Review article number 50: The Maxwell-Stefan approach to mass tranfer

Chemical Engineering Science

Volumn 52, Issue 6, 1997, Pages 861-911

  Krishna, R ^a   Wesselingh, J A ^b  

^a UNIVERSITY OF AMSTERDAM   (Netherlands)

^b UNIVERSITY OF GRONINGEN   (Netherlands)

Author keywords

Fick's law; Ionic diffusion; Membrane separations; Multicomponent diffusion; Porous media; Zeolities

Indexed keywords

ADSORBENTS; CATALYSTS; DIFFUSION IN SOLIDS; MATHEMATICAL MODELS; MEMBRANES; POROUS MATERIALS; THERMODYNAMICS; ZEOLITES;

FICK'S LAW; IONIC DIFFUSION; MAXWELL STEFAN APPROACH;

MASS TRANSFER;

EID: 0031094961     PISSN: 00092509     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0009-2509(96)00458-7     Document Type: Review

References (247)

1. Al-Ghawas, H. A. and Sandall, O. C. (1991) Simultaneous absorption of carbon dioxide, carbonyl sulfide and hydrogen sulfide in aqueous methyldiethanolamine. Chem. Engng Sci. 46, 665-676.
2. Anand, N., Manoja, B. G. R. and Gupta, A. K. (1994) Kinetics of adsorption on biporous solids - for a system with rectangular equilibrium - reanalysed. Chem. Engng Sci. 49, 3277-3290.
3. Aust, E., Dahlke, K. and Emig, G. (1989) Simulation of transport and self-diffusion in zeolites with the Monte Carlo method. J. Catal. 115, 86-97.
4. Barrer, R. M. (1978) Zeolites and Clay Minerals as Sorbents and Molecular Sieves. Academic Press, London, U.K.
5. Berg, D. A. and Harris, T. J. (1993) Characterisation of multicomponent diffusion effects in MTBE synthesis. Ind. Engng Chem. Res. 32, 2147-2158.
6. van den Berg, G. B. and Smolders, C. A. (1992) Diffusional phenomena in membrane separatin processes. J. Membrane Sci. 73, 103-118.
7. Bird, R. B., Stewart, W. E. and Lightfoot, E. N. (1960) Transport Phenomena. Wiley, New York, U.S.A.
8. Bres, M. and Hatzfield, C. (1977) Three gas diffusion - Experimental and theoretical studies. Pflügers Arch. 371, 227-233
9. van Brocklin, L. P. and David, M. M. (1972) Coupled ionic migration and diffusion during liquid phase controlled ion exchange. Ind. Engng Chem. Fundam. 11, 91-99.
10. van den Broeke, L. J. P. (1995) Simulation of diffusion in zeolitic structures. A.I.Ch.E. J. 41, 2399-2414.
11. van den Broeke, L. J. P. and Krishna, R. (1995) Experimental verification of the Maxwell-Stefan theory for micropore diffusion. Chem. Engng Sci. 50, 2507-2522.
12. van den Broeke, L. J. P., Nijhuis, S. A. and Krishna, R. (1992) Monte Carlo Simulations of diffusion in zeolites and comparison with the Generalized Maxwell-Stefan theory. J. Catal 136, 463-477.
13. Bungay, P. M. and Brenner, H. (1973) The motion of a closely fitting sphere in a fluid-filled tube. Int. J. Multiphase Flow 1, 25-26.
14. Burganos, V. N. and Sotirchos, S. V. (1987) Diffusion in pore networks: effective medium theory and smooth field approximation. A.I.Ch.E. J. 33, 1678-1689.
15. Burghardt, A. and Aerts, J. (1988) Pressure changes during diffusion with chemical reaction in a porous pellet. Chem. Engng Process. 23, 77-87.
16. Burghardt, A. and Patzek, T. W. (1983) Mass and energy transport in porous, granular catalysts in multicomponent and multireaction systems. Int. Chem. Engng 23, 739-751.
17. Chandrasekaran, S. K. and King, C. J. (1972) Multi-component diffusion and vapor-liquid equilibria of dilute organic components in aqueous sugar solutions. A.I.Ch.E. J. 18, 513-526.
18. Chang, H.-K. and Farhi, L. E. (1973) On mathematical analysis of gas transport in the lung. Respir. Physiol. 18, 370-385.
19. Chang, H.-K., Tai, R. C. and Farhi, L. E. (1975) Some implications of ternary diffusion in the lung. Respir. Physiol. 23, 109-120.
20. Chang, Y. C. and Myerson, A. S. (1986) Diffusivity of glycine in concentrated saturated and supersaturated aqueous solutions. A.I.Ch.E. J. 32, 1567-1569.
21. Chen, Y. D. and Yang, R. T. (1991) Concentration dependence of surface diffusion and zeolitic diffusion. A.I.Ch.E. J. 37, 1579-1582.
22. Chen, Y. D. and Yang, R. T. (1992) Predicting binary Fickian diffusivities from pure-component Fickian diffusivities for surface diffusion. Chem. Engng Sci. 47, 3895-3905.
23. Chen, Y. D. and Yang, R. T. (1993) Surface diffusion of multilayer adsorbed species. A.I.Ch.E. J. 39, 599-606.
24. Chen, Y. D., Yang, R. T. and Sun, L. M. (1993) Further work on predicting multi-component diffusivities from pure-component diffusivities for surface diffusion and diffusion in zeolites. Chem. Engng Sci. 48, 2815-2816.
25. Chen, Y. D., Yang, R. T. and Uawithya, P. (1994) Diffusion of oxygen, nitrogen and their binary mixtures in carbon molecular sieve. A.I.Ch.E. J. 40, 577-585.
26. Chen, N. Y., Degnan, T. F. and Smith, C. M. (1994) Molecular Transport and Reaction in Zeolites. Design and Application of Shape Selective Catalysts, VCH Publishers, New York, U.S.A.
27. Christensen, N. H. (1977) Multiphase ternary diffusion couples. J. Am. Chem. Soc. 60, 293-296.
28. Cichelli, M. T., Weatherford, W. D. and Bowman, J. R. (1951) Sweep diffusion gas separation process, Part I. Chem. Engng Progress, 47, 63-74.
29. Clark, W. M. and Rowley, R. L. (1986) The mutual diffusion coefficient of methanol - n-hexane near the consolute point. A.I.Ch.E. J. 32, 1125-1131.
30. Conlisk, A. T. (1996) Analytical solutions for falling film absorption of ternary mixtures - 1. Theory. Chem. Engng Sci. 51, 1157-1168.
31. Cooper, A. R. (1974) Vector space treatment of multi-component diffusion. In Geochemical Transport and Kinetics, Papers Presented at a Conference, Airlie House, Warrenton, Virginia, June 1973, eds. A. W. Hofmann, B. J. Giletti, H. S. Yoder Jr and R. A. Yund, pp. 15-30 Carnegie Institute of Washington, Carnegie.
32. Coumans, W. J., Kerkhof, P. J. A. M. and Bruin, S. (1994) Theoretical and practical aspects of aroma retention in spray drying and freeze drying. Drying Technol. 12, 99-149.
33. Cunningham, R. E. and Williams, R. J. J. (1980) Diffusion in Gases and Porous Media. Plenum Press, New York, U.S.A.
34. Curtiss, C. F. and Bird, R. B. (1996) Multicomponent diffusion in polymeric liquids. Proc. Nat. Acad. Sci. 93, 7440-7445.
35. Cussler, E. L. (1976) Multicomponent Diffusion. Elsevier, Amsterdam, The Netherlands.
36. Cussler, E. L. (1984) Diffusion: Mass Transfer in Fluid Systems. Cambridge University Press, Cambridge, U.S.A.
37. Cussler, E. L. and Breuer, M. M. (1972) Accelerating diffusion with mixed solvents. A.I.Ch.E. J. 18, 812-816.
38. Cussler, E. L. and Lightfoot, E. N. (1965) Multicomponent diffusion involving high polymers. III. Ternary diffusion in the system polystyrene 1-polystyrene 2-toluene. J. Phys. Chem. 69, 2875-2879.
39. Dahlke, K. D. and Emig, G. (1991) Diffusion in zeolites - A random-walk approach. Catal. Today 8, 439-450.
40. Deen, W. M. (1987) Hindered transport of large molecules in liquid-filled pores. A.I.Ch.E. J. 33, 1409-1425.
41. Doong, S.-J. and Yang, R. T. (1986) Bulk separation of multicomponent gas mixtures by pressure swing adsorption: pore/surface diffusion and equilibrium models. A.I.Ch.E. J. 32, 397-410.
42. Dribika, M. M. and Sandall, O. C. (1979) Simultaneous heat and mass transfer for multicomponent distillation in a wetted-wall column. Chem. Engng Sci. 34, 733-739.
43. Duncan, J. B. and Toor, H. L. (1962) An experimental study of three component gas diffusion. A.I.Ch.E. J. 8, 38-41.
44. Elnashaie, S. S., Abashar, M. E. and Al-Ubaid, A. S. (1989) Simulation and optimization of an industrial ammonia reactor. Ind. Engng Chem. Res. 27, 2015-2022
45. Elnashaie, S. S. E. H. and Abasher, M. E. E. (1993) Steam reforming and methanation effectiveness factors using the dusty gas model under industrial conditions. Chem. Engng Process. 32, 177-189.
46. Epstein, N. (1989) On the tortuosity and the tortuosity factor in flow and diffusion through porous media. Chem. Engng Sci. 44, 777-779.
47. Etzel, M. R. (1993) Thermodynamic mechanisms for the retention of aroma compounds during drying of foods. A.I.Ch.E. Symp. Ser. No. 297, 89, 32-38.
48. Farooq, S., Rathor, M. N. and Hidajat, K. (1993) A predictive model for a kinetically controlled pressure swing adsorption separation process. Chem. Engng Sci. 48, 4129-4141.
49. Farooq, S. and Ruthven, D.M. (1991) Numerical simulation of kinetically controlled pressure swing adsorption bulk separation based on a diffusion model. Chem. Engng Sci. 46, 2213-2224.
50. Frank, M. J. W., Kuipers, J. A. M., Krishna, R. and Van Swaaij, W. P. M. (1995b) Modelling of simultaneous mass and heat transfer with chemical reaction using the Maxwell-Stefan theory - II. Non-isothermal study. Chem. Engng. Sci. 50, 1661-1671.
51. Frank, M. J. W., Kuipers, J. A. M., Versteeg, G. F. and Van Swaaij, W. P. M. (1995a) Modelling of simultaneous mass and heat transfer with chemical reaction using the Maxwell Stefan theory - I. Model development and isothermal study. Chem. Engng Sci. 50, 1645-1659.
52. Frey, D. D. (1986) Prediction of liquid-phase mass transfer coefficients in multicomponent ion exchange: comparison of matrix, film-model, and effective diffusivity methods. Chem. Engng Commun. 47, 273-293.
53. Fullarton, D. and Schlünder, E. (1986) Diffusion distillation - a new separation process for azeotropic mixtures. Chem. Engng Process 20, 255-270.
54. Furno, J. S., Taylor, R. and Krishna, R. (1986) Condensation of vapor mixtures. II. Simulation of some test condensers. Ind. Engng Chem. Process Des. Dev. 25, 98-101.
55. Garg, D. R. and Ruthven, D. M. (1972) The effect of the concentration dependence of diffusivity on zeolitic sorption curves. Chem. Engng Sci. 27, 417-423.
56. Garside, J. (1985) Industrial crystallization from solution. Chem. Engng Sci. 40, 3-26.
57. Gibbs, B. P., Smith, E. J. and Powers, S. R. (1973) A mathematical model of mass transport in the lung. Int. J. Engng Sci. 11, 625-635.
58. Gilliland, E. R., Baddour, R. F., Perkinson, G. P. and Sladek, K. J. (1974) Diffusion on surfaces. I. Effect of concentration on the diffusivity of physically adsorbed gases. Ind. Engng Chem. Fundam. 13, 95-100.
59. Glasscock, D. A. and Rochelle, G. T. (1989) Numerical simulation of theories for gas absorption with chemical reaction. A.I.Ch.E. J. 35, 1271-1281.
60. Gorak, A. (1991) Berechnungsmethoden der Mehrstoffrektifikation - Theorie und Anwendungen. Habilitationsschrift, RWTH Aachen, Germany.
61. Gorak, A. (1995) Simulation thermischer Trennverfahren fluider Vielkomponentengemische. In Prozeβsimulation, ed. H. Schuler, pp. 349-408. VCH Verlagsgesellshaft mbH, Weinheim, Germany.
62. Graham, E. E. and Dranoff, J. S. (1982) Application of the Stefan Maxwell equations to diffusion in ion exchangers. Ind. Engng Chem. Fundam. 21, 360-369.
63. Grenier, P. (1966) Solvent counter-diffusion in gas absorption. Canad. J. Chem. Engng 44, 213-216.
64. Grimshaw, P. E., Grodzinsky, A. J., Yarmushm, M. L. and Yarmush, D. M. (1990) Selective augmentation of macromolecular transport in gels by electrodiffusion and electrokinetics. Chem. Engng Sci. 45, 2917-2929.
65. Gutsche, R. (1993) Concentration-dependent micropore diffusion analysed by measuring laboratory adsorber dynamics. Chem. Engng Sci. 48, 3723-3742.
66. Haase, R. and Siry, M. (1968) Diffusion im kritischen Entmischungsgebiet binärer flüssiger Systeme. Phys. Chem. Neue Folge 57, 56-73.
67. Habgood, H. W. (1958) The kinetics of molecular sieve action. Sorption of nitrogen-methane mixtures by Linde molecular sieve 4A. Canad. J. Chem. 36, 1384-1397.
68. von Halle, E. (1980) The countercurrent gas centrifuge for the Enrichment of U-235, In Recent Advances in Separation Techniques II. A.I.Ch.E. Symp. Ser. Vol. 76, pp. 82-87. A.I.Ch.E., New York.
69. Haynes, H. W. (1978) Calculation of gas phase diffusion and reaction in heterogeneous catalysts. The importance of viscous flow. Canad. J. Chem. Engng 56, 582-587.
70. Heintz, A. and Stephan, W. (1994) A generalized solution-diffusion model of the pervaporation process through composite membranes. J. Membrane Sci. 89, 143-169.
71. Helfferich, F. (1962) Ion-exchange kinetics. III. Experimental test of the theory of particle-diffusion controlled ion exchange. J. Phys. Chem. 66, 39-44.
72. Helfferich, F. (1983) Ion-exchange kinetics - Evolution of a theory. In Mass Transfer and Kinetics of Ion Exchange, eds. L. Liberti and F. G. Helfferich, NATO Advanced Study Institute Series E: Applied Sciences, No. 71. Martinus Nijhoff, The Hague.
73. Hindmarsh, A. C. and Johnson, S. H. (1988) Dynamic simulation of reversible solid fluid reactions in nonisothermal porous spheres with Stefan Maxwell diffusion. Chem. Engng Sci. 43, 3235-3258.
74. Hirschfelder, J. O., Curtiss, C. F. and Bird, R. B. (1964) Molecular Theory of Gases and Liquids (2nd corrected printing). Wiley, New York, U.S.A.
75. Hite, R. H. and Jackson, R. (1977) Pressure gradients in porous catalyst pellets in the intermediate diffusion regime. Chem. Engng Sci. 32, 703-709.
76. 4OH) on the diffusion of BSA in porous media. Chem. Engng Sci. 47, 151-164.
77. Jackson, R. (1977) Transport in Porous Catalysts. Elsevier, Amsterdam, The Netherlands.
78. Johansen, V., Jepsen, O. L., Christensen, N. H. and Gamborg Hansen, J. C. (1978) Ternary diffusion in cement clinker at 1500°C. Cement Concrete Res. 8, 301-310.
79. Kapila, D. and Plawsky, J. L. (1995) Diffusion processes for integrated waveguide fabrication in glasses: a solid state electrochemical approach. Chem. Engng Sci. 50, 2589-2600.
80. Kapoor, A., Krishnamurthy, K. R. and Shirley, A. (1993) Kinetic separation of carbon dioxide from hydrocarbons using carbon molecular sieve. Gas Separation Purification 7, 259-263.
81. Kapoor, A. and Yang, R. T. (1989) Surface diffusion on energetically heterogeneous surfaces. A.I.Ch.E. J. 35, 1735-1738.
82. Kapoor, A. and Yang, R. T. (1990) Surface diffusion on energetically heterogeneous surfaces. An effective medium approximation approach. Chem. Engng Sci. 45, 3261-3270.
83. Kapoor, A. and Yang, R. T. (1991) Contribution of concentration-dependent surface diffusion to rate of adsorption. Chem. Engng Sci. 46, 1995-2002.
84. Kapteijn, F., Bakker, W. J. W., van der Graaf, J., Zheng, G., Poppe, J. and Moulijn, J. A. (1995) Permeation and separation behaviour of a silicalite-1 membrane. Catal. Today 25, 213-218.
85. Kapteijn, F., Bakker, W. J. W., Zheng, G., Poppe, J. and Moulijn, J. A. (1994) The temperature and occupancy dependent diffusion on n-butane through a silicalite membrane. Microporous Mater. 3, 227-234.
86. Kärger, J. (1973) Some remarks on the straight and cross-coefficients in irreversible thermodynamics of surface flow and on the relation between diffusion and self diffusion. Surf. Sci. 36, 797-801.
87. Kärger, J. and Bülow, M. (1975) Theoretical prediction of uptake behaviour in adsorption of binary gas mixtures using irreversible thermodynamics. Chem. Engng Sci. 30, 893-896.
88. Kärger, J., Petzold, M., Pfeifer, H., Ernst, S. and Weitkamp, J. (1992) Single-file diffusion and reaction in zeolites. J. Catal. 136, 283-299.
89. Kärger, J. and Ruthven, D. M. (1992) Diffusion in Zeolites. Wiley, New York, U.S.A.
90. Katti, S. (1995) Gas-liquid-solid systems: an industrial perspective. Chem. Engng Res. Des. Trans. Ind Chem. Engng Part A, 73, 595-607.
91. Kaza, K. R. and Jackson, R. (1980) Diffusion and reaction of multicomponent gas mixtures in isothermal porous catalysts. Chem. Engng Sci. 35, 1179-1197.
92. Kedem, O. and Katchalsky, A. (1961) A physical interpretation of the phenomenological coefficients in membrane permeability. J. Gen. Physiol 45, 143.
93. Keil, F. J. (1996) Modelling of phenomena within catalyst particles. Chem. Engng Sci. 51, 1543-1567.
94. Kerkhof, P. J. A. M. (1996) A modified Maxwell-Stefan model for transport through inert membranes: the binary friction model. Chem. Engng J.
95. Keurentjes, J. T. F., Janssen, A. E. M., Broek, A. P., van der Padt, A., Wesselingh, J.A. and van "t Riet, K. (1992) Multicomponent diffusion in dialysis membrane. Chem. Engng Sci. 47, 1963-1971.
96. King C. J. (1980) Separation Processes, 2nd Edn. McGraw-Hill, New York, U.S.A.
97. Kleijn, C. R. and Hoogendoorn, C. J. (1991) A study of 2- and 3-D transport phenomena in horizontal chemical vapor deposition reactors. Chem. Engng Sci. 46, 321-334.
98. Kohl, A. L. and Riesenfeld, F. C. (1985) Gas Purification. 4th Edn, Gulf Publishing Co., TX, U.S.A.
99. Kouyoumdjiev, M. S., Vortsman, M. A. G. and Kerkhof, P. J. A. M. (1993) Single and multi-component adsorption from liquid phase on activated carbon in finite bath process. In Precision Process Technology, eds. M. P. C. Weijnen and A. A. H. Drinkenburg, pp. 257-266. Kluwer, Dordrecht, The Netherlands.
100. Kraaijeveld, G., Kuiken, G. D. C. and Wesselingh, J. A. (1994) Comments on "negative diffusion coefficients". Ind. Engng Chem. Res. 33, 750-851.
101. Kraaijeveld, G., Sumberova, V., Kuindersma, S. and Wesselingh, J. A. (1995) Modelling electrodialysis using the Maxwell-Stefan description. Chem. Engng J. 57, 163-176.
102. Kraaijeveld, G. and Wesselingh, J. A. (1993a) The kinetics of film diffusion limited ion exchange. Chem. Engng Sci. 48, 467-473.
103. Kraaijeveld, G. and Wesselingh, J. A. (1993b) Negative Maxwell-Stefan diffusion coeffficients. Ind. Engng Chem. Res. 32, 738-742.
104. Krishna, R. and Standart, G. (1976) A multicomponent film model incorporating an exact matrix method of solution to the Maxwell-Stefan equations. A.I.Ch.E. J. 22, 383-389.
105. Krishna, R. (1977a) A generalized film model for mass transfer in non-ideal fluid mixtures. Chem. Engng Sci. 32, 659-667.
106. Krishna, R. (1977b) A film model analysis of non-equimolar distillation of multicomponent mixtures. Chem. Engng Sci. 32, 1197-1203.
107. Krishna, R. (1978a) A note on the film and penetration models for multicomponent mass transfer. Chem. Engng Sci. 33, 765-767.
108. Krishna, R. (1978b) Penetration depths in multicomponent mass transfer. Chem. Engng Sci. 33, 1495-1497.
109. Krishna, R. (1979) A simplified film model description of multicomponent interphase mass transfer. Chem. Engng Commun. 3, 29-39.
110. Krishna, R. (1981a) Ternary mass transfer in a wettedwall column - significance of diffusional interactions. I - Stefan diffusion. Trans. Ind. Chem. Engng 59, 35-43.
111. Krishna, R. (1982) A turbulent film model for multi-component mass transfer. Chem. Engng J. 24, 163-172.
112. Krishna, R. (1987) Diffusion in multicomponent electrolyte systems. Chem. Engng J. 35, 19-24.
113. Krishna, R. (1989) Comments on "Simulation and optimization of an industrial ammonia reactor". Ind. Engng Chem. Res. 28, 1266.
114. Krishna, R. (1990) Multicomponent surface diffusion of adsorbed species. A description based on the generalized Maxwell-Stefan diffusion equations. Chem. Engng Sci. 45, 1779-1791.
115. Krishna, R. (1993a) Problems and pitfalls in the use of the Fick formulation for intraparticle diffusion. Chem. Engng Sci. 48, 845-861.
116. Krishna, R. (1993b) A unified approach to the modelling of intraparticle diffusion in adsorption processes. Gas Separation Purification 7, 91-104.
117. Krishna, R. and van den Broeke, L. J. P. (1995) The Maxwell-Stefan description of mass transport across zeolite membranes. Chem. Engng J, 57, 155-162.
118. Krishna, R., Low, C. Y., Newsham, D. M. T., Olivera-Fuentas, C. G. and Standart, G. L. (1985) Ternary mass transfer in liquid-liquid extraction. Chem. Engng Sci 40, 893-903.
119. Krishna, R., Salomo, R. M. and Rahman, M. A. (1981b) Ternary mass transfer in a wetted wall column. Significance of diffusional interactions. Part II. Equimolar diffusion. Trans. Ind. Chem. Engng 59, 44-53.
120. Krishnamurthy, R. and Taylor, R. (1985a) Non-equilibrium stage model of multicomponent separation processes. A.I.Ch.E. J. 32, 449-465.
121. Krishnamurthy, R. and Taylor, R. (1985b) Simulation of packed distillation and absorption columns. Ind. Engng Chem. Process Des. Dev. 24, 513-524.
122. Kuijlaars, K. J., Kleijn, C. R. and van den Akker, H. E. A. (1995) Multicomponent diffusion phenomena in multiple wafer chemical vapour deposition reactors. Chem. Engng J. 57, 127-136.
123. Kuijlaars, K. J. (1996) Modelling of transport phenomena and chemistry in chemical vapour deposition reactors. Ph.D. thesis, Delft University of Technology, Delft, The Netherlands.
124. Kuiken, G. D. C. (1994) Thermodynamics of Irreversible Processes: Applications to Diffusion and Rheology. Wiley, Chichester, U.K.
125. Lakshminarayaniah, N. (1969) Transport Phenomena in Membranes. Academic Press, New York, U.S.A.
126. Lao, M. and Taylor, R. (1994) Modelling mass transfer in three-phase distillation. Ind. Engng Chem. Res. 33, 2637-2650.
127. Lee, H. L., Lightfoot, E. N., Reis, J. F. G. and Waissbluth, M. D. (1977) The systematic description and development of separations processes. In Recent Developments in Separation Science, Vol. III, Part A, ed. N. N. Li, pp. 1-69. CRC Press, Cleveland, OH, U.S.A.
128. Lightfoot, E. N. (1974) Transport Phenomena and Living Systems. McGraw-Hill, New York, U.S.A.
129. 2 in alkanolamine solutions: The influence of parallel and consecutive reversible reactions and the coupled diffusion of ionic species. Chem. Engng Sci. 46, 2303-2313.
130. 2O. A.I.Ch.E. J. 35, 676-678.
131. Löwe, A. and Bub, G. (1976) Multiple steady states for isothermal catalytic gas-solid reactions with a positive reaction order. Chem. Engng Sci. 31, 175-178.
132. McDowell, J. K. and Davis, J. F. (1988) A characterization of diffusion distillation for azeotropic separation. Ind. Engng Chem. Res. 27, 2139-2148.
133. MacElroy, J. M. D. and Kelly, J. J. (1985) Hindered diffusion of gases in 'leaky' membranes using the dusty gas model. A.I.Ch.E. J. 31, 35-44.
134. Martinez, J. and Setterwall, F. (1991) Gas-phase controlled convective drying of solids wetted with multicomponent liquid mixtures. Chem. Engng Sci. 46, 2235-2252.
135. Mason, E. A. and del Castillo, L. F. (1985) The role of viscous flow in theories of membrane transport. J. Membrane Sci. 23, 199-220.
136. Mason, E. A. and Lonsdale, H. K. (1990) Statistical mechanical theory of membrane transport. J. Membrane Sci. 51, 1-81.
137. Mason, E. A. and Malinauskas, A. P. (1983) Gas Transport in Porous Media: The Dusty Gas Model. Elsevier, Amsterdam, The Netherlands.
138. Mason, E. A. and Viehland, L. A. (1978) Statistical mechanical theory of membrane transport for multi-component systems: Passive transport through open membranes. J. Chem. Phys. 68, 3562-3573.
139. Matsuoka, M. and Garside, J. (1991) Non-isothermal effectiveness factors and the role of heat transfer in crystal growth from solutions and melts. Chem. Engng Sci. 46, 183-192.
140. Maxwell, J. C. 1866. On the dynamical theory of gases. Phil. Trans. R. Soc. 157, 49-88.
141. Meerdink, G. and van 't Riet, K. (1993) Modeling segregation of solute material during drying of food liquids. A.I.Ch.E. J. 41, 732-736.
142. Mehta, G. D., Morse, T. F., Mason, E. A. and Daneshpajooh, M. H. (1976) Generalized Nernst-Planck and Stefan-Maxwell equations for membrane transport. J. Chem. Phys. 64, 3917-3923.
143. Mikami, H. (1970) Separation of a three-component gas mixture in an axisymmetric supersonic jet. Ind. Engng Chem. Fundam. 9, 121-128.
144. Modell, H. I. and Farhi, L. E. (1976) Ternary gas diffusion - in vitro studies. Respir. Physiol. 27, 65-71.
145. Modine, A. D. (1963) Ternary mass transfer. Ph.D. thesis, Carnegie Institute of Technology, Pittsburgh, PA, U.S.A.
146. Moore, R. M. and Katzer, J. R. (1972) Counterdiffusion of liquid hydrocarbons in Type Y zeolite: effect of molecular size, molecular type, and direction of diffusion. A.I.Ch.E. J. 18, 816-824.
147. Mulder, M. (1991) Basic Principles of Membrane Technology. Kluwer Academic Press, Dordrecht, The Netherlands.
148. Muralidhara, H. S. (1994) Enhance separations with electricity. Chemtech 24, 36-41.
149. Newman, J. (1991) Electrochemical Systems. 2nd Edn. Prentice-Hall, Englewood Cliffs, NJ, U.S.A.
150. Newman, J. (1995) Thermoelectric effects in electrochemical systems. Ind. Engng Chem. Res. 34, 3208-3216.
151. Niessen, W. (1991) Untersuchungen zur Diffusion und Gegendiffusion in Zeolithen mit Hilfe der FTIR-Spectroskopie. Ph.D. thesis, Fritz Haber Institut der Max Planck Gesellschaft, Berlin, Germany.
152. van Oers, C. W. (1994) Solute rejection in multicomponent systems during ultrafiltration. Ph.D. thesis, Eindhoven University of Technology, Eindhoven, The Netherlands.
153. Ofori, J. Y. and Sotirchos, S. V. (1996) Multicomponent mass transport in chemical vapor infiltration. Ind. Engng Chem. Res. 35, 1275-1287.
154. Okubo, T. and Inoue, H. (1988) Improvement of surface transport property by surface modification. A.I.Ch.E. J. 34, 1031-1033.
155. Olano, S., Nagura, S., Kosuge, H. and Asano, K. (1995) Mass transfer in binary and ternary distillation by a packed column with structured packing. J. Chem. Engng Japan 28, 750-757.
156. Othmer, H. G. and Scriven, L. E. (1969) Interactions of reaction and diffusion in open systems. Ind. Engng Chem. Fundam. 8, 302-313.
157. Palekar, M. G. and Rajadhyaksha, R. A. (1985) Sorption in zeolites - I. Sorption of single component and binary sorbate systems. Chem. Engng Sci. 40, 1085-1091.
158. Palekar, M. G. and Rajadhyaksha, R. A. (1986) Sorption in zeolites - III. Binary sorption. Chem. Engng Sci. 41, 463-468.
159. Peppas, N. A. and Meadows, D. L. (1983) Macromolecular structure and solute diffusion in membranes: An overview of recent theories. J. Membrane Sci. 16, 361-377.
160. Pertler, M., Blass, E. and Stevens, G. W. (1996) Fickian diffusion in binary mixtures that form two liquid phases. A.I.Ch.E. J. 42, 910-920.
161. Pinto, N. G. and Graham, E. E. (1986) Estimation of diffusivities in electrolyte solutions using Stefan-Maxwell equations. A.I.Ch.E. J. 32, 291-296.
162. Pinto, N. G. and Graham, E. E. (1987a) Multicomponent diffusion in concentrated electrolyte solutions: effect of solvation. A.I.Ch.E. J. 33, 436-443.
163. Pinto, N. G. and Graham, E. E. (1987b) Characterization of ionic diffusivities in ion-exchange resins. Ind. Engng Chem. Res. 26, 2331-2336.
164. Ptasinski, K. J. and Kerkhof, P. J. A. M. (1992) Electric field driven separations: phenomena and applications. Sep. Sci. Technol. 27, 995-1021.
165. Qureshi, W. R. and Wei, J. (1990) One- and two-component diffusion in zeolite ZSM-5. J. Catal. 126, 126-172.
166. Raal, J. D. and Khurana, M. K. (1973) Gas absorption with large heat effects in packed columns. Canad. J. Chem. Eng. 51, 162-167.
167. Rao, M. B. and Sircar, S. (1993) Nanoporous carbon membrane for gas separation. Gas Separation Purification 7, 279-284.
168. Reddy, K. V . and Murty, C. V. S. (1995) A methodology for the a priori selection of catalyst particle models. Ind. Engng Chem. Res. 34, 468-473.
169. Reed, D. A. and Ehrlich, G. (1981a) Surface diffusion, atomic jump rates and thermodynamics. Surf. Sci. 102, 588-609.
170. Reed, D. A. and Ehrlich, G. (1981b) Surface diffusivity and the time correlation of concentration fluctuations. Surf. Sci. 105, 603-628.
171. Reid, R. C., Prausnitz, J. M. and Poling, B. (1987) The Properties of Gases and Liquids. 4th Edn. McGraw-Hill, New York, U.S.A.
172. Reinhardt, D. and Dialer, K. (1981) Geometrical relationships for ternary gas diffusion balances and criteria for multicomponent phenomena. Chem. Engng Sci. 36, 1557-1566.
173. Remick, R. R. and Geankoplis, C. J. (1974) Ternary diffusion of gases in capillaries in the transition region between Knudsen and molecular diffusion. Chem. Engng Sci. 29, 1447-1455.
174. Riede, Th. and Schlünder, E. U. (1990a) Selective evaporation of a binary mixture into dry or humidified air.Chem. Engng Process. 21, 83-93.
175. Riede, Th. and Schlünder, E. U. (1990b) Selective evaporation of a ternary mixture containing one nonvolatile component with regard to drying processes. Chem. Engng Process. 28, 151-163.
176. Riekert, L. (1971) Rates of sorption and diffusion of hydrocarbons in zeolites. A.I.Ch.E. J. 17, 446-454.
177. Robertson, B. C. and Zydney, A. L. (1988) A Stefan-Maxwell analysis of protein transport in porous membranes. Sep. Sci. Technol. 23, 1799-1811.
178. Ronge, G. (1995) Überprüfung unterschiedelicher Modelle für den Stoffaustausch bei der Rektifikation in Packungskolonnen. Fortschritt-Berichte VDI Verfahrenstechnik No. 390, Düsseldorf.
179. Round, G. F., Habgood, H. W. and Newton, R. (1966) A numerical analysis of surface diffusion in a binary adsorbed film. Separ. Sci. 1, 219-244.
180. Ruthven, D. M. (1984) Principles of Adsorption and Adsorption Processes. Wiley, New York. U.S.A.
181. Ruthven, D. M., Farooq, S. and Knaebel, K. S. (1994) Pressure Swing Adsorption, VCH Publishers, New York, U.S.A.
182. Scattergood, E. M. and Lightfoot, E. N. (1968) Diffusional interaction in an ion-exchange membrane. Trans. Faraday Soc. 64, 1135-1143.
183. Schneider, P. (1975) Intraparticle diffusion in multi-component catalytic reactions. Catal, Rev. - Sci. Engng 12, 201-278.
184. Schnitzlein, K. and Hofmann, H. (1988) Solving the pellet problem for multicomponent mass transport and complex reactions. Comput. Chem. Engng 12, 1157-1161.
185. Seader, J. D. (1989) The rate-based approach for modeling staged separations. Chem. Engng Prog. 85, 41-49.
186. Seidel, A. and Carl, P. S. (1989) The concentration dependence of surface diffusion for adsorption on energetically heterogeneous adsorbents. Chem. Engng Sci. 44, 189-194.
187. Sentarli, I. and Hortaçsu, A. (1987) Solution of the linearized equations of multicomponent mass transfer with chemical reaction and convection for a film model, Ind. Engng Chem. Res. 26, 2409-2413.
188. Shaeiwitz, J. A. (1984) Coupled boundary layer transport involving particles. A.I.Ch.E. J. 30, 310-316.
189. Shaeiwitz, J. A. and Lechnick, W. J. (1984) Ternary diffusion formulation for diffusiophoresis. Chem. Engng Sci. 39, 799-807.
190. Sherwood, T. K., Pigford, R. L. and Wilke, C. R. (1975) Mass Transfer. McGraw-Hill, New York, U.S.A.
191. Sikavitsas, V. I. and Yang, R. T. (1995) Predicting multicomponent diffusivities for diffusion on surfaces and in molecular sieves with energy heterogeneity. Chem. Engng Sci. 50, 3057-3065.
192. Sloot, H. J. (1991) A non-permselective membrane reactor for catalytic gas phase reactions. Ph.D. thesis, University of Twente, Enschede, The Netherlands.
193. Smit, J. A. M, Eijsermans, J. C. and Staverman, A. J. (1975) Friction and partition in membranes. J. Phys. Chem. 79, 2168-2175.
194. Smith, T. G. and Dranoff, J. S. (1964) Film diffusion-controlled kinetics in binary ion exchange. Ind. Engng Chem. Fundam. 3, 195-200.
195. Spiegler, K. S. (1958) Transport processes in ionic membranes. Trans. Faraday Soc. 54, 1408-1428.
196. Srinivasan, R., Auvil, S. R. and Burban, P. M. (1994) Eluciditating the mechanism(s) of gas transport in poly[1-(trimethylsilyl)-1-propyne] (PTMSP) membranes. J. Membrane Sci. 86, 67-86.
197. Srinivasan, R., Auvil, S. R. and Schork, J. M. (1995) Mass transfer kinetic in carbon molecular sieves - an interpretation of "Langmuir kinetics". Chem. Engng J. 57, 137-144.
198. Sotirchos, S. V. (1991) Dynamic modeling of chemical vapor infiltration. A.I.Ch.E. J. 37, 1365-1378.
199. Sotirchos, S. V. and Burganos, V. N. (1988) Analysis of multicomponent diffusion in pore networks. A.I.Ch.E. J. 34, 1106-1118.
200. Standart, G. L., Taylor, R. and Krishna, R. (1979) The Maxwell-Stefan formulation of irreversible thermodynamics for simultaneous heat and mass transfer. Chem. Engng Commun. 3, 277-289.
201. Stefan, J. (1871) Über das Gleichgewicht und die Bewegung insbesondere die Diffusion von Gasgemengen. Sitzber. Akad. Wiss. Wien. 63, 63-124.
202. Stichlmair, J., Schmidt, J. and Proplech, R. (1992) Electroextraction: a novel separation technique. Chem. Engng Sci. 47, 3015-3022.
203. von Stockar, U. and Wilke, C. R. (1977) Rigorous and short-cut design calculations for gas absorption involving large heat effects. Ind. Engng Chem. Fundam. 16, 88-103.
204. Sundaresan, S. and Hall, C. K. (1986) Mathematical modelling of diffusion and reaction in blocked zeolite catalysis. Chem. Engng Sci. 41, 1631-1645.
205. Sundelöf, L.-O. (1979) Diffusion in macromolecular solutions. Ber. Bunsenges. Phys. Chem. 83, 329-342.
206. Sundmacher, K. and Hoffmann, U. (1994a) Macrokinetic analysis of MTBE synthesis in chemical potentials. Chem. Engng Sci. 49, 3077-3089.
207. Sundmacher, K. and Hoffmann, U. (1994b) Multi-component mass and energy transport on different length scales in a packed distillation column for heterogeneously catalysed fuel ether production. Chem. Engng Sci. 49, 4443-4464.
208. Tai, R. C. and Chang, H.-K. (1979) A mathematical study of non-equimolar ternary gas diffusion. Bull. Math. Biol. 41, 591-606.
209. Theodorou, D. and Wei, J. (1983) Diffusion and reaction in blocked and high occupancy zeolite catalysis, J. Catal. 83, 205-224.
210. Taylor, R. and Krishna, R. (1993) Multicomponent Mass Transfer. Wiley, New York, U.S.A.
211. Taylor, R., Krishnamurthy, R., Furno, J. S. and Krishna, R. (1986) Condensation of vapor mixtures. I. A mathematical model and a design method. Ind. Engng Chem. Process Des. Dev. 5, 83-97.
212. Taylor, R. and Lucia, A. (1995) Modeling and analysis of multicomponent separation processes. A.I.Ch.E. Symp. Ser. 304 91, 19-28. A.I.Ch.E., New York.
213. Toor, H. L. (1957) Diffusion in three component gas mixtures. A.I.Ch.E. J. 3, 198-207.
214. Tsikoyiannis, J. G. and Wei, J. (1991) Diffusion and reaction in high-occupancy zeolite catalysts - I. A stochastic theory. Chem. Engng Sci. 46, 233-253.
215. Tunison, M. E. and Chapman, T. W. (1976) The effect of a diffusion potential on the rate of liquid-liquid ion exchange. Ind. Engng Chem. Fundam. 15, 196-201.
216. Tuohey, P. G., Pratt, H. R. C. and Yost, R. S. (1982) Binary and ternary distillation in a stirred mass transfer cell. Chem. Engng Sic. 37, 1741-1750.
217. Umino, S. and Newman, J. (1993) Diffusion of sulfuric acid in concentrated solutions. J. Electrochem. Soc. 140, 2217-2221.
218. Ünal, A. (1987) Gaseous mass transport in porous media through a stagnant gas. Ind. Engng Chem. Res. 26, 72-77.
219. Valerio, S. and Vanni, M. (1994) Interfacial mass transfer and chemical reaction in non-ideal multi-component systems. Chem. Engng Sci. 49, 3297-3305.
220. Vanni, M., Valerio, S. and Baldi, G. (1995) The role of non-ideal phenomena in interfacial mass transfer with chemical reaction. Chem. Engng J. 57, 205-217.
221. 2: III, interdiffusion coefficients. J. Am. Chem. Soc. 55, 312-317.
222. Veldsink, J. W., van Damme, R. M. J., Versteeg, G. F. and van Swaaij, W. P. M. (1995) The use of the dusty gas model for the description of mass transport with chemical reaction in porous media. Chem. Engng J. 57, 115-125.
223. Vignes, A. (1966) Diffusion in binary solutions. Ind. Engng Chem. Fundam. 5, 189-199.
224. Vinograd, J. R. and McBain, J. W. (1941) Diffusion of electrolytes and ions in their mixtures. J. Am. Chem. Soc. 63, 2008-2015.
225. Vitagliano, V., Sartorio, R., Scala, S. and Spaduzzi, D. (1978) Difffusion in a ternary system and the critical mixing point. J. Solution Chem. 7, 605-621.
226. Vogelpohl, A. (1979) Murphree efficiencies in multi-component systems. Institution of Chem. Engng Symp. Ser. 56 79, 2.1, 25-31. I. Chem. E., Rugby, U.K.
227. Voight, W. (1982) Status and plans of the DOE uranium enrichment program. A.I.Ch.E. Symp. Ser. 78, 1-9. A.I.Ch.E., New York.
228. Vonk, P. (1994) Diffusion of large molecules in porous structures. Ph. D. Thesis, University of Groningen, Groningen, The Netherlands.
229. Ward, C. E. and Russel, W. B. (1981) On the short-residence time hydropyrolysis of single coal particles: the effect of unequal diffusivities. A.I.Ch.E. J. 21, 859-861.
230. Wei, J. (1994) Nonlinear phenomena in zeolite diffusion and reaction. Ind. Engng Chem. Res. 33, 2467-2472.
231. Wesselingh, J. A., Kraaijeveld, G. and Vonk, P. (1995) Exploring the Maxwell-Stefan description of ion exchange. Chem. Engng J. 57, 75-89.
232. Wesselingh, J. A. and Krishna, R. (1990. Mass Transfer. Ellis Horwood, Chichester, U.K.
233. Wijmans, J. G. and Baker, R. W. (1995) The solution-diffusion model: a review. J. Membrane Sci. 107, 1-21.
234. Wilke, C. R. (1950) Diffusional properties of multi-component gases. Chem. Engng Prog. 46, 95-104.
235. Wills, G. B. and Lightfoot, E. N. (1966) Transport phenomena in ion exchange membranes. Ind. Engng Chem. Fundam. 5, 114-120.
236. Wong, R. L. and Denny, V. E. (1975) Diffusion, flow and heterogeneous reaction of ternary mixtures in porous catalytic media. Chem. Engng Sci. 30, 709-716.
237. Worth, H. and Piiper, J. (1978) Diffusion of helium, carbon dioxide, and sulfur hexafluoride in gas mixtures similar to alveolar gas. Respir. Physiol. 32, 155-166.
238. Wright, P. G. (1972) Remarks on the Stefan-Maxwell equations for diffusion in a dusty gas. J. Chem. Soc. Faraday. Trans. 68, 1951-1954.
239. Xiao, J. and Wei, J. (1992) Diffusion mechanism of hydrocarbons in zeolites. Chem. Engng Sd. 47, 1123-1141.
240. Yang, R. T. (1987) Gas Separation by Adsorption Processes. Butterworth, Boston, U.S.A.
241. Yang, R. T., Chen, Y. D. and Yeh, Y. T. (1991) Predictions of cross-term coefficients in binary diffusion: diffusion in zeolite. Chem. Engng Sci. 46, 3089-3099.
242. Yoshida, H. and Kataoka, T. (1985) Migration of two ions during electrolysis of glass wave guide. J. Appl. Phys. 58, 1739-1743.
243. Yu, W.-C. and Astarita, G. (1987) Design of packed towers for selective chemical absorption. Chem. Engng Sci. 42, 425-433.
244. Zarzycki, R. and Chacuk, A. (1993) Absorption: Fundamentals and Applications. Pergamon Press, Oxford, U.K.
245. Zhdanov, V. P. (1985) General equations for description of surface diffusion in the framework of the lattice gas model. Surf. Sci. 194, L13-L17.
246. Zimmerman, A., Joulia, X., Gourdon, C. and Gorak, A. (1995) Maxwell-Stefan approach in extractor design. Chem. Engng J. 57, 229-236.
247. Zgrablich, G., Pereyra, V., Ponzi, M. and Marchese, J. (1986) Connectivity effects for surface diffusion of adsorbed gases. A.I.Ch.E. J. 32, 1158-1168.