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Literature Review

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Mathematical Modeling and Scale-Up of Liquid Chromatography

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Abstract

Many researchers have contributed to LC modeling. There exist a dozen or more theories with different complexities. A comprehensive review on the dynamics and mathematical modeling of isothermal adsorption and chromatography was given by Ruthven [1] who classified models into three general categories: equilibrium theory, plate models, and rate models.

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References

  1. Ruthven DM (1984) Principles of adsorption and adsorption processes. Wiley, New York

    Google Scholar 

  2. Glueckauf E (1949) Theory of chromatography. Part VII. The general theory of two solutes following non-linear isotherms. Discuss Faraday Soc 7:12–25

    Article  Google Scholar 

  3. Helfferich FG, Klein G (1970) Multicomponent chromatography: theory of interference. Dekker, New York

    Google Scholar 

  4. Rhee H-K, Aris R, Amundson NR (1970) On the theory of multicomponent chromatography. Philos Trans R Soc Lond A Math Phys Sci 267:419–455

    Article  CAS  Google Scholar 

  5. Rhee H-K, Amundson NR (1982) Analysis of multicomponent separation by displacement development. AIChE J 28:423–433

    Article  CAS  Google Scholar 

  6. Glueckauf E (1947) Theory of chromatography. Part II. Chromatograms of a single solute. J Chem Soc 1302–1308 (Resumed)

    Google Scholar 

  7. Helfferich F, James DB (1970) An equilibrium theory for rare-earth separation by displacement development. J Chromatogr A 46:1–28

    Article  CAS  Google Scholar 

  8. Bailly M, Tondeur D (1981) Two-way chromatography: flow reversal in non-linear preparative liquid chromatography. Chem Eng Sci 36:455–469

    Article  CAS  Google Scholar 

  9. Frenz J, Horvath CG (1985) High performance displacement chromatography: calculation and experimental verification of zone development. AIChE J 31:400–409

    Article  CAS  Google Scholar 

  10. Frenz J, Horvath C (1988) High performance liquid chromatography. In: Horvath C (ed) Advances and perspectives, vol 5. Academic, San Diego, CA, pp 211–314

    Google Scholar 

  11. Martin AJP, Synge RM (1941) A new form of chromatogram employing two liquid phases: a theory of chromatography. 2. Application to the micro-determination of the higher monoamino-acids in proteins. Biochem J 35:1358

    CAS  Google Scholar 

  12. Yang CM (1980) Affinity chromatography and plate model for nonlinear packed-column processes. Purdue University, West Lafayette, IN

    Google Scholar 

  13. Villermaux J (1981) Theory of linear chromatography. In: Rodrigues AE, Tondeur D (eds) Percolation processes: theory and applications. Sijthoff and Noordhoff, Rockville, MA, pp 83–140

    Chapter  Google Scholar 

  14. Eble JE, Grob RL, Antle PE, Snyder LR (1987) Simplified description of high-performance liquid chromatographic separation under overload conditions, based on the Craig distribution model. III. Computer simulations for two co-eluting bands assuming a Langmuir isotherm. J Chromatogr A 405:1–29

    Article  CAS  Google Scholar 

  15. Seshadri S, Deming SN (1984) Simulation of component interactions in high-performance liquid chromatography. Anal Chem 56:1567–1572

    Article  CAS  Google Scholar 

  16. Solms DJ, Smuts TW, Pretorius V (1971) Displacement peaks in liquid elution chromatography. J Chromatogr Sci 9:600–603

    Article  Google Scholar 

  17. Ernst P (1987) Radial flow chromatography. Aust J Biotechnol 1:22–24

    CAS  Google Scholar 

  18. Velayudhan A, Ladisch MR (1993) Plate models in chromatography: analysis and implications for scale-up. In: Tsao GT (ed) Chromatography. Springer, Berlin, pp 123–145

    Chapter  Google Scholar 

  19. Glueckauf E, Coates JI (1947) Theory of chromatography. Part IV. The influence of incomplete equilibrium on the front boundary of chromatograms and on the effectiveness of separation. J Chem Soc 1315–1321 (Resumed)

    Google Scholar 

  20. Rhee H, Amundson NR (1974) Shock layer in two solute chromatography: effect of axial dispersion and mass transfer. Chem Eng Sci 29:2049–2060

    Article  CAS  Google Scholar 

  21. Bradley WG, Sweed NH (1975) Rate controlled constant pattern fixed-bed sorption with axial dispersion and non-linear multicomponent equilibria. AIChE Symp Ser 71:59

    CAS  Google Scholar 

  22. Farooq S, Ruthven DM (1990) A comparison of linear driving force and pore diffusion models for a pressure swing adsorption bulk separation process. Chem Eng Sci 45:107–115

    Article  CAS  Google Scholar 

  23. Lin B, Golshan-Shirazi S, Ma Z, Guiochon G (1988) Shock effects in nonlinear chromatography. Anal Chem 60:2647–2653

    Article  CAS  Google Scholar 

  24. Santacesaria E, Morbidelli M, Servida A, Storti G, Carra S (1982) Separation of xylenes on Y zeolites. 2. Breakthrough curves and their interpretation. Ind Eng Chem Process Des Dev 21:446–451

    Article  CAS  Google Scholar 

  25. Carra S, Santacesaria E, Morbidelli M, Storti G, Gelosa D (1982) Separation of xylenes on Y zeolites. 3. Pulse curves and their interpretation. Ind Eng Chem Process Des Dev 21:451–457

    Article  CAS  Google Scholar 

  26. Lee W-C, Huang SH, Tsao GT (1988) A unified approach for moments in chromatography. AIChE J 34:2083–2087. doi:10.1002/aic.690341221

    Article  CAS  Google Scholar 

  27. Chase HA (1984) Affinity separations utilising immobilised monoclonal antibodies—a new tool for the biochemical engineer. Chem Eng Sci 39:1099–1125. doi:10.1016/0009-2509(84)85074-5

    Article  CAS  Google Scholar 

  28. Chase HA (1984) Prediction of the performance of preparative affinity chromatography. J Chromatogr A 297:179–202. doi:10.1016/S0021-9673(01)89041-5

    Article  CAS  Google Scholar 

  29. Arnold FH, Blanch HW, Wilke CR (1985) Analysis of affinity separations II: The characterization of affinity columns by pulse techniques. Chem Eng J 30:B25–B36. doi:10.1016/0300-9467(85)80017-4

    Article  CAS  Google Scholar 

  30. Arnold FH, Blanch HW, Wilke CR (1985) Analysis of affinity separations. I: Predicting the performance of affinity adsorbers. Chem Eng J 30:B9–B23. doi:10.1016/0300-9467(85)80016-2

    Article  CAS  Google Scholar 

  31. Arnold FH, Schofield SA, Blanch HW (1986) Analytical affinity chromatography: I. Local equilibrium theory and the measurement of association and inhibition constants. J Chromatogr A 355:1–12. doi:10.1016/S0021-9673(01)97299-1

    Article  CAS  Google Scholar 

  32. Arnold FH, Blanch HW (1986) Analytical affinity chromatography: II. Rate theory and the measurement of biological binding kinetics. J Chromatogr A 355:13–27. doi:10.1016/S0021-9673(01)97300-5

    Article  CAS  Google Scholar 

  33. Arve BH, Liapis AI (1987) Modeling and analysis of biospecific adsorption in a finite bath. AIChE J 33:179–193. doi:10.1002/aic.690330203

    Article  CAS  Google Scholar 

  34. Arve BH, Liapis AI (1988) Modeling and analysis of elution stage of biospecific adsorption in finite bath. Biotechnol Bioeng 31:240–249. doi:10.1002/bit.260310310

    Article  CAS  Google Scholar 

  35. Carta G, Bauer JS (1990) Analytic solution for chromatography with nonuniform sorbent particles. AIChE J 36:147–150

    Article  CAS  Google Scholar 

  36. Ma Z, Whitley RD, Wang N-H (1996) Pore and surface diffusion in multicomponent adsorption and liquid chromatography systems. AIChE J 42:1244–1262

    Article  CAS  Google Scholar 

  37. Gu T, Tsai G-J, Tsao GT (1990) New approach to a general nonlinear multicomponent chromatography model. AIChE J 36:784–788. doi:10.1002/aic.690360517

    Article  CAS  Google Scholar 

  38. Liapis AI, Rippin DWT (1978) The simulation of binary adsorption in activated carbon columns using estimates of diffusional resistance within the carbon particles derived from batc. Chem Eng Sci 33:593–600. doi:10.1016/0009-2509(78)80021-9

    Article  CAS  Google Scholar 

  39. Mansour AR (1989) The simulation of multicomponent sorption processes with axial diffusion. Sep Sci Technol 24:1047–1058

    Article  CAS  Google Scholar 

  40. Yu Q, Wang NHL (1989) Computer simulations of the dynamics of multicomponent ion exchange and adsorption in fixed beds—gradient-directed moving finite element method. Comput Chem Eng 13:915–926

    Article  CAS  Google Scholar 

  41. Mansour A, Von Rosenberg DU, Sylvester ND (1982) Numerical solution of liquid-phase multicomponent adsorption in fixed beds. AIChE J 28:765–772. doi:10.1002/aic.690280510

    Article  CAS  Google Scholar 

  42. Villadsen J, Michelsen ML (1978) Solutions of differential equation models by polynomial approximation. Prentice Hall, Englewood Cliff, NJ

    Google Scholar 

  43. Finlayson BA (2003) Nonlinear analysis in chemical engineering. Ravenna Park Publishing, Seattle

    Google Scholar 

  44. Antia FD, Horváth C (1989) Operational modes of chromatographic separation processes. Ber Bunsenges Phys Chem 93:961–968. doi:10.1002/bbpc.19890930907

    Article  CAS  Google Scholar 

  45. Rathore A, Velayudhan A (2002) Scale-up and optimization in preparative chromatography: principles and biopharmaceutical applications. CRC, Boca Raton, FL

    Book  Google Scholar 

  46. Brown PN, Byrne GD, Hindmarsh AC (1989) VODE: a variable-coefficient ODE solver. SIAM J Sci Stat Comput 10:1038–1051. doi:10.1137/0910062

    Article  Google Scholar 

  47. Ladisch MR (2001) Bioseparations engineering: principles, practice, and economics. Wiley, New York

    Google Scholar 

  48. Snyder LR, Kirkland JJ, Glajch JL (2012) Practical HPLC method development. Wiley, New York

    Google Scholar 

  49. Guiochon G, Felinger A, Shirazi DGG (2006) Fundamentals of preparative and nonlinear chromatography. Academic, Waltham, MA

    Google Scholar 

  50. Knox JH, Pyper HM (1986) Framework for maximizing throughput in preparative liquid chromatography. J Chromatogr A 363:1–30. doi:10.1016/S0021-9673(00)88988-8

    Article  CAS  Google Scholar 

  51. Li Z, Gu Y, Gu T (1998) Mathematical modeling and scale-up of size-exclusion chromatography. Biochem Eng J 2:145–155. doi:10.1016/S1369-703X(98)00027-8

    Article  CAS  Google Scholar 

  52. Gu T, Zheng Y (1999) A study of the scale-up of reversed-phase liquid chromatography. Sep Purif Technol 15:41–58. doi:10.1016/S1383-5866(98)00083-5

    Article  CAS  Google Scholar 

  53. Gu T, Hsu KH, Syu MJ (2003) Scale-up of affinity chromatography for purification of enzymes and other proteins. Enzym Microb Technol 33:430–437

    Article  CAS  Google Scholar 

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Authors and Affiliations

  1. Department of Chemical & Biomolecular Engineering, Ohio University, Athens, Ohio, USA

    Tingyue Gu

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Gu, T. (2015). Literature Review. In: Mathematical Modeling and Scale-Up of Liquid Chromatography. Springer, Cham. https://doi.org/10.1007/978-3-319-16145-7_2

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