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BOOKS AND MONOGRAPHS

1.        Lauer, B. E. and W. B. Krantz (eds.), Chemical Engineering Laboratory Problems - Vol. IV, University of Colorado, Boulder, 532 pages (1974).

2.        Krantz, W. B. and R. D. Gunn, (eds.), Underground Coal Gasification: The State of the Art, A.I.Ch.E. Symposium Series, No. 226, Vol. 79, American Institute of Chemical Engineers, New York, 185 pages (1983).

3.        Krantz, W. B., D. T. Wasan and R. K. Jain, (eds.), Thin Liquid Film Phenomena, A.I.Ch.E. Symposium Series, No. 252, Vol. 82, American Institute of Chemical Engineers, New York, 194 pages (1986).

4.        Krantz, W. B., D. T. Wasan, and P. V. Nerad,  (eds.), Interfacial Phenomena in the New and Emerging Technologies, National Science Foundation, Washington, D.C., 404 pages, (1987).

5.        Krantz, W. B., Scaling Analysis in Modeling Transport and Reaction Processes – A Systematic Approach to Model Building and the Art of Approximation, John Wiley & Sons, New York , ISBN 978-0-471-77261-3, 529 pages (2007).

PUBLISHED PAPERS AND ARTICLES (207 total - arranged topically in chronological order):

Education:

1.      Krantz, W.B., “Scaling Initial and Boundary Value Problems as a Teaching Tool for a Course in Transport Phenomena,” Chemical Engineering Education, 4(3), 145-152 (1970).

2.      Krantz, W.B., “College of Engineering,” Parents and Campus, 2, No. 2, 3 (1980).

3.      Krantz, W.B., “ChE Is Running Well at Colorado University,” Chemical Engineering Education, 14(2), 54 (1980).

4.      Krantz, W.B., “Undergraduate Research in Chemical Engineering at the University of Colorado,” Chemical Engineering Education, 15(3), 137 (1981).

5.      Krantz, W.B. and R.L. Dobbs, “Process Design for Membrane Separations,” pp. 279-294 in Chemical Engineering Education in a Changing Environment, S.L. Sandler and B.A. Finlayson (eds.), Engineering Foundation, New York (1988).

6.      Krantz, W.B. and J.G. Sczechowski, Scaling Initial and Boundary Value Problems - A Tool in Engineering Teaching and Practice,” Chemical Engineering Education, 28(4), 236-253 (1994).

7.      Krantz, W.B., “Opportunities for International Cooperation in Membrane Education and Technology Transfer, Membrane Quarterly, 11(2), 6-9 (1996).

8.      Krantz, W.B., “Extending the Extended Classroom via an NSF I/U CRC,” 2000 ASEE Annual Conference and Exposition Proceedings, June 18-21, 2000, St. Louis, Missouri (available on CD-ROM).

9.      Krantz, W.B., “An Alternate Method for Teaching and Implementing Dimensional Analysis,” Chemical Engineering Education,  34(3), 216-221, (2000).

10.   Kopaygorodsky, E.M., W.B. Krantz, and V.V. Guliants, “Scaling Analysis – A Valuable Technique in Engineering Teaching and Practice,” 2001 ASEE Annual Conference and Exposition Proceedings, June 24-27, 2001, Albuquerque, NM (available on CD-ROM).

11.   Krantz, W.B., K. Cedercreutz and A.F. Dardy, “Cooperative Engineering Education Program,” 2002 ASEE Annual Conference and Exposition Proceedings, June 16-19, 2002, Montreal, Quebec, Canada (available on CD-ROM).

12.   Krantz, W.B., “Pediment Graduate Course in Transport Phenomena,” 2003 ASEE Annual Conference and Exposition Proceedings, June 22-25, 2003, Nashville, TN (available on CD-ROM).

13.   Krantz, W.B., “Membrane Science and Technology in the 21st Century,” Chemical Engineering Education, 37(2), 94-99 (2004).

14.   Krantz, W.B., “Scaling Analysis as a Pedagogical Tool in Teaching Transport and Reaction Processes,” 2007 ASEE Annual Conference and Exposition Proceedings, June 24-27, 2007, Honolulu, HI (available on CD-Rom).

15.   Krantz, W.B., “From Third World to First – in Water Resources Management,” in What’s in a Name?, E. Fung (ed.),  National University of Singapore Development Office Yearbook, Republic of Singapore (2007).

16.   Krantz, W.B., “Oral Communication Skills Workshop for Students in Engineering and Applied Science,” accepted for publication in 2008 ASEE Annual Conference and Exposition Proceedings, June 22-25, 2008, Pittsburgh, PA (available on CD-ROM).

Fluid Mechanics and Interfacial Phenomena:

1.      Krantz, W.B. and S.L. Goren, “Finite Amplitude, Long Waves on Liquid Films Flowing Down a Plane,” Ind. Eng. Chem. Fundamentals, 9, 107 (1970).

2.      Krantz, W.B. and S.L. Goren, “Stability of Thin Liquid Films Flowing Down a Plane,” Ind. Eng. Chem. Fundamentals, 10, 91 (1971).

3.      Krantz, W.B. and S.L. Goren, “Bimodal Wave Formation on Thin Liquid Films Flowing Down a Plane,” A.I.Ch.E. Journal, 17, 494 (1971).

4.      Krantz, W.B., J.F. Carley, and A.M. Al-taweel, “Levitation of Solid Spheres in Pulsating Liquids,” Ind. Eng. Chem. Fundamentals, 12, 391 (1973).

5.      Krantz, W.B. and W.B. Owens, “Spatial Formulation of the Orr-Sommerfeld Equation for Thin Liquid Films Flowing Down a Plane,” A.I.Ch.E. Journal, 19, 1163 (1973).

6.      Zollars, R.L. and W.B. Krantz, “Hydrodynamic Stability of Thin Liquid Film Flow Down a Cone,” Proceedings of the GVC/AIChE-Joint Meeting and Jahrstreffen 1974 der Verfahrens-Ingenieure, Munich, West Germany, September 17-20, 1974, p. G5-4.

7.      Krantz, W.B., P.C. Martin, and W.A. Weers, “Device to Measure Surfactant Concentration, Analytical Chemistry, 9, 799A (1974).

8.      Krantz, W.B., “Additional Comments on the Spatial Formulation of the Orr-Sommerfeld Equation for Thin Liquid Films,” A.I.Ch.E Journal, 21, 179 (1975).

9.      Krantz, W.B. and W.B. Owens, “Stationary Wave Formation on Thin Liquid Films Flowing Down a Plane,” Ind. Eng. Chem. Fundamentals, 14, 33 (1975).

10.   Krantz, W.B., “Additional Comments on Spatially Growing Disturbances in Liquid Films,” A.I.Ch.E. Journal,  21, 596 (1975).

11.   Zollars, R.L. and W.B. Krantz, “Laminar Film Flow Down a Right Circular Cone,” Ind. Eng. Chem. Fundamentals, 15, 91 (1976).

12.   Krantz, W.B. and R.L. Zollars, “The Linear Hydrodynamic Stability of Film Flow Down a Vertical Cylinder,” A.I.Ch.E. Journal, 22, 930 (1976).

13.   Shuler, P.J. and W.B. Krantz, “The Equivalence of the Spatial and Temporal Formulations for the Linear Stability of Falling Film Flow,” A.I.Ch.E. Journal, 22, 934 (1976).

14.   Krantz, W.B., “Stability of Film Flow Down a Vertical Cylinder,” A.I.Ch.E. Journal, 23, 776 (1977).

15.   Shuler, P.J. and W.B. Krantz, “Spatially Growing Three-Dimensional Waves in Falling Film Flow,” International J. Multiphase Flow,  3(6), 609 (1977).

16.   Krantz, W.B., P.C. Martin, and L.F. Brown, “Adsorption-Desorption Phenomena at Dynamic Liquid-Gas Interfaces: Interfacial Stagnation Flow,” Ind. Eng. Chem. Fundamentals, 17, 341 (1978).

17.   Carley, J.F., T. Endo, and W.B. Krantz, “Realistic Analysis of Flow in Wire-Coating Dies,” Polymer Engineering and Science, 19, 1178 (1979).

18.   Zollars, R.L. and W.B. Krantz, “Non-Parallel Flow Effects on the Stability of Film Flow Down a Right Circular Cone,” J. Fluid Mech., 96, part 3, 583 (1980).

19.   Gyure, D.C. and W.B. Krantz, “Laminar Film Flow Over a Sphere,” Ind. Eng. Chem. Fundamentals, 22, 405 (1983).

20.   Krantz, W. B. and W. Visser, “Capillary Wave Propagation at an Interfacial Stagnation Line,” J. Colloid and Interface Science, 107, 96 (1985).

21.   Nerad, B.A. and W.B. Krantz, “Film Instabilities Arising from Steep Concentration or Temperature Gradients,” in Thin Liquid Film Phenomena, A.I.Ch.E. Symposium Series, No. 252, Vol.. 82, 34-49 (1986).

22.   Krantz, W.B., D.. Wasan and R.K. Jain, “Thin Liquid Film Phenomena - Introduction,” in Thin Liquid Film Phenomena, A.I.Ch.E. Symposium Series, No. 252, Vol. 82, 1-4 (1986).

23.   Nerad, B.A., W.B. Krantz and C. Maldarelli, “Interrelationship Between the Marangoni, Thin Film and Gradient-Driven Instability Mechanisms:  The Thin Film Problem,” Proceedings of the 1987 ASME-JSME Thermal Engineering Joint Conference - Volume Two, P.J. Marto and I. Tanasawa (eds.), American Society of Mechanical Engineers, New York, 587-594 (1987).

24.   Krantz, W.B. and B.A. Nerad, “A New Mechanism for Inducing Spontaneous Free Convection During Materials Processing in Low-G Fields,” pp. 27-53 in Low-Gravity Sciences, Vol.. 67, Science and Technology Series, J.N. Koster (ed.), Univelt, Inc., San Diego (1987).

25.   Thiessen, D.B. and W.B. Krantz, “Bimodal Terminal Velocities Using the Falling Needle Viscometer,” Rev. Sci. Instrum., 63(9), 4200-4204 (1992).

26.   Krantz, W. B., “Thermodynamics of Surfaces,” chapter 46 in The Engineering Handbook, R. C. Dorf (ed.), CRC Press, Boca Raton, Florida, 487-494 (1996).

27.   Thiessen, D.B., D.J. Chione, C.B. McCreary, and W.B. Krantz, “Robust Digital Image Analysis of Pendant Drop Shapes,” J. of Colloid and Interface Sci., 177, 658-665 (1996).

28.   Krantz, W. B., “Thermodynamics of Surfaces,” chapter 48 in The Engineering Handbook, R. C. Dorf (ed.), CRC Press, Boca Raton, Florida, 48-1 to 48-8 (2005) USBN 0-8493-1586-7.

Heat Transfer, Mass Transfer, and Reactor Design:

1.      Cannon, J.N., F. Kreith, and W.B. Krantz, “An Improved Theoretical Model for the Analysis of Evapotranspiration,” J. of the Colorado-Wyoming Academy of Science, 6, 2 (1969).

2.      Krantz, W.B. and D.T. Wasan, “Heat, Mass and Momentum Transfer Analogies for the Fully Developed Turbulent Flow of Power-Law Fluids in Circular Tubes,” Proceedings of the Fluid Dynamics Symposium, McMaster University, Hamilton, Ontario, Canada, August 25-27, 1970.

3.      Krantz, W.B. and D.T. Wasan, “A Correlation for Velocity and Eddy Diffusivity for the Flow of Power Law Fluids Close to a Pipe Wall,” Ind. Eng. Chem. Fundamentals, 10, 424 (1971).

4.      Krantz, W.B. and D.T. Wasan, “Heat, Mass, and Momentum Transfer Analogies for the Fully Developed Turbulent Flow of Power Law Fluids in Circular Tubes,” A.I.Ch.E Journal, 17, 1360 (1971).

5.      Krantz, W.B. and D.T. Wasan, “Axial Dispersion in the Turbulent Flow of Power Fluids in Straight Tubes,” Ind. Eng. Chem. Fundamentals,  13, 56 (1974).

6.      Booras, G.S. and W.B. Krantz, “Dispersion of Power-Law Fluids in Laminar Flow Through Straight Tubes,” Ind. Eng. Chem. Fundamentals, 15, 249 (1976).

7.      Cannon, J. N., W. B. Krantz, F. Kreith, and D. Naot, “A Study of Transpiration from Porous Flat Plates Simulating Plant Leaves,” Int. J. Heat Mass Transfer, 22, 469 (1979).

8.      Johnson, J.A., W.B. Krantz, C.M. Hrenya, and A.W. Weimer, “Sensitivity Analysis of the Rapid Carbothermal Reduction Synthesis of Ultra-Fine Silicon Carbide Powders,” J. of Aerosol Science and Technology, 36, 1087-1098 (2002).

9.      Kopaygorodsky, E.M., V.V. Guliants, and W.B. Krantz “Predictive Dynamic Model of Single-Stage Ultra-Rapid Pressure Swing Adsorption,” A.I.Ch.E. Journal, 50(5), 953 (2004).

10.   Dahl, J.K., W.B. Krantz, and  A.W. Weimer, “Sensitivity Analysis of the Rapid Decomposition of Methane in an Aerosol Flow Reactor,” Intl. J. Hydrogen Energy, 29(1), 57-65 (2004).

11.   Balaji, S., S. Lakshminarayanan, and William B. Krantz, “Scaling and Sensitivity Analysis of a Reverse Flow Reactor,” Chem. Eng. Sci., 63(2), 342-355 (2008).

12.   Rama Rao, V., S. Farooq, and W.B. Krantz, “Design of a Two-Step Pulsed Pressure-Swing Adsorption-Based Oxygen Concentrator,” submitted to A.I.Ch.E. Journal (2008).

Synfuels and Energy:

1.      Krantz, W.B. and R.D. Gunn, “Linear Stability of Reverse Combustion for In-Situ Coal Gasification,” Proceedings of the Third Underground Coal Conversion Symposium, Lawrence Livermore Laboratory, Rept. Conf.- 770652, 146 (1977).

2.      Levie, B.E., W.B. Krantz, D.W. Camp, R.D. Gunn, and A.D. Youngberg, “Application of the Spalling-Enhanced Drying Model in Predicting Cavity Geometry and Operating Strategy for the Hanna 2, Phase 2 UCG Field Test,” Proceedings of the Seventh Underground Coal Conversion Symposium, Lawrence Livermore Laboratory, Rept. Conf-810923, 178 (1981).

3.      Levie, B.E., W.B. Krantz, R.D. Gunn, and A.D. Youngberg, “A Model for Roof Spalling and Its Application to Predicting Cavity Shape for the Hanna III UCG Field Test,” Proceedings of the Eighth Underground Coal Conversion Symposium, Sandia National Laboratory, Rept. SAND82-2355, 321 (1982).

4.      Gunn, R.D. and W.B. Krantz, “Fundamental Research Needs in Underground Coal Gasification,” Proceedings of the Eighth Underground Coal Conversion Symposium, Sandia National Laboratory, Rept. SAND82-2355, 467 (1982).

5.      Britten, J.A., W.B. Krantz, and R.D. Gunn, “Modeling Studies of Reverse Combustion Linking at High Pressure,” Proceedings of the Eighth Underground Coal Conversion Symposium, Sandia National Laboratory, Rept. SAND82-2355, 515 (1982).

6.      Tidball, R.K., W.B. Krantz, and R.D. Gunn, “Mathematical Modeling of Electrolinking,” 1983 International Gas Research Conference Proceedings, L.H. Hirsch, (ed.), Government Institutes, Inc., Rockville, MD, 1174 pages (1983), pp. 522-530.

7.      Krantz, W.B. and R.D. Gunn, “Mathematical Modeling Studies of In Situ Coal Gasification,” 1983 International Gas Research Conference Proceedings, L. H. Hirsch, (ed.), Government Institutes, Inc., Rockville, MD, 1174 pages (1983), pp. 531-538.

8.      Gunn, R.D. and W.B. Krantz, “Reverse Combustion Instabilities in Tar Sands and Coal,” Paper 6735, presented at SPE-AIME 52nd Annual Fall Meeting, Denver, October 9-12, 1977.

9.      Krantz, W.B., M. Keyashian, R.L. Zollars, and R.D. Gunn, “Stability of Forward and Reverse Wet Combustion Fronts in Porous Media,” Paper 7523, presented at SPE-AIME 53rd Annual Fall Meeting, Houston, Texas, October 1-4, 1978.

10.   Krantz, W.B., “Improved Oil Recovery,” NSF Annual Report, 1977, U.S. Government Printing Office, Washington, DC, Stock Number 038-000-00374-7, 145 pages, (1978) pp. 19-20.

11.   Krantz, W.B., D.W. Camp, and R.D. Gunn, “A Water-Influx Model for UCG,” Proceedings of the Sixth Underground Coal Conversion Symposium, Laramie Energy Technology Center, Rept. Conf-800716, III-21, (1980).

12.   Gunn, R.D., G.J. Bell, T.C. Bartke, D.W. Camp, and W.B. Krantz, “A Technical Analysis of the Hanna III Field Test Data,” Proceedings of the Sixth Underground Coal Conversion Symposium, Laramie Energy Technology Center, Rept. Conf-800716, VIII-6 (1980).

13.   Camp, D.W., W.B. Krantz, and R.D. Gunn, “A Water-Influx Model for UCG with Spalling-Enhanced Drying,” Proceedings of the 15th Intersociety Energy Conversion Engineering Conference, Seattle, Washington, August 18-22, 1980, p. 1304.

14.   Gunn, R.D. and W.B. Krantz, “Reverse Combustion Instabilities in Tar Sands and Coal,” Society of Petroleum Engineers Journal, 20, 267 (1980).

15.   Krantz, W.B. and R.D. Gunn, “An Overview of Underground Coal Gasification - A Comparison of Modeling Studies with Field Test Data,” Proceedings of  the 64th Canadian Chemical Conference, Halifax, Nova Scotia, May 31-June 3, 1981, pp. 468-475.

16.   Krantz, W.B. and R.D. Gunn, “Use of Stability Theory in Interpreting UCG Field Test Data,” In Situ, 5(3), 199-219 (1981).

17.   Krantz, W.B. and R.D. Gunn, “Underground Coal Gasification: The State of the Art,” in Underground Coal Gasification:  The State of the Art, A.I.Ch.E. Symposium Series, No. 226, Vol. 79, 1 (1983).

18.   Krantz, W.B. and R.D. Gunn, “Modeling the Underground Coal Gasification Process:  Part I - Reverse Combustion,” in Underground Coal Gasification:  The State of the Art, A.I.Ch.E. Symposium Series, No. 226, Vol. 79, 89 (1983).

19.   Krantz, W.B. and R.D. Gunn, “Modeling the Underground Coal Gasification Process:  Part II - Water Influx,” in Underground Coal Gasification:  The State of the Art, A.I.Ch.E. Symposium Series, No. 226, Vol. 79, 121 (1983).

20.   Krantz, W.B. and R.D. Gunn, “Modeling the Underground Coal Gasification Process: Part III - Subsidence,” in Underground Coal Gasification:  The State of the Art, A.I.Ch.E. Symposium Series, No. 226, Vol. 79, 129 (1983).

21.   Britten, J.A. and W.B. Krantz, “Linear Stability of a Planar Combustion Front Propagating Through a Porous Medium Against a Forced Oxidant Flux,” Chemical Instabilities, G. Nicolis and F. Baras (eds.), D. Reidel Publishing Co., Dordrecht, Holland, 420 pages (1983), pp. 117-135.

22.   Krantz, W.B., R.K. Tidball, B. Dautresme, and R.D. Gunn, “A Process Model for the Initial Stages of Electrolinking,” Proceedings of the Ninth Underground Coal Gasification Symposium, Morgantown Energy Technology Center Rept. DOE/METC/84-7, 405 (1983).

23.   Glaser, R.R., R.D. Gunn, W.B. Krantz, K.P. Breidung, and H. Gudenau, “Unexpected Aspects of Reverse Combustion - Effects of Pressure, Volatility, and Chemical Reactivity,” Proceedings of the Ninth Underground Coal Gasification Symposium, Morgantown Energy Technology Center Rept. DOE/METC/84-7, 219 (1983).

24.   Gunn, R.D., A.C. Bumb, and W.B. Krantz, “Stability Theory of Reverse Combustion in Coal Beds:  I. Effects of Spherical Geometry,” in Heat Transfer - Niagara Falls 1984, A.I.Ch.E. Symposium Series, No. 236, Vol. 80, 35 (1984).

25.   Dautresme, B., W.B. Krantz, J.F. Fuller, and R.D. Gunn, “Modeling and Experimental Studies of Electrolinking,” Proceedings of the Tenth Annual Underground Coal Gasification Symposium, Morgantown Energy Technology Center Rept. DOE/METC-85/5, 369 (1985).

26.   Britten, J.A., W.B. Krantz, W. Visser, and R.D. Gunn, “Theoretical and Experimental Studies of Reverse Combustion,” Proceedings of the Tenth Annual Underground Coal Gasification Symposium, Morgantown Energy Technology Center Rept. DOE/METC-85/5, 359 (1985).

27.   Tantekin, S.B., W.B. Krantz, and R.D. Gunn, “Use of Post-Burn Coring Data from the Hanna III Field Test to Infer the Spalling Characteristics, Water Influx and Heat Losses,” Proceedings of the Tenth Annual Underground Coal Gasification Symposium, Morgantown Energy Technology Center Rept. DOE/METC-85/5, 479 (1985).

28.   Britten, J.A. and W.B. Krantz, “Linear Stability of Planar Reverse Combustion in Porous Media,” Combustion and Flame, 60, 125 (1985).

29.   Visser, W., W.B. Krantz, J.A. Britten, and R.D. Gunn, “Experiments in Reverse Combustion,” Proceedings of the Eleventh Underground Coal Gasification Symposium, Morgantown Energy Technology Center Rept. DOE/METC-85/6028, 340 (1985).

30.   Britten, J.A. and W.B. Krantz, “Asymptotic Structure of Planar Nonadiabatic Reverse Combustion Fronts in Porous Media,” Combustion and Flame, 65, 151 (1986).

31.   Dindi, H., W.B. Krantz, and J.F. Fuller, “Modeling and Laboratory Studies of Electrolinking,” Proceedings of the Twelfth Annual Underground Coal Gasification Symposium, U.S. Dept. of Energy Rept. DOE/FE/60922-H1, 196 (1986).

32.   Tantekin, S.B. and W.B. Krantz, “Laboratory Characterization of Overburden Spalling Properties in Underground Coal Gasification,” Proceedings of the Twelfth Annual Underground Coal Gasification Symposium, U.S. Dept. of Energy Rept. DOE/FE/60922-H1, 315 (1986).

33.   Gunn, R.D. and W.B. Krantz, “Theoretical and Experimental Investigations of Underground Coal Gasification,” U.S. Dept. of Energy Rept. DOE/LC/10887-2153, 98 pages, (1986).

34.   Dindi, H. and W.B. Krantz, “Modeling Studies of Electrolinking for Underground Gasification of Coal,” Proceedings of the Thirteenth Annual Underground Coal Gasification Symposium, U.S. Dept. of Energy Rept. DOE/METC-88/6095, 110-119 (1987).

35.   Dindi, H., X.-H. Bai, and W.B. Krantz, “Thermal and Electrical Property Measurements of an Illinois Basin Bituminous Coal,” Proceedings of the Thirteenth Annual Underground Coal Gasification Symposium, U.S. Dept. of Energy Rept. DOE/METC-88/6095, 190-201, (1987).

36.   Dobbs II, R.L. and W.B. Krantz, “Optimizing Reverse Combustion Linking with Promoters and Inhibitors,” Proceedings of the Thirteenth Annual Underground Coal Gasification Symposium, U.S. Dept. of Energy Rept. DOE/METC-88/6095, 202-210 (1987).

37.   Tantekin, S.B., W.B. Krantz, and D.P. Sperry, “Characterization of the Overburden Spalling Properties for the Rocky Mountain I UCG Field Test Site,” Proceedings of the Thirteenth Annual Underground Coal Gasification Symposium, U.S. Dept. of Energy Rept. DOE/METC-88/6095, 408-416, (1987).

38.   Gunn, R.D. and W.B. Krantz, “Underground Coal Gasification:  Development of Theory, Laboratory Experimentation, Interpretation, & Correlation With the Hanna Field Tests,” U.S. Dept. of Energy Rept. DOE/LC/10442-2545, 128 pages (1987).

39.   Tantekin, S.B., D.P. Sperry, W.B. Krantz and J.A. Britten, “Laboratory Characterization of the Spalling Properties of the Rock Cores from the UCG Test Site Near Porto Alegre in Brazil,” Lawrence Livermore Laboratory Rept. UCID-21339, 12 pages (1988).

40.   Camp, D.W., S.B. Tantekin, and W.B. Krantz, “Darcy Flow to a Vertical Fracture Intersecting a Cylindrical Cavity - Application to Water Permeation in UCG,” In Situ, 12(1 & 2), 15-40 (1988).

41.   Dindi, H. and W.B. Krantz, “Modeling and Laboratory Studies of Electrolinking,” U.S. Dept. of Energy Rept. DOE/MC/21082-2597, 122 pages (1988).

42.   Dindi, H., G.J. McCarthy, R.J. Stevenson, and W.B. Krantz, “Laboratory Characterization of Overburden Cores from Rocky Mountain 1 UCG Test Site,” Proceedings of the Fourteenth Annual Underground Coal Gasification Symposium, U.S. Dept. of Energy Rept. DOE/METC-88/6097, 51-59 (1988).

43.   Dobbs, R.L. and W.B. Krantz, “A Transient Model of Reverse Combustion Channel Propagation,” Proceedings of the Fourteenth Annual Underground Coal Gasification Symposium, U.S. Dept. of Energy Rept. DOE/METC-88/6097, 102-106 (1988).

44.   Dindi, H., X.-H. Bai, and W.B. Krantz, “Thermal and Electrical Property Measurements for Coal,” Fuel, 68, 185-192 (1989).

45.   Dindi, H., J.A. Britten, and W.B. Krantz, “Combustion and Dielectric Breakdown Front Instabilities in Porous Media,” Earth-Science Reviews, 29(1-4), 401-417 (1990).

46.   Dobbs, R.L. II and W.B. Krantz, “Combustion Front Propagation in Underground Coal Gasification,” U.S. Dept. of Energy Rept. DOE/PC90512-2942, 390 pages (1990).

Geophysics:

1.      Ray, R.J., W.B. Krantz, T.N. Caine, and R.D. Gunn, “A Model for Sorted Patterned Ground Regularity,” J. of Glaciology, 29, No. 102, 317 (1983).

2.      Ray, R.J., W.B. Krantz, T.N. Caine, and R.D. Gunn, “A Mathematical Model for Patterned Ground:  Sorted Polygons and Stripes, and Underwater Polygons,” Permafrost-Fourth International Conference Proceedings, T. L. Pewe and J. Brown, (eds.), National Academy Press, Washington, DC, 1524 pages (1983), pp. 1036-1041.

3.      Krantz, W.B., T.N. Caine, and R.D. Gunn, “Patterned Ground - A Geophysical Curiosity of the High Country,” University of Colorado Chapter of the Society of Sigma Xi Research Newsletter, 1, No. 1, 17 (1984).

4.      Gleason, K.J., W.B. Krantz, T.N. Caine, J.H. George, and R.D. Gunn, “Geometrical Aspects of Sorted Patterned Ground in Recurrently Frozen Soils” Science, 232, 216-220 (1986).

5.      Gleason, K.J., W.B. Krantz and T.N. Caine, “Parametric Effects in the Filtration Free Convection Model for Patterned Ground,” Permafrost-Fifth International Conference Proceedings Volume, K. Senneset (ed.), Tapir Publishers, Trondheim, Norway, (1988), pp. 349-354.

6.      Krantz, W.B., K.J. Gleason, and N. Caine, “Patterned Ground,” Scientific American, 259(6), 68-76 (1988).

7.      Krantz, W., K. Gleason, and N. Caine, “Les sols polygonaux,” (in French), Pour La Science, No. 136, 18-24, February (1989).

8.      Krantz, W.B., K.J. Gleason, and N. Caine, “Frostmusterböden,” (in German), Spektrum der Wissenschaft, 62-68, February (1989).

9.      Krantz, W.B., K.J. Gleason, and N. Caine, “Patterned Ground,” (in Japanese), Scientific American - Japanese edition, 26-34, February (1989).

10.   Krantz, W.B., K J. Gleason, and N. Caine, “Terrenos configurados,” (in Spanish), Investigacion Y Ciencia, 40-47, February (1989).

11.   Krantz, W.B., K.J. Gleason, and N. Caine, “Fagymintás talaj,” (in Hungarian), Tudomány, 36-41, February (1989).

12.   Krantz, W.B., K.J. Gleason, and N. Caine, “Suoli poligonali,” (in Italian), Le Scienze, No. 246, 46-52, February (1989).

13.   Krantz, W.B., K.J. Gleason, and N. Caine, “Patterned Ground,” (in Russian), Scientific American - Russian edition, 32-39, February (1989).

14.   Krantz, W.B., K.J. Gleason, and N. Caine, “Patterned Ground,” (in Arabic), Scientific American - Arabic edition, 56-63, February (1989).

15.   Baum, B.A., W.B. Krantz, J H. Fink, and R.E. Dickinson, “Taylor Instability in Rhyolite Lava Flows, Journal of Geophysical Research, 94(B5), 5815-5828 (1989).

16.   Krantz, W.B., “Self Organization Manifest as Patterned Ground in Recurrently Frozen Soils,” Earth-Science Reviews, 29(1-4), 117-130 (1990).

17.   Lewis, G.C., W.B. Krantz, and N. Caine, “A Model for the Initiation of Patterned Ground Owing to Differential Secondary Frost Heave,” Permafrost-Sixth International Conference Proceedings, G. Cheng (ed..), 2, South China University of Technology Press, Wushan Guangzhou, 1044-1049 (1993).

18.   Fowler, A.C., C.G. Noon, and W.B. Krantz, “A Computationally Feasible Reduction of the O’Neill-Miller Model of Secondary Frost Heave,” Permafrost-Sixth International Conference Proceedings, G. Cheng (ed.), 2, South China University of Technology Press, Wushan Guangzhou, 1100-1104 (1993).

19.   Walker, D.A., B.E. Lewis, W.B. Krantz, E.T. Price, and R.D. Tabler, “Hierarchic Studies of Snow-Ecosystem Interactions - A 100-Year Snow-Alteration Experiment,” 61st Western Snow Conference Proceedings, Quebec City, Quebec, Canada, 407-414 (1993).

20.   Fowler, A.C. and W.B. Krantz, Generalized Secondary Frost Heave Model, SIAM J. Appl. Math., 54(6), 1650-1675 (1994).

21.   Krantz, W.B. and K.E. Adams, “Application of a Fully Predictive Model for Secondary Frost Heave,” Arctic and Alpine Research, 28(3), 284-293 (1996).

22.   Peterson, R.A. and W.B. Krantz, “A Linear Stability Analysis for the Inception of Differential Frost Heave,” Permafrost-Seventh International Conference Proceedings, M. Allard (ed.), University of Laval, Toronto, Canada, 883-890 (1998).

23.   Peterson, R.A., D.A. Walker, V.R. Romanovsky, J.A. Knudsen, M.K. Raynolds, and W.B. Krantz, “A Differential Frost Heave Model:  Cryoturbation-Vegetation Interactions,”  Proceedings of the Eighth International Conference on Permafrost, M. Phillips, S.M. Springman, and L.U. Arenson (eds.), A.A. Balkema Publishers Lisse / Abingdon / Exton (PA) / Tokyo, 885-890 (2003).

24.   Peterson, R.A. and W.B. Krantz, “A Mechanism for Differential Frost Heave and its Implications for Patterned Ground Formation, “ J. Glaciology, 49(164), 69-80 (2003).

25.   Walker, D.A., H.E. Epstein, W.A. Gould, A.N. Kade, A.M. Kelley, J.A. Knudson, W.B. Krantz, G. Michaelson, R.A. Peterson, C.-L. Ping., M.A. Raynolds, V.E. Romanovsky, and Y. Shur, “Frost-Boil Ecosystems: Complex Interactions between Landforms, Soils, Vegetation and Climate” Permafrost and Periglacial Processes, 15, 171-188 (2004).

26.   Peterson, R.A. and W.B. Krantz, “Differential Frost Heave Model for Patterned Ground Formation: Corroboration with Observations along a North American Arctic Transect,” Journal of Geophysical Research, 113 (G3), S304 (2008).

27.   Walker, D.A., H.E. Epstein, V.E. Romanovsky, C.L. Ping., G.J. Michaelson, R.P. Daanen, Y. Shur, R.A. Peterson, W.B. Krantz, M.K. Raynolds, W.A. Gould, G. Gonzalez, D.J. Nickolsky, C.M. Vonlanthen, A.N. Kade, P. Kuss, A.M. Kelley, C.A. Munger, C.T. Tarnocai, N.V. Matveyeva, and F.J.A. Daniëls “Arctic Patterned-Ground Ecosystems:  A Synthesis of Field Studies and Models along a North American Arctic Transect,” Journal of Geophysical Research – Biogeosciences, 113(G3), S301 (2008).

Membrane Science:

1.      Krantz, W.B., “Track-Etched Membrane Research,” NSF Engineering Program Report, 2, 20 (1978).

2.      Ray, R.J., W.B. Krantz, and R.L. Sani, “Linear Stability Theory Model for Finger Formation in Asymmetric Membranes,” J. of Membrane Science, 23, 155 (1985).

3.      Krantz, W.B., R.J. Ray, R.L. Sani, and K.J. Gleason, “Theoretical Study of the Transport Processes Occurring During the Evaporation Step in Asymmetric Membrane Casting,” J. Membrane Science, 29, 11 (1986).

4.      Nerad, B.A., K.J. Gleason, W.B. Krantz and R.J. Ray “Application of the Gradient-Driven Instability Mechanism to Asymmetric Polymeric Membrane Morphology,” in Thin Liquid Film Phenomena, A.I.Ch.E. Symposium Series, No. 252, Vol. 82, 167-178 (1986).

5.      Krantz, W.B., S.W. McFarland, M.D. Wray, and A.R. Greenberg, “Experimental and Theoretical Studies of Polymeric Membrane Morphology,” Proceedings of the Industry-University Advanced Materials Conference, J. G. Morse ( ed.), The Metallurgical Society, Inc., 119-121 (1987).

6.      Greenberg, A.R., K.J. Gleason, M.D. Wray and W.B. Krantz, “Influence of Processing on the Morphology of Cellulose Acetate Thin Films,” Polymer Preprints, 29, 579-580 (1988).

7.      Gleason, K.J., A.R. Greenberg, M.D. Wray and W.B. Krantz, “Thermal Behavior of Secondary (CA) and Tertiary (CTA) Cellulose Acetates,” Proceedings of the 17th N. Amer. Thermal Analysis Soc. Conf., 809-814 (1988).

8.      Tantekin, S.B., W.B. Krantz, and A.R. Greenberg, “Theoretical and Experimental Aspects of the Evaporation Step in the Preparation of Solvent-Cast Asymmetric Polymeric Membranes,” Proceedings of the Industry-University Advanced Materials Conference, F. W. Smith (ed.), Advanced Materials  Institute, Golden, CO, 357-364 (1989).

9.      Gleason, K.J., A.R. Greenberg, and W.B. Krantz, “Study of Polymeric Membrane Materials by Combined DSC, SAED, and XRD Methods,” Proceedings of the Industry-University Advanced Materials Conference, F. W. Smith (ed.), Advanced Materials Institute, Golden, CO, 679-686 (1989).

10.   Shojaie, S.S., A.R. Greenberg, and W.B. Krantz, “Influence of Electric Fields on Interfacial Stability During Polymeric Membrane Formation,” Proceedings of the Industry-University Advanced Materials Conference, F. W. Smith (ed.), Advanced Materials Institute, Golden, CO, 687-693 (1989).

11.   Tantekin, S.B., W.B. Krantz, and A.R. Greenberg, “The Dynamics of Evaporation in Polymer/Solvent Films - Importance in Asymmetric Polymeric Membrane Formation,” Polymer Preprints, 30, 36-37 (1989).

12.   Shojaie, S.S., A.R. Greenberg, and W.B. Krantz, “Influence of Electric Fields on Large Scale Structures in Non-Solvent Precipitated Polymeric Membranes,” Polymer Preprints, 31, 382-383 (1990).

13.   Shojaie, S.S., W.B. Krantz, and A.R. Greenberg, “Development and Validation of a Model for the Formation of Evaporatively Cast Polymeric Films,” J. Materials Proc. & Manufacturing Sci., 1, 181-194 (1992).

14.   Shojaie, S.S., A.R. Greenberg, and W.B. Krantz, “Modeling and Experimental Studies of the Formation of Evaporatively Cast Dense Polymeric Films,” Proceedings of the International Conference on Transport Phenomena in Processing, S. I. Guceri (ed..), Technomic Pub. Co. Inc., Lancaster - Basel, 1469-1479 (1992).

15.   Shojaie, S.S., A.R. Greenberg, and W.B. Krantz, “Use of an Electric Field to Alter Membrane Morphology in a Polysulfone-Polyvinylpyrrolidone Blend,” J. of Membrane Science, 79, 115-122 (1993).

16.   Paulsen, F.G., S.S. Shojaie, and W.B. Krantz, “Effect of Evaporation Step on Macrovoid Formation in Wet-Cast Polymeric Membranes,” J. Membrane Science, 91, 265-282 (1994).

17.   Chai, G.-Y. and W.B. Krantz, “Formation and Characterization of Polyamide Membranes via Interfacial Polymerization,” J. Membrane Science, 93, 175-192 (1994).

18.   Shojaie, S.S., W.B. Krantz, and A.R. Greenberg, “Dense Polymer Film and Membrane Formation via the Dry-Cast Process:  Part I. Model Development,” J. Membrane Science, 94, 255-280 (1994).

19.   Shojaie, S.S., W.B. Krantz, and A.R. Greenberg, “Dense Polymer Film and Membrane Formation via the Dry-Cast Process:  Part II. Model Validation and Morphological Studies,” J. Membrane Science, 94, 281-298 (1994).

20.   Bond, L.J., A.R. Greenberg, A.P. Mairal, G. Loest, J.H. Brewster, and W.B. Krantz, “Real-Time Nondestructive Characterization of Membrane Compaction and Fouling,” Review of Progress in Quantitative Nondestructive Evaluation, D. O. Thompson and D. E. Chimenti (eds.), 14, Plenum Press, New York, 1167-1173 (1995).

21.   Greenberg, A.R., V.P. Khare, and W.B. Krantz, “Development of a Technique for the In Situ Measurement of the Mechanical Properties of Ultra-thin Interfacially Polymerized Films,” Mat. Res. Soc. Symp. Proc., 356, Materials Research Society, 541-546 (1995).

22.   Konagurthu, S., W.B. Krantz, and P. Todd, “Use of Low-G to Test Alternative Hypotheses for Macrovoid Growth in Polymeric Membranes,” Proceedings of the EuroMembrane ’95, W. R. Bowen, R. W. Field and J. A. Howell (eds..), 1, European Society for Membrane Science and Technology, C4 (1995).

23.   Greenberg, A.R., S.S. Shojaie, W.B. Krantz, and S.B. Tantekin-Ersolmaz, “Use of Infrared Thermography for Temperature Measurement During Evaporative Casting of Thin Polymeric Films,” J. Membrane Science, 107, 249-261 (1995).

24.   Tan, L., W.B. Krantz, A.R. Greenberg, and R.L. Sani, “Studies of Convective Transport in Evaporative Casting of Dense Polymer Films,” J. Membrane Science, 108, 245-255 (1995).

25.   Konagurthu, S., R. Peterson, L.J. Bond, A.R. Greenberg, W.B. Krantz, D. Kishoni, D. Kuhns, L. Burgess, and A.M. Brodsky, “Development of an Acoustic Technique for Assessing Structure-Property Characteristics of Polymeric Thin Films Under High Pressure,” 1996 IEEE Ultrasonics Symposium, ISSN 1051-0117, vol. 1, 413-417 (1996).

26.   Krantz, W.B., R.R. Bilodeau, M.E. Voorhees and R.J. Elgas, “Use of Axial Membrane Vibrations to Enhance Mass Transfer in a Hollow Tube Oxygenator,” J. Membrane Science, 124, 283-299 (1997).

27.   Kools, W.F.C., S. Konagurthu, A.R. Greenberg, L.J. Bond, W.B. Krantz, T. van den Boomgaard, and H. Strathmann, “Use of Ultrasonic Time-Domain Reflectometry for Real-Time Measurement of Thickness Changes During Evaporative Casting of Polymeric Films,” J. Appl. Polym. Sci., 69, 2013-2019 (1998).

28.   Peterson R.A., A.R. Greenberg, L.J. Bond, and W.B. Krantz, “Use of Ultrasonic TDR for Real-time Noninvasive Measurement of Compressive Strain During Membrane Compaction,” Desalination, 116, 115-122  (1998).

29.   Konagurthu S., M.R. Pekny, P. Todd, A.R. Greenberg, and W.B. Krantz, “Influence of Solutocapillary Convection on Macrovoid Defect Formation in Polymeric Membranes, Proceedings of the 1998 NASA Microgravity Materials Science Conference, Huntsville, Alabama, NASA/CP-1999-209092, February 1999.

30.   Mairal, A.P., A.R. Greenberg, W.B. Krantz, and L.J. Bond, “Real-Time Measurement of Inorganic Membrane Fouling in RO Desalination Using Ultrasonic Time-Domain Reflectometry,” J. Membrane Science, 159, 185-196 (1999).

31.   Mairal, A.P., A.R. Greenberg, and W.B. Krantz, “Investigation of Membrane Fouling and Cleaning Using Ultrasonic Time-Domain Reflectometry,” Desalination, 130 (1), 45-60 (2000).

32.   Li, D., W.B. Krantz, R.L. Sani, and A.R. Greenberg, "Modeling Study of the Thermally Induced Phase Separation (TIPS) Membrane Formation Process," Proceedings of the 3rd Joint China-USA Chemical Engineering Conference, 1(4), 209-212, 2000.

33.   Pekny, M.R., J. Zartman, A.R. Greenberg, W.B. Krantz, and P. Todd, "Influence of Buoyancy and Surfactant Solutes on Macrovoid Defect Formation in Dry-Cast Cellulose Acetate Membranes," ACS Polymer Preprints, 41, 1060-61, 2000.

34.   Zartman, J., V. Khare, M.R. Pekny, A.R. Greenberg, P. Todd, and W.B. Krantz, “Solutocapillary-Convection-Driven Macrovoid Defect Formation in Polymeric Membranes,” Proceedings of the 39th Aerospace Sciences Meeting & Exhibit, January 8-11, 2000, Reno, Nevada, AIAA-2001-0461, 1-9 (2001).

35.   Pekny, M.R., J. Zartman, A.R. Greenberg, P. Todd and W.B. Krantz, "Influence of Solutocapillary Convection on Macrovoid Defect Formation in Polymeric Membranes, Proceedings of the 2000 NASA Microgravity Materials Science Conference, (N. Ramachandran, N. Bennett, D. McCauley, K. Murphy and S. Poindexter (eds.), Huntsville, Alabama, NASA/CP-2001-210827 (2001). 

36.   Todd, P., M.R. Pekny, J. Zartman, W.B. Krantz and A.R. Greenberg,, "Instrumentation for Studying Polymer Film Formation in Low Gravity," Polymer Research in Microgravity, J.P. Downey and J.A. Pojman (eds.)., ACS Symposium Series 793, American Chemical Society, Washington, DC, 126-137 (2001).

37.   Khare, V., A.R. Greenberg, W.B. Krantz, H. Lee, P. Todd and S. Dunn, “Polymer Thin Film Formation on Low-Gravity Aircraft and On ISS,” AIAA Paper 2001-5024, Proceedings of the Conference & Exhibit on International Space Station Utilization – 2001, Cape Canaveral, Florida, October 2001.

38.   Krantz, W.B., J. Zartman, V. Hare, A.R. Greenberg and P. Todd, “Observation of Solutocapillary Flow During Polymer Membrane Casting,” AIAA Paper 2001-5022, Proceedings of the Conference & Exhibit on International Space Station Utilization – 2001, Cape Canaveral, Florida, October 2001.

39.   Chai, G.-Y., W.B. Krantz, and A.R. Greenberg, “Measurement of Membrane Fouling in Spiral-Wound Modules,”  Proceedings of the 6th World Congress of Chemical Engineering, September 23-27, 2001, Melbourne, Australia (available on CD ROM).

40.   Aerts, P., A.R. Greenberg, R. Leysen, W.B. Krantz, V.E. Reinsch and P.A. Jacobs, “The Influence of Filler Concentration on the Compaction and Filtration Properties of Zirfon Composite Ultrafiltration Membranes,” Separation and Purification Technology, 22-23, 663-669 (2001).

41.   Todd, P., J.C. Vellinger, S. Sengupta, M.G. Sportiello, A.R. Greenberg, and W.B. Krantz, “Sliding-Cavity Fluid Contactors in Low-Gravity Fluids, Materials and Biotechnology Research,” Proceedings of the Microgravity Transport Processes in Fluid, Thermal, Biological and Materials Sciences II, Sept. 30-Oct. 5, 2001, Banff, Alberta, Canada,  Proceeding MTP-01-71, 1-6 (2001).

42.   Krantz, W.B., J. Zartman, V. Khare, A.R. Greenberg and P. Todd,  “Observation of Solutocapillary Flow During Polymer Membrane Casting,” Proceedings of the International Space Station Utilization Conference, October 15-18, 2001, Kennedy Space Center, Florida, AIAA 2001-5022 (10 pages).

43.   Pekny, M.R., A.R. Greenberg, V. Khare, J. Zartman, W.B. Krantz, and P. Todd, “Macrovoid Pore Formation in Dry-Cast Cellulose Acetate Membranes: Buoyancy Studies,” J. Membrane Science, 205, 11-21 (2002).

44.   Khare, V.P., A.R. Greenberg, J. Zaartman, W.B. Krantz and P. Todd, “Macrovoid Growth During Polymer Membrane Casting,” Desalination, 145, 17-23 (2002).

45.   Kelley, S.S., A.R. Greenberg, J. Filley, R. Peterson, and W.B. Krantz, "Chemical Modification of Cellulose Acetate with Titanium Isopropoxide", International Journal of Polymer Analysis and Characterization, 7, 162-180 (2002).

46.   Greenberg, A.R., V.P. Khare, J. Zartman, W.B. Krantz and P. Todd, “Macrovoid Defect Growth During Evaporative Casting of Polymeric Membranes,” Proceedings of the NASA Microgravity Materials Science Conference, Huntsville, Alabama, June 2002.

47.   Pekny, M.R., J. Zartman, W.B. Krantz, A.R. Greenberg and P. Todd, “Flow Visualization During Macrovoid Pore Formation in Dry-Cast Cellulose Acetate Membranes,” J. Membrane Science, 71-90, 211 (2002).

48.   Ramaswamy, S., A.R. Greenberg and W.B. Krantz, “Fabrication of Poly (ECTFE) Membranes via Thermally Induced Phase Separation,” J. Membrane Science, 210, 175-180 (2002).

49.   Greenberg, A.R. and W.B. Krantz, “UTDR-Based Sensors for Real-Time Quantification of Membrane Module Fouling and Cleaning,” Fluid/Particle Separation Journal, 15(1) 43-49 (2003).

50.   Zhang, Zh.-X., A.R. Greenberg, W.B. Krantz and G.-Y. Chai, “Study of Membrane Fouling and Cleaning in Spiral Wound Modules Using Ultrasonic Time-Domain Reflectometry,” in New Insights into Membrane Science and Technology: Polymeric, Inorganic and Biofunctional Membranes, A.A. Butterfield and D. Bhattacharyya (eds.), Elsevier, Amsterdam, 65-88 (2003).

51.   Khare, V., A.R. Greenberg and W.B. Krantz, “Development of Pendant Drop Mechanical Analysis (PDMA) as a Technique for Determining the Stress Relaxation and Water Permeation Properties of Interfacially Polymerized Barrier Layers,” J. Applied Polymer Science, 90(10), 2618-2628 (2003).

52.   Soice, N.P., A.C. Maladono, D.Y. Takigawa, A.D. Norman, W.B. Krantz and A.R. Greenberg, “Oxidative Degradation of Polyamide RO Membranes: Insights from Molecular Model Compounds and Membrane Studies,” J. Applied Polymer  Science, 90(5), 1173-1184 (2003).

53.   Chai, G.-Y., A.R. Greenberg and W.B. Krantz, “Study of Using In-Situ Ultrasonic Measurement Technique in Membrane Separation,” Journal of Membrane Science and Technology (China), 23(4) 135-141 (2003).

54.   Khare, V.P., A.R. Greenberg, and W.B. Krantz, “Investigation of the Viscoelastic and Transport Properties of Interfacially Polymerized Barrier Layers Using Pendant Drop Mechanical Analysis,” J. Applied Polymer Science, 94, 558-568 (2004).

55.   Hellman, D.J., A.R. Greenberg and W.B. Krantz, “A Novel Process for Membrane Fabrication:  Thermally –Assisted Evaporative Phase Separation,” J. Membrane Science, 230, 99-109 (2004).

56.   Soice, N.P., A.R. Greenberg, W.B. Krantz, and A.D. Norman, “Studies of Oxidative Degradation in Polyamide RO Membrane Barrier Layers using Pendant Drop Mechanical Analysis,” J. Membrane Science, 243, 245-255 (2004).

57.   Gabelman, A., S.-T. Hwang, and W.B. Krantz, “Dense Gas Extraction using a Hollow Fiber Membrane Contactor:  Experimental Results vs. Model Predictions,” J. Membrane Science, 257, 11-36 (2005).

58.   Khare, V.K., A.R. Greenberg, and W.B. Krantz, “Vapor Induced Phase Separation - Effect of the Humid Air Exposure Step on Membrane Morphology: Part I.  Insights from Mathematical Modeling,” J. Membrane Science, 258, 140-156 (2005).

59.   Jia, Y., R. Wang, A.G. Fane, and W.B. Krantz, “Effect of Air Bubbling on Atrazine Adsorption in Water by Powdered Activated Carbons - Competitive Adsorption of Impurities,” Separation and Purification Technology, 46(1-2), 79-87 (2005).

60.   French, D.A., R. Flannery, S. Kleene, W.B. Krantz, and C. Groetsch, “Numerical Approximation of Solutions of a Nonlinear Inverse Problem arising in Olfaction Experimentation,” Mathematical and Computer Modeling, 43, 945-956 (2006).

61.   Li, D., A.R. Greenberg, W.B. Krantz, and R.L. Sani, “Membrane Formation via Thermally Induced Phase Separation (TIPS): Model Development and Validation,” J. Membrane Science, 279, 50-60 (2006).

62.   Lee, H., S.R. Chaudhuri, W.B. Krantz, and S.-T. Hwang, “A Model for Evaporative Casting of Polymeric Membranes Incorporating Convection due to Density Changes,” J. Membrane Science, 284, 161-172 (2006).

63.   Gupta, V.K., Hwang, S.-T., W.B. Krantz and A.R. Greenberg, “Characterization of Nanofiltration and Reverse Osmosis Membrane Performance for Aqueous Salt Solutions using Irreversible Thermodynamics,” Desalination, 208, 1-18 (2007).

64.   Chai, G.-Y., A.R. Greenberg, and W.B. Krantz, “Ultrasound, Gravimetric, and SEM Studies of Inorganic Fouling in Spiral-Wound Membrane Modules,” Desalination, 208, 277-293 (2007).

65.   Anim-Mensah, A.R., J.E. Franklin, J.E., L.A. Salazar, D.B. Mast, J.E. Mark, S. J. Clarson,  and W. B. Krantz, “Use of Ultrasound to Determine Selected Mechanical Properties of Silicone Films,” chapter in Science and Technology of Silicone and Silicone-Modified Materials, #964 ACS Symposium Series, by S.J. Clarson, J.J. Fitzgerald, M.J. Owen, S.S. Smith, and M.E. Van Dyke (eds.), Oxford University Press, UK, 203-219 (2007).

66.   Anim-Mensah, A.R., J.E. Mark, and W.B. Krantz, “Use of Solubility Parameters for Predicting the Separation Characteristics of Poly(dimethyl-siloxane) and Siloxane-Containing Membranes,” Chapter 14 in Science and Technology of Silicone and Silicone-Modified Materials, ACS Symposium Series #964, by S.J. Clarson, J.J. Fitzgerald, M.J. Owen, S.D. Smith, and M.E. Van Dyke (eds.), Oxford University Press, UK (2007).

67.   N. Widjojo, T.S. Chung, and W.B. Krantz “A Morphological and Structural Study of Ultem/P84 Copolyimide Dual-Layer Hollow Fiber Membranes with Delamination-Free Morphology” Journal of Membrane Science, 294, 132-146 (2007).

68.   Li, Yi, W.B. Krantz, and T.-S. Chung, “A Novel Primer to prevent Nanoparticle Agglomeration in Mixed Matrix Membranes,” A.I.Ch.E. Journal, 53(9), 2470-2475 (2007).

69.   Bonyadi, S., T.-S. Chung, and W.B. Krantz, “Investigation of Corrugation Phenomenon in the Inner Contour of Hollow Fibers during Non-solvent Induced Phase Separation Process,” J. Membrane Science, 299(1-2), 200-210 (2007).

70.   Cheng, J., L. Yi, T.-S. Chung, Chen, S.-B., and W.B. Krantz, “High-Performance Protein Separation by Ion Exchange Membrane Partitioned Free-Flow Isoelectric Focusing System,” Chem. Eng. Sci., 63, 2241-2251 (2008).

71.   Anim-Mensah, A.R., W.B. Krantz, and R. Govind, “Studies on Polymeric Nanofiltration-Based Water-Softening and the Effect of Anion Properties on the Softening Process,” European Polymer Journal,  44(7), 2244-2252 (2008).

72.   Krantz, W.B. and A.R. Greenberg, “Use of Ultrasonic Time-Domain Reflectometry for Membrane Characterization,” chapter in Membrane Characterization to be published by John Wiley & Sons, New York, accepted for publication.

73.   Anim-Mensah, A.R., W.B. Krantz, J.E. Mark, D.B. Mast, K. Abhinava, and R. Govind, “Use of Ultrasonic Reflectometry to Study Simultaneous Membrane Compaction and Permeation in Real-Time,” submitted to J. Membrane Science (2008).

74.   Ray Chaudhuri, S., G.B. Kasting, and W.B. Krantz, “Percutaneous Absorption of Volatile Solvents Following Transient Liquid Phase Exposures I. Model Development,” submitted to Chem. Eng. Sci. (2008).

75.   Ray Chaudhuri, S., G.B. Kasting, and W.B. Krantz, “Percutaneous Absorption of Volatile Solvents Following Transient Liquid Phase Exposures II. Experimental Studies,” submitted to Chem. Eng. Sci. (2008).

76.   Lee, H., W.B. Krantz, and S.-T. Hwang, “A Model for Wet-Casting of Polymeric Membranes Incorporating Convection due to Densification,” submitted to J. Membrane Sci. (2008).

77.   Ray Chaudhuri, S., W.B. Krantz, and G.B. Kasting, “Scaling (approximation) Analysis of Transient Solution-Diffusion Problem of Permeation through a Mult-lamellar Membrane I. Pure Liquids,” Chem. Eng. Sci., to be submitted for publication (2008).

78.   Hellman, D.J., W.B. Krantz, and A.R. Greenberg, “Boundary Condition Effects on Evaporative Casting of Polymeric Membranes Part 1. Modeling and Sensitivity Analysis,” J. Membrane Science, to be submitted for publication (2008).

 

 

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