Review of 3D CFD modeling of flow and mass transfer in narrow spacer-filled channels in membrane modules

Chemical Engineering and Processing: Process Intensification

Volumn 49, Issue 7, 2010, Pages 759-781

  Fimbres Weihs, G A ^a   Wiley, D E ^a  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Computational Fluid Dynamics (CFD); Mass transfer; Novel spacer; Spacer design complex geometries

Indexed keywords

ANALYSIS TOOLS; CFD MODELING; CFD MODELS; FLOW CONDITION; FLOW PROBLEMS; FLOW STUDIES; GEOMETRIC PARAMETER; IONIC COMPONENT; MASS TRANSFER ENHANCEMENT; MEMBRANE MODULE; MEMBRANE SEPARATION; NOVEL SPACER; SPACER DESIGN; SPACER GEOMETRY; SPACER-FILLED CHANNELS; SPIRAL WOUND MEMBRANES; THREE-DIMENSIONAL (3D);

FLUID DYNAMICS; FLUIDS; GEOMETRY; MASS TRANSFER; NUMERICAL METHODS; RELIABILITY ANALYSIS; THREE DIMENSIONAL;

COMPUTATIONAL FLUID DYNAMICS;

EID: 77955983527     PISSN: 02552701     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cep.2010.01.007     Document Type: Article

References (133)

1. Thomas D.G. Forced convection mass transfer. Part II. Effect of wires located near the edge of the laminar boundary layer on the rate of forced convection from a flat plate. AIChE J. 1965, 11:848-852.
2. Thomas D.G. Forced convection mass transfer. Part III. Increased mass transfer from a flat plate caused by the wake from cylinders located near the edge of the boundary layer. AIChE J. 1966, 12:124-130.
3. Da Costa A.R., Fane A.G., Fell C.J.D., Franken A.C.M. Optimal channel spacer design for ultrafiltration. J. Membr. Sci. 1991, 62:275-291.
4. Hicks R.E., Mandersloot W.G.B. The effect of viscous forces on heat and mass transfer in systems with turbulence promoters and in packed beds. Chem. Eng. Sci. 1968, 23:1201-1210.
5. Schock G., Miquel A. Mass transfer and pressure loss in spiral wound modules. Desalination 1987, 64:339-352.
6. Fimbres-Weihs G.A., Wiley D.E., Fletcher D.F. Unsteady flows with mass transfer in narrow zigzag spacer-filled channels: a numerical study. Ind. Eng. Chem. Res. 2006, 45:6594-6603.
7. Fimbres-Weihs G.A., Wiley D.E. Numerical study of mass transfer in three-dimensional spacer-filled narrow channels with steady flow. J. Membr. Sci. 2007, 306:228-243.
8. Thomas D.G., Griffith W.L., Keller R.M. The role of turbulence promoters in hyperfiltration plant optimization. Desalination 1971, 9:33-50.
9. Li Y.-L., Tung K.-L. CFD simulation of fluid flow through spacer-filled membrane module: selecting suitable cell types for periodic boundary conditions. Desalination 2008, 233:351-358.
10. Da Costa A.R., Fane A.G. NeT-type spacers: effect of configuration on fluid flow path and ultrafiltration flux. Ind. Eng. Chem. Res. 1994, 33:1845-1851.
11. Kang I.S., Chang H.N. The effect of turbulence promoters on mass transfer-numerical analysis and flow visualization. Int. J. Heat Mass Tran. 1982, 25:1167-1181.
12. A.R. Da Costa, Fluid flow and mass transfer in spacer-filled channels for ultrafiltration, Thesis (Doctor of Philosophy), 1993, School of Chemical Engineering and Industrial Chemistry, The University of New South Wales, Sydney. 273 p.
13. Gimmelshtein M., Semiat R. Investigation of flow next to membrane walls. J. Membr. Sci. 2005, 264:137-150.
14. Li H., Fane A.G., Coster H.G.L., Vigneswaran S. Direct observation of particle deposition on the membrane surface during crossflow microfiltration. J. Membr. Sci. 1998, 149:83-97.
15. Neal P.R., Li H., Fane T., Wiley D.E. The effect of filament orientation on critical flux and particle deposition in spacer-filled channels. J. Membr. Sci. 2003, 214:165-178.
16. Versteeg H.K., Malalasekera W. An Introduction to Computational Fluid Dynamics: The Finite Volume Method 1995, Prentice Hall, London.
17. Ghidossi R., Veyret D., Moulin P. Computational fluid dynamics applied to membranes: state of the art and opportunities. Chem. Eng. Process 2006, 45:437-454.
18. Schwinge J., Wiley D., Fletcher D.F. Simulation of the flow around spacer filaments between channel walls. 1. Hydrodynamics. Ind. Eng. Chem. Res. 2002, 41:2977-2987.
19. Fletcher D.F., Wiley D. A computational fluids dynamics study of buoyancy effects in reverse osmosis. J. Membr. Sci. 2004, 245:175-181.
20. Cao Z., Wiley D., Fane A.G. CFD simulations of net-type turbulence promoters in a narrow channel. J. Membr. Sci. 2001, 185:157-176.
21. Geraldes V., Semiao V., de Pinho M.N. Flow and mass transfer modelling of nanofiltration. J. Membr. Sci. 2001, 191:109-128.
22. Koutsou C.P., Yiantsios S.G., Karabelas A.J. Numerical simulation of the flow in a plane-channel containing a periodic array of cylindrical turbulence promoters. J. Membr. Sci. 2004, 231:81-90.
23. Koutsou C.P., Yiantsios S.G., Karabelas A.J. Direct numerical simulation of flow in spacer-filled channels: effect of spacer geometrical characteristics. J. Membr. Sci. 2007, 291:53-69.
24. Karode S.K., Kumar A. Flow visualization through spacer filled channels by computational fluid dynamics. I. Pressure drop and shear rate calculations for flat sheet geometry. J. Membr. Sci. 2001, 193:69-84.
25. Ranade V.V., Kumar A. Fluid dynamics of spacer filled rectangular and curvilinear channels. J. Membr. Sci. 2006, 271:1-15.
26. Li F., Meindersma W., De Haan A.B., Reith T. Optimization of commercial net spacers in spiral wound membranes modules. J. Membr. Sci. 2002, 208:289-302.
27. Rahimi M., Madaeni S.S., Abbasi K. CFD modeling of permeate flux in cross-flow microfiltration. J. Membr. Sci. 2005, 255:23-31.
28. Yang K.-S. Numerical investigation of instability and transition in an obstructed channel flow. AIAA J. 2000, 38:1173-1178.
29. Bird R.B., Stewart W.E., Lightfoot E.N. Transport Phenomena 1960, Wiley, New York.
30. Belfort G. Fluid mechanics in membrane filtration: recent developments. J. Membr. Sci. 1989, 40:123-147.
31. McCabe W.L., Smith J.C., Harriot P. Unit Operations of Chemical Engineering 1993, McGraw-Hill, Inc., New York. fifth ed.
32. Huang H.-Z., Tao W.-Q. An experimental study on heat/mass transfer and pressure drop characteristics for arrays of nonuniform plate length positioned obliquely to the flow direction. J. Heat Trans. - T. ASME 1993, 115:568-575.
33. Issacson M.S., Sonin A.A. Sherwood number and friction factor correlations for electrodialysis systems, with application to process optimization. Ind. Eng. Chem. Process Des. Dev. 1976, 15:313-321.
34. Massay B.S. Mechanics of Fluids 1989, Chapman & Hall, London.
35. Wang C.Y. Exact solutions of the steady-state Navier-Stokes equations. Annu. Rev. Fluid. Mech. 1991, 23:159-177.
36. Narang B.S. Exact solution for entrance region flow between parallel plates. Int. J. Heat Fluid Fl. 1983, 4:177-181.
37. Wiley D., Fletcher D.F. Techniques for computational fluid dynamics modelling of flow in membrane channels. J. Membr. Sci. 2003, 211:127-137.
38. Kedem O., Katchalsky A. Thermodynamic analysis of the permeability of biological membranes to non-electrolytes. Biochim. Biophys. Acta 1958, 27:229.
39. Merten U. Flow relationships in reverse osmosis. Ind. Eng. Chem. Fundam. 1963, 2:229-232.
40. Rosén C., Trägårdh C. Computer simulations of mass transfer in the concentration boundary layer over ultrafiltration membranes. J. Membr. Sci. 1993, 85:139-156.
41. Sourirajan S. Reverse Osmosis 1970, Academic Press, New York, NY.
42. Chong T.H., Wong F.S., Fane A.G. Enhanced concentration polarization by unstirred fouling layers in reverse osmosis: detection by sodium chloride tracer response technique. J. Membr. Sci. 2007, 287:198-210.
43. Ndinisa N.V., Wiley D.E., Fletcher D.F. Computational fluid dynamics simulations of Taylor bubbles in tubular membranes-model validation and application to laminar flow systems. Chem. Eng. Res. Des. 2005, 83:40-49.
44. Miranda J.M., Campos J.B.L.M. Mass transfer in the vicinity of a separation membrane-the applicability of the stagnant film theory. J. Membr. Sci. 2002, 202:137-150.
45. Geraldes V., Afonso M.D. Generalized mass-transfer correction factor for nanofiltration and reverse osmosis. AIChE J. 2006, 52:3353-3362.
46. Orszag S.A., Patterson G.S. Numerical simulation of three dimensional homogeneous isotropic turbulence. Phys. Rev. Lett. 1972, 28:76-79.
47. Tangborn A.V., Zhang S.Q., Lakshiminarayanan V. A three-dimensional instability in mixed convection with streamwise periodic heating. Phys. Fluids 1995, 7:2648-2658.
48. Fimbres-Weihs G.A., Wiley D.E. Numerical study of two-dimensional multi-layer spacer designs for minimum drag and maximum mass transfer. J. Membr. Sci. 2008, 325:809-822.
49. Yuan Z.-X., Tao W.-Q., Wang Q.-W. Numerical prediction for laminar forced convection heat transfer in parallel-plate channels with streamwise-periodic rod disturbances. Int. J. Numer. Meth. Fluids 1998, 28:1371-1387.
50. Rosaguti N.R., Fletcher D.F., Haynes B.S. Laminar flow and heat transfer in a periodic serpentine channel. Chem. Eng. Technol. 2005, 28:353-361.
51. Li B., Feng B., He Y.-L., Tao W.-Q. Experimental study on friction factor and numerical simulation on flow and heat transfer in an alternating elliptical axis tube. Appl. Therm. Eng. 2006, 26:2336-2344.
52. Darcovich K., Dal-Cin M.M., Gros B. Membrane mass transport modeling with the periodic boundary condition. Comput. Chem. Eng. 2009, 33:213-224.
53. Schwinge J., Wiley D., Fletcher D.F. Simulation of unsteady flow and vortex shedding for narrow spacer-filled channels. Ind. Eng. Chem. Res. 2003, 42:4962-4977.
54. Koutsou C.P., Yiantsios S.G., Karabelas A.J. A numerical and experimental study of mass transfer in spacer-filled channels: effects of spacer geometrical characteristics and Schmidt number. J. Membr. Sci. 2009, 326:234-251.
55. Lau K.K., Abu Bakar M.Z., Ahmad A.L., Murugesan T. Feed spacer mesh angle: 3D modeling, simulation and optimization based on unsteady hydrodynamic in spiral wound membrane channel. J. Membr. Sci. 2009, 343:16-33.
56. Carluccio E., Starace G., Ficarella A., Laforgia D. Numerical analysis of a cross-flow compact heat exchanger for vehicle applications. Appl. Therm. Eng. 2005, 25:1995-2013.
57. Patankar S.V., Liu C.H., Sparrow E.M. Fully developed flow and heat transfer in ducts having streamwise-periodic variations of cross-sectional area. J. Heat Trans. 1977, 99:180-186.
58. Wiley D.E., Fell C.J.D., Fane A.G. Optimisation of membrane module design for brackish water desalination. Desalination 1988, 52:249-265.
59. Gill W.N., Wiley D.E., Fell C.J.D., Fane A.G. Effect of viscosity on concentration polarization in ultrafiltration. AIChE J. 1988, 34:1563-1567.
60. Skelland A.H.P. Diffusional Mass Transfer 1974, John Wiley & Sons, New York.
61. Feron P., Solt G.S. The influence of separators on hydrodynamics and mass transfer in narrow cells: flow visualisation. Desalination 1991, 84:137-152.
62. Pellerin E., Michelitsch E., Darcovich K., Lin S., Tam C.M. Turbulent transport in membrane modules by CFD simulation in two dimensions. J. Membr. Sci. 1995, 100:139-153.
63. Belfort G., Nagata N. Fluid mechanics and cross-flow filtration: some thoughts. Desalination 1985, 53:57-79.
64. Yakhot V., Orszag S.A. Renormalization group analysis of turbulence. I. Basic theory. J. Sci. Comput. 1986, 1:3-51.
65. Menter F.R. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J. 1994, 32:1598-1605.
66. Belfort G., Guter G.A. An experimental study of electrodialysis hydrodynamics. Desalination 1972, 10:221-262.
67. Focke W.W. On the mechanism of mass transfer enhancement by eddy promoters. Electrochim. Acta 1983, 28:1137-1146.
68. Oberkampf W.L., Trucano T.G. Verification and validation in computational fluid dynamics. Prog. Aerosp. Sci. 2002, 38:209-272.
69. Roache P.J., Knupp P.M. Completed Richardson extrapolation. Commun. Numer. Methods Eng. 1993, 9:365-374.
70. Roache P.J. Quantification of uncertainty in computational fluid dynamics. Annu. Rev. Fluid. Mech. 1997, 29:123-160.
71. Brian P.L.T. Mass transport in reverse osmosis. Desalination by Reverse Osmosis 1966, MIT Press, Cambridge, p. 161-202. U. Merten (Ed.).
72. Berman A.S. Laminar flow in channels with porous walls. J. Appl. Phys. 1953, 24:1232-1235.
73. Karode S.K. Laminar flow in channels with porous walls, revisited. J. Membr. Sci. 2001, 191:237-241.
74. Brian P.L.T. Concentration polarization in reverse osmosis desalination with variable flux and incomplete salt rejection. Ind. Eng. Chem. Fundam. 1965, 4:439-445.
75. Kimura S., Sourirajan S. Concentration polarization effects in reverse osmosis using porous cellulose acetate membranes. Ind. Eng. Chem. Process Des. Dev. 1968, 7:41-48.
76. Shah Y.T. Mass transport in reverse osmosis in case of variable diffusivity. Int. J. Heat Mass Tran. 1971, 14:921-930.
77. Kleinstreuer C., Paller M.S. Laminar dilute suspension flows in plate-and-frame ultrafiltration units. AIChE J. 1983, 29:529-533.
78. Miyoshi H., Fukuumoto T., Kataoka T. A consideration on flow distribution in an ion exchange compartment with spacer. Desalination 1982, 42:47-55.
79. Bhattacharyya D., Back S.L., Kermode R.I., Roco M.C. Prediction of concentration polarization and flux behavior in reverse osmosis by numerical analysis. J. Membr. Sci. 1990, 48:231-262.
80. Zhou W., Song L., Guan T.K. A numerical study on concentration polarization and system performance of spiral would RO membrane modules. J. Membr. Sci. 2006, 271:38-46.
81. T. Barber, Validation and Verification, 2003. Lecture notes: The University of New South Wales, p. 8.
82. Iwatsu R., Ishii K., Kawamura K., Kuwahara K., Hyun J.M. Numerical simulation of three-dimensional flow structure in a driven-cavity. Fluid Dyn. Res. 1989, 5:173-189.
83. Iwatsu R., Hyun J.M., Kuwahara K. Analyses of three-dimensional flow calculations in a driven cavity. Fluid Dyn. Res. 1990, 6:91-102.
84. Kim W.S., Park J.K., Chang H.N. Mass transfer in a three-dimensional net-type turbulence promoter. Int. J. Heat Mass Tran. 1987, 30:1183-1192.
85. Li F., Meindersma W., De Haan A.B., Reith T. Novel spacers for mass transfer enhancement in membrane separations. J. Membr. Sci. 2005, 253:1-12.
86. Santos J.L.C., Geraldes V.M., Velizarov S., Crespo J.G. Investigation of flow patterns and mass transfer in membrane module channels filled with flow-aligned spacers using Computational Fluid Dynamics (CFD). J. Membr. Sci. 2007, 305:103-117.
87. Shakaib M., Hasani S.M.F., Mahmood M. Study on the effects of spacer geometry in membrane feed channels using three-dimensional computational flow modeling. J. Membr. Sci. 2007, 297:74-89.
88. Da Costa A.R., Fane A.G., Wiley D.E. Spacer characterization and pressure drop modelling in spacer-filled channels for ultrafiltration. J. Membr. Sci. 1994, 87:79-98.
89. Schwinge J., Neal P.R., Wiley D.E., Fletcher D.F., Fane A.G. Spiral wound modules and spacers: review and analysis. J. Membr. Sci. 2004, 242:129-153.
90. Geraldes V., Semiao V., de Pinho M.N. Flow management in nanofiltration spiral wound modules with ladder-type spacers. J. Membr. Sci. 2002, 203:87-102.
91. Geraldes V., Semiao V., Pinho M.N. Hydrodynamics and concentration polarization in NF/RO spiral-wound modules with ladder-type spacers. Desalination 2003, 157:395-402.
92. Geraldes V., Semiao V., de Pinho M.N. Concentration polarisation and flow structure within nanofiltration spiral-wound modules with ladder-type spacers. Comput. Struct. 2004, 82:1561-1568.
93. Al-Bastaki N., Abbas A. Use of fluid instabilities to enhance membrane performance: a review. Desalination 2001, 136:255-262.
94. Moll R., Veyret D., Charbit F., Moulin P. Dean vortices applied to membrane process. Part I. Experimental approach. J. Membr. Sci. 2007, 288:307-320.
95. Moll R., Veyret D., Charbit F., Moulin P. Dean vortices applied to membrane process. Part II. Numerical approach. J. Membr. Sci. 2007, 288:321-335.
96. Chung K.Y., Brewster M.E., Belfort G. Dean vortices with wall flux in a curved channel membrane system: 3. Concentration polarization in a spiral reverse osmosis slit. J. Chem. Eng. Jpn. 1998, 31:683-693.
97. Ranade V.V., Kumar A. Comparison of flow structures in spacer-filled flat and annular channels. Desalination 2006, 191:236-244.
98. Schwinge J., Wiley D., Fletcher D.F. Simulation of the flow around spacer filaments between channel walls. 2. Mass-transfer enhancement. Ind. Eng. Chem. Res. 2002, 41:4879-4888.
99. Schwinge J., Wiley D.E., Fane A.G. Novel spacer design improves observed flux. J. Membr. Sci. 2004, 229:53-61.
100. Fiebig M. Embedded vortices in internal flow: heat transfer and pressure loss enhancement. Int. J. Heat Fluid Fl. 1995, 16:376-388.
101. A. Grosse-Gorgemann, W. Hahne, M. Fiebig, Influence of rib heights on oscilations, heat transfer and pressure drop in laminar channel flow, in Eurotherm 31 " Vortices and Heat Transfer" , Bochum, Germany.
102. A. Grosse-Gorgemann, W. Hahne, M. Fiebig, Self-sustained oscillations: heat transfer and flow losses in laminar channel flow with rectangular vortex generator, in Eurotherm 31 " Vortices and Heat Transfer" , Bochum, Germany.
103. Amon C.H., Mikić B.B. Numerical prediction of convective heat and mass transfer in self-sustained oscillatory flows. J. Thermophys. Heat Trans. 1990, 4:239-246.
104. Schwinge J., Neal P.R., Wiley D.E., Fane A.G. Estimation of foulant deposition across the leaf of a spiral-wound module. Desalination 2002, 146:203-208.
105. Schausberger P., Norazman N., Li H., Chen V., Friedl A. Simulation of protein ultrafiltration using CFD: comparison of concentration polarisation and fouling effects with filtration and protein adsorption experiments. J. Membr. Sci. 2009, 337:1-8.
106. Yee K.W.K., Wiley D.E., Bao J. A unified model of the time dependence of flux decline for the long-term ultrafiltration of whey. J. Membr. Sci. 2009, 332:69-80.
107. Anderson D.E., Graf D.L. Multicomponent electrolyte diffusion. Annu. Rev. Earth Pl. Sci. 1976, 4:95-121.
108. Krishna R., Wesselingh J.A. The Maxwell-Stefan approach to mass transfer. Chem. Eng. Sci. 1997, 52:861-911.
109. Onsager L. Theories and problems of liquid diffusion. Ann. N.Y. Acad. Sci. 1945, 46:241-265.
110. 2O at 25°C. Geochim. Cosmochim. Ac. 1991, 55:113-131.
111. Maxwell J.C. On the dynamical theory of gases. Phil. Trans. R. Soc. 1866, 157:49-88.
112. Stefan J. Über das Gleichgewicht und die Bewegung insbesondere die Diffusion von Gasgemengen. Sitzber. Akad. Wiss. Wien. 1871, 63:63-124.
113. Spiegler K.S. Transport processes in ionic membranes. Trans. Faraday Soc. 1958, 54:1408-1428.
114. Lightfoot E.N., Cussler E.L., Rettig R.L. Applicability of the Stefan-Maxwell equations to multicomponent diffusion in liquids. AIChE J. 1962, 8:708-710.
115. Standart G.L., Taylor R., Krishna R. The Maxwell-Stefan formulation of irreversible thermodynamics for simultaneous heat and mass transfer. Chem. Eng. Commun. 1979, 3:277-289.
116. Krishna R. Diffusion in multicomponent electrolyte systems. Chem. Eng. J. 1987, 35:19-24.
117. Graham E.E., Dranoff J.S. Application of the Stefan-Maxwell equations to diffusion in ion exchangers. I. Theory. Ind. Eng. Chem. Fundam. 1982, 21:360-365.
118. Lightfoot E.N. Transport Phenomena in Living Systems 1974, Wiley, New York.
119. Heintz A., Wiedemann E., Ziegler J. Ion exchange diffusion in electromembranes and its description using the Maxwell-Stefan formalism. J. Membr. Sci. 1997, 137:121-132.
120. van der Stegen J.H.G., van der Veen A.J., Weerdenburg H., Hogendoorn J.A., Versteeg G.F. Application of the Maxwell-Stefan theory to the transport in ion-selective membranes used in the chloralkali electrolysis process. Chem. Eng. Sci. 1999, 54:2501-2511.
121. Bellara S.R., Cui Z. Maxwell-Stefan approach to modelling the cross-flow ultrafiltration of protein solutions in tubular membranes. Chem. Eng. Sci. 1998, 53:2153-2166.
122. Noordman T.R., Wesselingh J.A. Transport of large molecules through membranes with narrow pores: the Maxwell-Stefan description combined with hydrodynamic theory. J. Membr. Sci. 2002, 210:227-243.
123. Palmeri J., Sandeaux J., Sandeaux R., Lefebvre X., David P., Guizard C., Amblard P., Diaz J.-F., Lamaze B. Modeling of multi-electrolyte transport in charged ceramic and organic nanofilters using the computer simulation program NanoFlux. Desalination 2002, 147:231-236.
124. Mohammad A.W., Takriff M.S. Predicting flux and rejection of multicomponent salts mixture in nanofiltration membranes. Desalination 2003, 157:105-111.
125. Garcia-Aleman J., Dickson J.M. Mathematical modeling of nanofiltration membranes with mixed electrolyte solutions. J. Membr. Sci. 2004, 235:1-13.
126. Aguilella W.M., Garrido J., Mafé S., Pellicer J. A finite-difference method for numerical solution of the steady-state Nernst-Planck equations with non-zero convection and electric current density. J. Membr. Sci. 1986, 28:139-149.
127. Newman J.S. Electrochemical Systems 1973, Prentice Hall, Englewood Cliffs, NJ.
128. Wesselingh J.A., Vonk P., Kraaijeveld G. Exploring the Maxwell-Stefan description of ion exchange. Chem. Eng. J. 1995, 57:75-89.
129. Cussler E.L., Diffusion: Mass Transfer in Fluid Systems 1997, Cambridge University Press, USA. 2nd ed.
130. Poling B.E., Prausnitz J.M., O'Connell J.P. The Properties of Gases and Liquids 2001, McGraw-Hill, New York. 5th ed.
131. Robinson R.A., Stokes R.H. Electrolyte Solutions 1965, Butterworths, London.
132. Reid R.C., Prausnitz J.M., Sherwood T.K. The Properties of Gases and Liquids 1997, McGraw-Hill, USA. 3rd ed.
133. Harned H.S., Owen B.B. The Physical Chemistry of Electrolytic Solutions 1950, Reinhold Pub. Corp., New York. 2nd ed.