	C_L-丙交酯=96.63%, C_M-丙交酯=1.71%,C_乳酸=1.2%, ∆T=20℃, t_c=60min, t_s=50min	C_L-丙交酯=97.72%	[42]

分离方式	结晶器	原料	工艺参数	产品纯度、收率	文献
悬浮熔融结晶	倾斜塔式熔融结晶器	对二氯苯+邻二氯苯	C_对二氯苯=80%~93%（质量分数，本表下同）, θ=45°, n=15r/min, T_c=25~30℃, τ=48h	C_对二氯苯=99.997%	[29]
层式熔融结晶	降膜熔融结晶器	α-甲基萘+β-甲基萘	C_α_-甲基萘=5.69%, C_β-甲基萘=84.7%	C_β_-甲基萘=96%	[31]
层式熔融结晶	静态熔融结晶器	2,4’-MDI+4, 4’-MDI	C_4,4’-MDI=92.1%	C_4,4’-MDI>99% （四次熔融结晶）	[32]
层式熔融结晶	鼓泡降膜熔融结晶器	对甲酚+间甲酚	C_对甲酚=97%~98%, Q_氮气=90L/min, T_ci=40℃, t_c=40min, R_c=0.6~0.8℃/min, T_s=25~35℃, R_s=0.2~0.3℃/min, t_s=40min	C_对甲酚=99.42%	[33]
层式熔融结晶	降膜熔融结晶器	6-叔丁基间甲酚+ 2-叔丁基对甲酚	C_{6-叔丁基间甲酚}=95.8%	C_{6-叔丁基间甲酚}=99.9%,η=72.4%（两次结晶)	[34]
层式熔融结晶	降膜熔融结晶器	1,2,4,5-四甲基苯+ 1,2,3,4-四甲基苯+ 1,2,3,5-四甲基苯	C_{1,2,4,5-四甲基苯}=94.02%, T_c=73℃,R_c=0.03℃/min, T_s=77℃, t_s=30min	C_{1,2,4,5-四甲基苯}=99.06%,η=75.29%	[35]
悬浮结晶+区域熔融结晶	MSMPR结晶器+箱式区域熔融结晶器	2,4-TDI+2,6-TDI	悬浮结晶原料:C_2,4-TDI=80%, C_2,6-TDI=20%; 区域熔融结晶原料: C_2,4-TDI=90.1%	C_2,4-TDI=90.1%, η_悬浮结晶=12.61%（3次悬浮结晶）;C_2,4-TDI>98.5%, η_熔融结晶=60%（6次熔融结晶）	[36]
层式熔融结晶	降膜熔融结晶器	2,4-DNT+2,6-DNT	C_{2, 4-DNT}=76.2%, C_2,6-DNT=19.8%, R_c=0.12~0.2℃/min, T_c=25~30℃, R_s<0.1℃/min,T_s=66~68℃, τ=10~15h	C_2,4-DNT=98.5%,η=25%~35%	[37]
悬浮熔融结晶	塔式悬浮熔融结晶器	对二甲苯+间二甲苯	C_对二甲苯=93.8%	C_对二甲苯>99%	[38]
层式熔融结晶	降膜熔融结晶器	2,4-TDI+2,6-TDI	C_2,4-TDI=80%	C_2,4-TDI>95%（一级熔融结晶）,C_2,4-TDI>99%（二级熔融结晶）,η_总>40%	[39]
层式熔融结晶	静态熔融结晶器	对硝基氯苯+间硝基氯苯	C_{对硝基氯苯}=60%~68%	C_{对硝基氯苯}>99% （两级结晶）	[40]
层式熔融结晶	静态熔融结晶器	2,4-二硝基氯苯+ 2,6-二硝基氯苯	C_{2,4-二硝基氯苯}=84.77%, T_ci=49℃, T_cf=47℃, R_c=0.1℃/min, T_sf=49℃, R_s=0.05℃/min	C_{2,4-二硝基氯苯}=99.94% （三级熔融结晶）	[41]
层式熔融结晶	鼓泡降膜熔融结晶器	L-丙交酯+M-丙交酯	C_L-丙交酯=96.63%, C_M-丙交酯=1.71%,C_乳酸=1.2%, ∆T=20℃, t_c=60min, t_s=50min	C_L-丙交酯=97.72%	[42]

分离方式	结晶器	原料	工艺参数	产品纯度、收率	文献
层式熔融结晶	降膜熔融结晶器	对二甲苯粗品	C_二甲苯=95%（质量分数，本表下同）, C_二甲苯=5%, R_c=8℃/h, T_cf=-1℃, R_s=2.5℃·h^-1, T_sf=13℃	C_二甲苯=99.52%,η=65.88%	[43]
层式熔融结晶	静态熔融结晶器	对苯二甲酰氯粗品	C_{对苯二甲酰氯}=96%, R_c=0.05℃/min, T_cf=-64℃,R_s=0.1℃/min, T_sf=77℃	C_{对苯二甲酰氯}>99.9%	[44]
层式熔融结晶	降膜熔融结晶器	丁二腈粗品	C_丁二腈=99.84%, T_c=-47℃, R_c=0.017℃/min,T_s=56℃, R_s=0.03℃/min	C_丁二腈=99.959%, η=61.9%	[45]
层式熔融结晶	静态熔融结晶器	2, 6-二叔丁基对甲酚粗品	C_BHT=90%, R_c=4℃/min, T_cf=50℃, t_c=20min,T_s=67℃, t_s=1h	C_BHT=99.95%,η=75.91%	[46]
层式熔融结晶	静态熔融结晶器	芴粗品	C_芴=95%, C_甲基氧芴=2.8%, R_c=0.067℃/min,T_cf=108℃, R_s=0.02℃/min, T_s=113℃	C_芴=97.14%,η=49.2%	[47]
层式熔融结晶	静态熔融结晶器	乙二醇+乙二醇单甲醚; 乙二醇+1,2-丁二醇; 乙二醇+1,2-丙二醇	C_乙二醇=94.66%（乙二醇+乙二醇单甲醚体系），C_乙二醇=93.42%（乙二醇+1, 2-丁二醇体系），C_乙二醇=94.87%（乙二醇+1, 2-丙二醇体系）	C_乙二醇≥99.8%	[48-49]
层式熔融结晶	静态熔融结晶器	对苯二胺粗品	C_对苯二胺=92.35%, T_c1=125℃, R_c1=4℃·h^-1,T_sf1=134℃, R_s1=3℃·h^-1; T_c2=128℃, R_c2=2℃·h^-1, T_sf2=139℃, R_s2=2℃·h^-1	C_对苯二胺=99.7%,η=77.21%（两级熔融结晶）	[50]
层式熔融结晶	静态熔融结晶器	异丙苯脱苯塔塔顶馏出液	C_苯=55.554%, T_cf=-28℃, t_cg=90min,R_s=0.1℃/min, T_sf=-15℃, t_ss=90min	C_苯=99.5% （两级熔融结晶）	[51]
层式熔融结晶	降膜结晶器	2-吡咯酮粗品	C_2-吡咯酮=99.5%, T_pre=25℃, Q_F=1.5L·h^-1, R_c=6℃·h^-1, T_cf=8℃, R_s=4℃·h^-1, T_sf=19℃	C_2-吡咯酮>99.9%,η>73.3%	[52]
层式熔融结晶	MWB结晶器	N-乙烯基-2-吡咯烷酮粗品	C_NVP=99.27%, R_c=0.07℃/min, T_cf=11℃,R_s=0.4℃/min, T_sf=14℃, t_s=20min	C_NVP>99.99% （两级熔融结晶）	[53]

分离方式	结晶器	原料	工艺参数	产品纯度、收率	文献
层式熔融结晶	降膜熔融结晶器	对二甲苯粗品	C_二甲苯=95%（质量分数，本表下同）, C_二甲苯=5%, R_c=8℃/h, T_cf=-1℃, R_s=2.5℃·h^-1, T_sf=13℃	C_二甲苯=99.52%,η=65.88%	[43]
层式熔融结晶	静态熔融结晶器	对苯二甲酰氯粗品	C_{对苯二甲酰氯}=96%, R_c=0.05℃/min, T_cf=-64℃,R_s=0.1℃/min, T_sf=77℃	C_{对苯二甲酰氯}>99.9%	[44]
层式熔融结晶	降膜熔融结晶器	丁二腈粗品	C_丁二腈=99.84%, T_c=-47℃, R_c=0.017℃/min,T_s=56℃, R_s=0.03℃/min	C_丁二腈=99.959%, η=61.9%	[45]
层式熔融结晶	静态熔融结晶器	2, 6-二叔丁基对甲酚粗品	C_BHT=90%, R_c=4℃/min, T_cf=50℃, t_c=20min,T_s=67℃, t_s=1h	C_BHT=99.95%,η=75.91%	[46]
层式熔融结晶	静态熔融结晶器	芴粗品	C_芴=95%, C_甲基氧芴=2.8%, R_c=0.067℃/min,T_cf=108℃, R_s=0.02℃/min, T_s=113℃	C_芴=97.14%,η=49.2%	[47]
层式熔融结晶	静态熔融结晶器	乙二醇+乙二醇单甲醚; 乙二醇+1,2-丁二醇; 乙二醇+1,2-丙二醇	C_乙二醇=94.66%（乙二醇+乙二醇单甲醚体系），C_乙二醇=93.42%（乙二醇+1, 2-丁二醇体系），C_乙二醇=94.87%（乙二醇+1, 2-丙二醇体系）	C_乙二醇≥99.8%	[48-49]
层式熔融结晶	静态熔融结晶器	对苯二胺粗品	C_对苯二胺=92.35%, T_c1=125℃, R_c1=4℃·h^-1,T_sf1=134℃, R_s1=3℃·h^-1; T_c2=128℃, R_c2=2℃·h^-1, T_sf2=139℃, R_s2=2℃·h^-1	C_对苯二胺=99.7%,η=77.21%（两级熔融结晶）	[50]
层式熔融结晶	静态熔融结晶器	异丙苯脱苯塔塔顶馏出液	C_苯=55.554%, T_cf=-28℃, t_cg=90min,R_s=0.1℃/min, T_sf=-15℃, t_ss=90min	C_苯=99.5% （两级熔融结晶）	[51]
层式熔融结晶	降膜结晶器	2-吡咯酮粗品	C_2-吡咯酮=99.5%, T_pre=25℃, Q_F=1.5L·h^-1, R_c=6℃·h^-1, T_cf=8℃, R_s=4℃·h^-1, T_sf=19℃	C_2-吡咯酮>99.9%,η>73.3%	[52]
层式熔融结晶	MWB结晶器	N-乙烯基-2-吡咯烷酮粗品	C_NVP=99.27%, R_c=0.07℃/min, T_cf=11℃,R_s=0.4℃/min, T_sf=14℃, t_s=20min	C_NVP>99.99% （两级熔融结晶）	[53]

分离方式	结晶器	原料	工艺参数	产品纯度、收率、杂质含量	文献
区域熔融结晶	箱式区域熔融结晶器	联苄粗品	C_联苄=98.35%（质量分数，本表下同）, v=8.8mm·h^-1, N=8, T_h=60℃, T_c=15℃, Z=0.13	C_联苄=99.84%, η=50%	[30]
层式熔融结晶	指型结晶器	苯甲酸粗品	C_{邻苯二甲酸}=1335.59mg·kg^-1, R_c=1.5℃·h^-1,T_cf=110℃, R_s=6℃·h^-1, T_sf=122℃	C_{邻苯二甲酸}=97.83mg·kg^-1, η=56.08%	[54]
层式熔融结晶	静态熔融结晶器	2-氯-5-三氟甲基吡啶粗品	C_{2-氯-5-三氟甲基吡啶}=89%, C_{3-氯-5-三氟甲基吡啶}=2.8%, C_{2-氯-3-三氟甲基吡啶}=1.7%, R_c=0.071℃/min, T_cf=16~19℃, R_s=0.062~0.083℃/min,T_sf=28~30℃	C_{2-氯-5-三氟甲基吡啶}=99%,η=40%	[55]
层式熔融结晶	静态熔融结晶器	邻碘苯胺粗品	C_邻碘苯胺=70.95%, R_c=0.06℃/min, T_cf=28℃, t_cg=2h, R_s=0.04℃/min, T_sf=40℃	C_邻碘苯胺=99.07%,η=61.75%	[56]
减压精馏+层式熔融结晶	降膜熔融结晶器	人造麝香粗品	C_DDHI=85%, R_c=4℃·h^-1, t_c=2h, R_s=6℃·h^-1, t_s=30min, 通氮气, 二级结晶	C_DDHI=99.2%, η=63.2%	[57]
层式熔融结晶	翅片式降膜结晶器	苯甲酸粗品	C_苯甲酸=94.5%	C_苯甲酸=99.5%	[58]
层式熔融结晶	静态熔融结晶器	棕榈油		硬酯:C_棕榈酸=42.63%, C_油酸=34.71%; 软酯:C_棕榈酸=50.02%, C_油酸=30.89%	[59]
区域熔融结晶		菲粗品	C_菲=98%, N=30	C_菲>98.5%	[60]
区域熔融结晶	箱式区域熔融结晶器	联苄粗品	C_联苄=98.35%, v=4.97mm·h^-1或12.35mm·h^-1, T_h=60℃, T_c=10~30℃	C_联苄(变熔区)>C_联苄(恒熔区), C_联苄(双熔区)>C_联苄(单熔区)	[61]

$G = G 0 + λ s A λ s A - j l G 0 R i Λ ρ s 3 λ s A - j l G 0 τ$ , $G 0 = j l 2 + 4 Λ ρ s λ s A - j l / 2 Λ ρ s$ ,

j_l=α_l∆T_l, ∆T_l=(T_l₀-T₀)exp(-lα_l/c_p_lΓ)

①过程温度的改变对液膜物性的影响可以忽略。②晶层与液膜之间的接触面温度等于结晶温度T₀，液膜的平均浓度C_l决定T₀。③液膜的平均浓度和流速在结晶管轴向方向上数值一致。④局部对流传热系数ɑ_l不随着管长变化。⑤过程喷淋密度Γ的变化忽略不计

[43]

悬浮熔融结晶

对二甲苯

沿塔高的浓度分布： W_L=a+(W_L,0-a)exp(-bz),

$a = k u s P R - K a ρ L A 1 R + 1 w P + P k u s R + 1 1 - w P k u s P R - K a ρ L A 1 R + 1$ ,

$b = k u s P R - K a ρ L A 1 R + 1 L + k u s D a x ρ L A ε + K t ρ L 2 A 2 P R + 1 D a x ε$

①提纯段为稳定状态。②径向无浓度差。③晶体相和回流熔融液以及其他参数沿提纯段不变

[38]

区域熔融结晶

联苄、TDI

一次区熔：(1)区域1（0≤x<1-z），C₁(x)/C₀=1-(1-k_e)exp(-k_ex/z)；(2) 区域2（1-z<x≤1），C₁(x)/C₀={1-(1-k_e)exp[-k_e(1-z)/z]}×{1-[x-(1-z)]/z} $k e - 1$

多次区熔：

(1) 区域1（x=0）， $C S, N 0 C 0 = k e Δ x z ∑ i = 0 M - 1 C S, N - 1 x i C 0$ ；

(2) 区域2（0<x≤1-z），

$C S, N x C 0 = C S, N x - Δ x C 0 + k e Δ x z C S, N - 1 x + z - Δ x - C S, N x - Δ x C 0$ ；

(3) 区域3（1-z<x<1），

$C S, N x C 0 = k e 1 - x k e - 1 z - k e C 0 - ∑ j = 0 R - 1 C S, N x j Δ x C 0$ ；

(4) 区域4（x=1）， $C S, N 1 C 0 = Q - ∑ p = 1 Q - 1 C S, N x p C 0$

①恒定的熔区长度。②恒定的熔区移动速度。③恒定和相等的切面面积。④恒定的密度（在固体和液体中）。⑤均一的起始浓度。⑥冷凝界面上处于平衡状态。⑦平整的结晶界面。⑧恒定的扩散系数（在熔化物中）。⑨固体中没有扩散

[63-64]

结晶类型

提纯体系

模型方程

模型假设

文献

动态层式熔融结晶

对二甲苯

$G = G 0 + λ s A λ s A - j l G 0 R i Λ ρ s 3 λ s A - j l G 0 τ$ , $G 0 = j l 2 + 4 Λ ρ s λ s A - j l / 2 Λ ρ s$ ,

j_l=α_l∆T_l, ∆T_l=(T_l₀-T₀)exp(-lα_l/c_p_lΓ)

[43]

悬浮熔融结晶

对二甲苯

沿塔高的浓度分布： W_L=a+(W_L,0-a)exp(-bz),

$a = k u s P R - K a ρ L A 1 R + 1 w P + P k u s R + 1 1 - w P k u s P R - K a ρ L A 1 R + 1$ ,

$b = k u s P R - K a ρ L A 1 R + 1 L + k u s D a x ρ L A ε + K t ρ L 2 A 2 P R + 1 D a x ε$

①提纯段为稳定状态。②径向无浓度差。③晶体相和回流熔融液以及其他参数沿提纯段不变

[38]

区域熔融结晶

联苄、TDI

一次区熔：(1)区域1（0≤x<1-z），C₁(x)/C₀=1-(1-k_e)exp(-k_ex/z)；(2) 区域2（1-z<x≤1），C₁(x)/C₀={1-(1-k_e)exp[-k_e(1-z)/z]}×{1-[x-(1-z)]/z} $k e - 1$

多次区熔：

(1) 区域1（x=0）， $C S, N 0 C 0 = k e Δ x z ∑ i = 0 M - 1 C S, N - 1 x i C 0$ ；

(2) 区域2（0<x≤1-z），

$C S, N x C 0 = C S, N x - Δ x C 0 + k e Δ x z C S, N - 1 x + z - Δ x - C S, N x - Δ x C 0$ ；

(3) 区域3（1-z<x<1），

$C S, N x C 0 = k e 1 - x k e - 1 z - k e C 0 - ∑ j = 0 R - 1 C S, N x j Δ x C 0$ ；

(4) 区域4（x=1）， $C S, N 1 C 0 = Q - ∑ p = 1 Q - 1 C S, N x p C 0$

[63-64]

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