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吸附剂在静、动态吸附过程中的传质数学模型综述
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Abstract:
通常研究吸附剂的吸附模型主要分为静态吸附和动态色谱柱吸附两大类。各类色谱模型包括可得到分析解的模型都是从最简单理想色谱模型衍生出来的。模型的建立与求解连接着一系列的数学问题，所以对模型理论的研究一定会涉及数学工具。本文介绍了静态、动态吸附模型的发展历史及相关分类。
Generally, the adsorption models are mainly divided into static adsorption and dynamic column adsorption models. Various chromatographic, i.e., dynamic column adsorption models, including those that have analytic solution, are all derived from the simplest ideal chromatographic model. The establishment and solution of the model are connected with a series of mathematical problems, so the study of model theory must involve mathematical tools. The development history and classification of static and dynamic adsorption models are introduced in this paper.
| [1] | Saiers, J.E., Hornberger, G.M. and Liang, L. (1994) First- and Second-Order Kinetics Approaches for Modeling the Transport of Colloidal Particles in Porous Media. Water Resources Research, 30, 2499-2506.
https://doi.org/10.1029/94WR01046 |
| [2] | McCoy, M. and Liapis, A. (1991) Evaluation of Kinetic Models for Bi-ospecific Adsorption and Its Implications for Finite Bath and Column Performance. Journal of Chromatography A, 548, 25-60.
https://doi.org/10.1016/S0021-9673(01)88591-5 |
| [3] | Venkata Mohan, S., Chandrasekhar Rao, N. and Karthikeyan, J. (2002) Adsorptive Removal of Direct Azo Dye from Aqueous Phase onto Coal Based Sorbents: A Kinetic and Mechanistic Study. Journal of Hazardous Materials, 90, 189-204. https://doi.org/10.1016/S0304-3894(01)00348-X |
| [4] | Chu, K. and Hashim, M. (2003) Modeling Batch Equilib-rium and Kinetics of Copper Removal by Crab Shell. Separation Science and Technology, 38, 3927-3950. https://doi.org/10.1081/SS-120024712 |
| [5] | O’Shannessy, D.J. and Winzor, D.J. (1996) Interpretation of Devia-tions from Pseudo-First-Order Kinetic Behavior in the Characterization of Ligand Binding by Biosensor Technology. Analytical Biochemistry, 236, 275-283.
https://doi.org/10.1006/abio.1996.0167 |
| [6] | Zaror, C.A. (1997) Enhanced Oxidation of Toxic Effluents Using Simultaneous Ozonation and Activated Carbon Treatment. Journal of Chemical Technology and Biotechnology, 70, 21-28.
https://doi.org/10.1002/(SICI)1097-4660(199709)70:1<21::AID-JCTB706>3.0.CO;2-3 |
| [7] | Lagergren, S. (1898) Zur theorie der sogenannten adsorption gel？ster stoffe. Kungliga Svenska Vetenskapsakademiens, Handlingar, 24, 1-39. |
| [8] | Zeldowitsch, J. (1934) über den mechanismus der katalytischen oxydation von CO an MnO2. Acta Physi-cochimica URSS, 1, 364-449. |
| [9] | Ho, Y. (1995) Adsorption of Heavy Metals from Waste Streams by Peat. University of Birmingham, Edgbaston, Birmingham. |
| [10] | Ho, Y. and McKay, G. (1998) Sorption of Dye from Aqueous Solution by Peat. Chemical Engineering Journal, 70, 115-124. https://doi.org/10.1016/S0923-0467(98)00076-1 |
| [11] | Ho, Y. and McKay, G. (1999) Pseudo-Second Order Model for Sorption Processes. Process Biochemistry, 34, 451-465.
https://doi.org/10.1016/S0032-9592(98)00112-5 |
| [12] | Ho, Y.S. and McKay, G. (2000) The Kinetics of Sorption of Divalent Metal Ions onto Sphagnum Moss Peat. Water Research, 34, 735-742. https://doi.org/10.1016/S0043-1354(99)00232-8 |
| [13] | Onganer, Y. (1998) Adsorption Dynamics of Fe(III) from Aqueous Solutions onto Activated Carbon. Journal of Colloid and Interface Science, 205, 241-244. https://doi.org/10.1006/jcis.1998.5616 |
| [14] | Yamuna, R. and Namasivayam, C. (1993) Color Removal from Aqueous Solution by Biogas Residual Slurry. Toxicological & Environmental Chemistry, 38, 131-143. https://doi.org/10.1080/02772249309357884 |
| [15] | Kandah, M. (2001) Zinc Adsorption from Aqueous Solutions Using Disposal Sheep Manure Waste (SMW). Chemical Engineering Journal, 84, 543-549. https://doi.org/10.1016/S1385-8947(01)00138-3 |
| [16] | Namasivayam, C. and Kanchana, N. (1992) Waste Banana Pith as Adsorbent for Color Removal from Wastewaters. Chemosphere, 25, 1691-1705. https://doi.org/10.1016/0045-6535(92)90316-J |
| [17] | Panday, K., Prasad, G. and Singh, V. (1985) Copper(II) Re-moval from Aqueous Solutions by fly Ash. Water Research, 19, 869-873. https://doi.org/10.1016/0043-1354(85)90145-9 |
| [18] | Shubha, K., Raji, C. and Anirudhan, T. (2001) Immobilization of Heavy Metals from Aqueous Solutions Using Polyacrylamide Grafted Hydrous Tin(IV) Oxide Gel Having Carboxylate Functional Groups. Water Research, 35, 300-310.
https://doi.org/10.1016/S0043-1354(00)00234-7 |
| [19] | Atun, G. and Sismanoglu, T. (1996) Adsorption of 4,4’-Iso Propylidene Diphenol and Diphenylolpropane 4,4’ Dioxyaceticacid from Aqueous Solution on Kaolinite. Journal of En-vironmental Science and Health Part A, 31, 2055-2069.
https://doi.org/10.1080/10934529609376474 |
| [20] | 姜志新, 谌竟清, 宋正孝, 等. 离子交换分离工程[M]. 天津: 天津大学出版社, 1992. |
| [21] | Krishna, R. and Wesselingh, J. (1997) The Maxwell-Stefan Approach to Mass Transfer. Chemical Engineering Science, 52, 861-911. https://doi.org/10.1016/S0009-2509(96)00458-7 |
| [22] | Sobkowski, J. and Czerwinski, A. (1974) Kinetics of Carbon Dioxide Adsorption on a Platinum Electrode. Journal of Electroanalytical Chemistry and Interfacial Electrochemistry, 55, 391-397.
https://doi.org/10.1016/S0022-0728(74)80433-X |
| [23] | Ritchie, A. (1977) Alternative to the Elovich Equation for the Kinetics of Adsorption of Gases on Solids. Journal of the Chemical Society, Faraday Transactions 1, 73, 1650-1653. https://doi.org/10.1039/f19777301650 |
| [24] | Blanchard, G., Maunaye, M. and Martin, G. (1984) Removal of Heavy Metals from Waters by Means of Natural Zeolites. Water Research, 18, 1501-1507. https://doi.org/10.1016/0043-1354(84)90124-6 |
| [25] | 邹汉法, 张玉奎, 佩章. 高效液相色谱法[M]. 北京: 科学出版社, 1998. |
| [26] | Giddings, J.C. (1965) Dynamic of Chromatography. M. Dekker, New York. |
| [27] | (美)赛恩费尔德, 拉皮德里, 著. 化工过程数学模型理论[M]. 赵维彭, 等, 译. 江苏: 江苏科学技术出版社, 1981. |
| [28] | 侯镜德, 扬锡尧. 物理化学的气相色语研究法[M]. 北京: 北京大学出版社, 1989. |
| [29] | Lapidus, L. and Amundson, N.R. (1952) Mathematics of Adsorption in Beds. VI. The Effect of Longitudinal Diffusion in Ion Exchange and Chromatographic Columns. The Journal of Physical Chemistry, 56, 984-988.
https://doi.org/10.1021/j150500a014 |
| [30] | Van Deemter, J., Zuiderweg, F. and Klinkenberg, A. (2005) Longitudinal Diffusion and Resistance to Mass Transfer as Causes of Nonideality in Chromatography. Chemical Engineering Science, 5, 271-289.
https://doi.org/10.1016/0009-2509(56)80003-1 |
| [31] | Wilson, J.N. (1940) A Theory of Chromatography. Journal of the American Chemical Society, 62, 1583-1591.
https://doi.org/10.1021/ja01863a071 |
| [32] | DeVault, D. (1943) The Theory of Chromatography. Journal of the American Chemical Society, 65, 532-540.
https://doi.org/10.1021/ja01244a011 |
| [33] | Thomas, H.C. (1944) Heterogeneous Ion Exchange in a Flowing System. Journal of the American Chemical Society, 66, 1664-1666. https://doi.org/10.1021/ja01238a017 |
| [34] | Goldstein, S. and Murray, J. (1959) On the Mathematics of Exchange Processes in Fixed Columns. V. The Equilibrium-Theory and Perturbation Solutions, and their Connexion with Kinetic-Theory Solutions, for General Entry Conditions. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 252, 360-375.
https://doi.org/10.1098/rspa.1959.0158 |
| [35] | Houghton, G. (1963) Band Shapes in Non-Linear Chromatography with Axial Dispersion. The Journal of Physical Chemistry, 67, 84-88. https://doi.org/10.1021/j100795a019 |
| [36] | Gluckauf, E. (1946) Contributions to the Theory of Chromatography. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 186, 35-57. https://doi.org/10.1098/rspa.1946.0034 |
| [37] | Helfferich, F.G. and Klein, G. (1970) Multicomponent Chromatog-raphy: Theory of Interference. M. Dekker, New York. |
| [38] | Aris, R. and Amundson, N.R. (1973) Mathematical Meth-ods in Chemical Engineering. Prentice-Hall, Upper Saddle River. |
| [39] | Rhee, H.K. (1981) Equilibrium Theory of Mul-ticomponent Chromatography. In: Rodrigues, A.E. and Tondeur, D., Eds., Percolation Processes: Theory and Applica-tions, Sijthoff & Noordhoff, Alphen aan den Rijn, The Netherlands, 285-328. |
| [40] | Ding, J.Q. and Zhu, B.L. (1962) Application of electronic simulation method to calculation of elution curves of chromatography. Scieotia Sinica, 6, 1269. |
| [41] | Guiochon, G. and Jacob, L. (1971) Theory of Chromatography at Finite Concentration. Chromatographic Reviews, 14, 77-120. https://doi.org/10.1016/0009-5907(71)80004-2 |
| [42] | Rouchon, P., Schonauer, M., Valentin, P. and Guiochon, G. (1987) Numerical Simulation of Band Propagation in Nonlinear Chromatography. Separation Science and Technology, 22, 1793-1833.
https://doi.org/10.1080/01496398708057614 |
| [43] | Golshan-Shirazi, S. and Guiochon, G. (1988) Comparison be-tween Experimental and Theoretical Band Profiles in Nonlinear Liquid Chromatography with a Binary Mobile Phase. Analytical Chemistry, 60, 2634-2641.
https://doi.org/10.1021/ac00174a020 |
| [44] | Guiochon, G., Ghodbane, S., Golshan-Shirazi, S., Huang, J.X., Katti, A., Lin, B.C., et al. (1989) Nonlinear Chromatography: Recent Theoretical and Experimental Results. Talanta, 36, 19-33.
https://doi.org/10.1016/0039-9140(89)80079-7 |
| [45] | Knoxand, J.H. and Saleem, M. (1969) A Comparison of Plate Efficiencies in Gas and Liquid Chromatography Using Various Supports. Journal of Chromatographic Science, 7, 745-751. https://doi.org/10.1093/chromsci/7.12.745 |
| [46] | Katti, A. and Guiochon, G. (1988) Prediction of Band Profiles in Displacement Chromatography by Numerical Integration of a Semi-Ideal Model. Journal of Chromatography A, 449, 25-40.
https://doi.org/10.1016/S0021-9673(00)94365-6 |
| [47] | Golshan-Shirazi, S. and Guiochon, G. (1989) Theoretical Study of System Peaks and Elution Profiles for Large Concentration Bands in the Case of a Binary Eluent Containing a Strongly Sorbed Additive. Journal of Chromatography A, 461, 1-18. https://doi.org/10.1016/S0021-9673(00)94271-7 |
| [48] | Cox, G.B. and Snyder, L.R. (1988) Preparative and Pro-cess-Scale HPLC Aquantotative Picture for Isocratic Separation. liquid gas chromatography, 6, 894. |
| [49] | Mazzotti, M., Storti, G. and Morbidelli, M. (1997) Robust Design of Countercurrent Adsorption Separation Processes: 4. Desorbent in the Feed. AIChE Journal, 43, 64-72. https://doi.org/10.1002/aic.690430109 |
| [50] | Guiochon, G., Golshan-Shirazi, S. and Katti, A. (1994) Fundamentals of Nonlinear and Preparative Chromatography. Academic Press, Boston. |
| [51] | Lin, B., Ma, Z., Golshan-Shirazi, S. and Guiochon, G. (1989) Study of the Representation of Competitive Isotherms and of the Intersection between Adsorption Isotherms. Journal of Chromatography A, 475, 1-11.
https://doi.org/10.1016/S0021-9673(00)91411-0 |
| [52] | Heuer, C., Seidel-Morgenstern, A. and Hugo, P. (1995) Experimental Investigation and Modelling of Closed-Loop Recycling in Preparative Chromatography. Chemical Engi-neering Science, 50, 1115-1127.
https://doi.org/10.1016/0009-2509(94)00498-G |
| [53] | Bellot, J. and Condoret, J. (1991) Liquid Chromatography Modelling: A Review. Process Biochemistry, 26, 363-376.
https://doi.org/10.1016/0032-9592(91)85027-L |
| [54] | Klatt, K.U. (1999) Modellierung und effektive numerische Simulation von chromatographischen Trennprozessen im SMB-Betrieb. Chemie Ingenieur Technik, 71, 555-566. https://doi.org/10.1002/cite.330710603 |
| [55] | Sang, L., Luo, Y., Chu, G.-W., Liu, Y.-Z., Liu, X.-Z. and Chen, J.-F. (2017) Modeling and Experimental Studies of Mass Transfer in the Cavity Zone of a Rotating Packed Bed. Chemical Engineering Science, 170, 355-364.
https://doi.org/10.1016/j.ces.2016.12.041 |
| [56] | Song, Q., Wu, Z., Xie, W. and Qian, W. (2017) Adsorptive Re-covery of Geniposidic Acid from Gardenia Yellow Pigment Extraction Wastewater by Anion Exchange: Equilibrium, Thermodynamics and Mechanism Modeling and Simulation. Research on Chemical Intermediates, 43, 2215-2235. https://doi.org/10.1007/s11164-016-2757-7 |
| [57] | Qian, W., Song, Q., Ding, H. and Xie, W. (2019) Computational Simulations of the Mass Transfer Zone in GS Adsorption Column Packed with Fe3+ Type Ion Exchanger. Chemosphere, 215, 507-514.
https://doi.org/10.1016/j.chemosphere.2018.10.054 |
| [58] | Gu, T., Tsai, G.J. and Tsao, G.T. (1990) New Approach to a General Nonlinear Multicomponent Chromatography Model. AIChE Journal, 36, 784-788. https://doi.org/10.1002/aic.690360517 |
| [59] | Gu, T., Tsao, G.T., Tsai, G.J. and Ladisch, M.R. (1990) Displacement Effect in Multicomponent Chromatography. AIChE Journal, 36, 1156-1162. https://doi.org/10.1002/aic.690360805 |
