LEONARD WILLIAM SCHWARTZ

EDUCATION

• 1969 - 1972 Stanford University. Ph. D. Fluid Mechanics
• 1964 - 1965 Cornell University. Master of Engineering (Aero.).
• 1960 - 1965 Cornell University. Bachelor of Engineering Physics

EMPLOYMENT HISTORY

1987-pres.

Professor of Mechanical Engineering and Professor of Mathematical Sciences, University of Delaware.

1980-1986

Senior Staff Mathematician, Exxon Corporate Research Laboratory, Clinton, New Jersey.

1975-1980

Lecturer, Senior Lecturer, Department of Applied Mathematics, University of Adelaide, Adelaide, Australia.

1974 -1975

Research Scientist, Flow Research Inc., Kent, Washington.

1973-1974

National Research Council Fellow, Computational Fluid Dynamics Branch, NASA Ames Research Center.

1965 - 1969

Aerodynamicist, Lockheed Missiles & Space Co.

VISITING AND OTHER APPOINTMENTS

PUBLICATIONS (About 100 archival publications. See attached list.)

DOCTORAL STUDENTS

• J. M. Vanden-Broeck, 1978 (Currently Prof. of Mathematics, U. East Anglia, UK.)
• L. K. Forbes, 1981 (Currently Professor of Mathematics, U. Tasmania, Australia.)
• J. A. Moriarty, 1991 (Currently Research Scientist, Baxter Healthcare)
• D. E. Weidner, 1993
• V. M. Harik, 1997 (Currently Research Scientist, NIST)
• M. H. Eres, 1998 (Currently Sr. Scientist, Southampton Univ., UK.)
• P. L. Evans, 2000 (Currently Research Scientist, Industrial Research Ltd., NZ)

Technical Publications - L. W. Schwartz

• "Steady and unsteady solutions for coating flow on a rotating horizontal cylinder; two-dimensional theoretical and numerical modeling" (with P. L. Evans and R. V. Roy), Physics of Fluids 2003 (submitted).
• "Morphological stability \& nonlinear evolution of capillary ridges" (with R. V. Roy), J. Fluid Mech. 2003 (submitted).
• Theoretical and numerical results for spin coating of viscous liquids, (with R. V. Roy) Physics of Fluids, 2002 (submitted).
• "A mathematical model for an expanding foam," (with R. V. Roy) J. Colloid Interf. Sci. 2003 (in press).
• "Recent progress in the theoretical and numerical modeling of thin-layer flow," Acoustics, Mechanics, and the Related Problems of Mathematical Analysis, A. Wirgin, Ed., World Scientific, London, 2003.
• "Milton Van Dyke, the Man and His Work," Ann. Rev. Fluid Mech. 34, 1 - 18, 2002.
• "Spraying and spreading processes on moving substrates," (with M. H. Eres) pp. 95 - 102 in "ECS2001, 4th European Coating Smposium, Advances in Coating Processes," (J-M Buchlin & J. Anthoine, Eds.) VKI/ULB Brussels, 2002.
• "Mathematical and numerical modeling of spin coating," (with R. V. Roy) pp. 243 - 248 in "ECS2001, 4th European Coating Smposium, Advances in Coating Processes," (J-M Buchlin & J. Anthoine, Eds.) VKI/ULB Brussels, 2002.
• "Numerical modeling of liquid withdrawal from gravure cavities in coating operations; the effect of cell pattern," J. Engrg. Maths. 42, 243-253, 2002.
• "Flow of architectural coatings on complex surfaces; theory and experiment." (with R. R. Eley) J. Engrg. Maths. 43, 153-171, 2002.
• "Interaction of rheology, geometry, and process in coating flows," (with R. R. Eley) J. Coatings Technology 74, 43-53, 2002.
• "Theory and modeling of thin film flows," (with S. B. G. O'Brien) pp 5283 - 5297 in Encyclopedia of Surface and Colloid Science (A. Hubbard, Ed.) Marcel Dekker, New York, 2002.
• "Some results concerning the potential energy of interfaces with nonuniformly distributed surfactant," (with R. V. Roy) Phys. of Fluids 13, 3089 - 3092, 2001.
• "De-wetting patterns in a drying liquid film," (with R. V. Roy, R. R. Eley & S. Petrash) J. Colloid Interf. Sci.234, 363-374, 2001.
• "On the asymptotic analysis of stress-driven thin-layer flow," J. Engrg. Math. 39, 171 - 188, 2001.
• "A mathematical model for soap film draining," (with R. V. Roy) pp. 174 - 180 in Foams, Emulsions and their Applications, P. Zitha, J. Banhart & G. Verbist, Eds., Verlag MIT, Bremen, 2000.
• "Extensional fall of a very viscous fluid drop," (with Y. Stokes & E. O. Tuck) Q. J. Mech. Appl. Maths. 53, 565 -582, 2000.
• "Fingering Phenomena for Driven Coating Films," (with M. H. Eres & R. V. Roy) Phys. of Fluids 12, 1278 - 1295 2000.
• "A mathematical model for crater defect formation in a drying paint layer," (with P. L. Evans & R. V. Roy), J. Colloid Interf. Sci. 227, 191 - 205, 2000.
• "Theoretical and numerical modeling of coating flow on simple and complex substrates including rheology, drying and Marangoni effects," in Adv. in Coating and Drying of Thin Films, F. Durst & H. Raszillier, Eds., pp. 105-128, Shaker Verlag, Aachen, 1999.
• "Morphological stability and nonlinear evolution of capillary ridges," (with R. V. Roy) in Adv. in Coating and Drying of Thin Films, F. Durst & H. Raszillier, Eds., pp. 131-136, Shaker Verlag, Aachen, 1999.
• "Modeling thin layer flows with strong surface tension gradient effect," (with R. V. Roy) in Adv. in Coating and Drying of Thin Films, F. Durst & H. Raszillier, Eds., pp. 145-150, Shaker Verlag, Aachen, 1999.
• "Influence of gravity on the stability of capillary liquid ridges, (with R. V. Roy) J. Fluid Mech., 1999 (submitted).
• "On the stability of liquid ridges," (with R. V. Roy) J. Fluid Mech. 391, 293-318, 1999.
• " Modeling draining flow in mobile and immobile soap films," (with R. V. Roy) J. Colloid & Interf. Sci. 218, 309-323, 1999.
• "Three-dimensional direct numerical simulation of surface-tension-gradient effects on the leveling of an evaporating multi-component fluid," (with M. H. Eres & D. E. Weidner) Langmuir 15, 1859-1871, 1999.
• "Hysteretic effects in droplet motions on heterogeneous substrates," Langmuir 14, 3440-3453, 1998.
• "Three-dimensional numerical simulation of droplet motion on heterogeneous surfaces," (with R. R. Eley) Proc. 2nd European Coating Symposium (Euromech 367), 475 - 484, 1998.
• "Coating flows over curved substrates," (with R. V. Roy) Proc. 2nd European Coating Symposium, (Euromech 367), 18 - 27, 1998.
• "Simulation of droplet motion on low-energy and heterogeneous surfaces," (with R. R. Eley) J. Colloid & Interf. Sci. 202, 173-188, 1998 .
• "Numerical modeling of liquid withdrawal from gravure cavities in coating operations," (with P. Moussalli, P. Campbell, & R. R. Eley) Trans. Inst. Chem. Engrs. 76, 22-29 (1998).
• "Unsteady simulation of viscous thin-layer flows," a chapter in the monograph 'Free-Surface Flows with Viscosity,' P. Tyvand, Ed., pp. 203 - 233, Computational Mech. Publ., Southampton (1997).
• "Slow slumping of a very viscous liquid bridge," (with E. O. Tuck & Y. Stokes) J. Engr. Math. 32, 27-40 (1997).
• "Simulation of coating layer evolution and drop formation on horizontal cylinders," (with D. E. Weidner & M. H. Eres) J. Colloid & Interf. Sci. 187, 243-258 (1997).
• "Free-surface and contact line motion of liquid in microgravity," Proc. Third Microgravity Fluid Physics Conference, NASA Conf. Publ. 3338, 609-614, 1996.
• "Anomalous behavior during leveling of thin coating layers with surfactant," (with R. A. Cairncross & D. E. Weidner) Physics of Fluids 8, 1693-1695, 1996.
• "Role of Surface Tension Gradients in Correcting Coating Defects in Corners," (with D. E. Weidner & R. R. Eley) J. Colloid & Interf. Sci. 179, 66-75, 1996.
• "An Analysis of the Effect of Surfactant on the Leveling Behavior of a Thin Liquid Coating Layer," (with D. E. Weidner & R. R. Eley) Langmuir 11, 3690-3693, 1995.
• "Modeling of Coating Flows on Curved Surfaces." (with D. E. Weidner) J. Engineering Mathematics 29, 91-103, 1995.
• "Surface-tension-gradient effects on flow in thin coating layers," (with D. E. Weidner, & R. R. Eley), Polym. Mater. Sci. Eng. 73, 490-1, 1995.
• "Dip Coating of Spectacle Lenses," in Proceedings of the 1994 Australian Mathematics in Industry Study Group (J. Hewitt, ed.), pp. 109-123, 1995.
• "Contact-line motion of shear-thinning liquids," (with D. E. Weidner) Physics of Fluids 6(11), 3535-3538, 1994.
• "Dynamic Considerations in the Closing and Opening of Holes in Thin Liquid Films," (with J. A. Moriarty), J. Colloid & Interface Science 161, 335-342, 1993.
• "Coating Flows on Curved Surfaces," Proceedings of the Workshop on Filtration and Nonlinear Diffusion Processes, pp. 21-24, Centre for Nonlinear Partial Differential Equations at Delft-Leiden, Netherlands, 1992.
• "Effective Slip in Numerical Calculations of Moving-contact-line Problems" (with J. A. Moriarty), J. Engineering Mathematics 26, 81-86, 1992.
• "An Experimental and Numerical Investigation of Buoyancy-Driven Two-Phase Displacement," (with D. E. Weidner), Physics of Fluids A3, 2076-2080, 1991.
• "Unsteady Spreading of Thin Liquid Films with Small Surface Tension," (with J. A. Moriarty & E. O. Tuck), Physics of Fluids A3, 733-742, 1991.
• "Thin Static Drops with a Free Attachment Boundary," (with E. O. Tuck) J. Fluid Mechanics 223, 313-324, 1991.
• "A Numerical and Asymptotic Study of Some Third-Order Ordinary Differential Equations Relevant to Draining and Coating Flows," (with E. O. Tuck), S.I.A.M. Review 32, 453-469, 1990.
• "Viscous Flows Down an Inclined Plane: Instability and Finger Formation," Physics of Fluids A1, 443-445 (1989).
• "Instability and Fingering in a Rotating Hele-Shaw Cell or Porous Medium," Physics of Fluids A1, 167-170 (1989).
• "Gravity Flow of a Viscous Liquid Down a Slope with Injection," (with E. E. Michaelides) Physics of Fluids 31, 2739-2741 (1988).
• "Two-Phase Flow in Hele-Shaw Cells: Numerical Studies of Sweep Efficiency in a Five-Spot Pattern," (with A. DeGregoria), J. Austral. Math. Soc. Ser. B. 29, 375-400 (1988).
• "Recent Developments in Hele-Shaw Flow Modelling," in Numerical Simulation in Oil Recovery (M. F. Wheeler, ed.), 249-262, Springer-Verlag, New York, 1988.
• "Saffman-Taylor Finger Width at Low Interfacial Tension," (with A. DeGregoria), Phys. Rev. Lett., 58, 1742-1744,1987.
• "A Theory of Extensional Viscosity for Flowing Foam," (with H. Princen), J. Colloid & Interf. Sci., 118, 201-211,1987.
• "A Perturbation Solution for Compressible Viscous Channel Flows", J. Engrg. Math., 21, 69-85, 1987.
• "A Boundary-integral Method for Two-Phase Displacement in Hele-Shaw Cells," (with A. DeGregoria), J. Fluid Mech. 164, 383 -400, 1986.
• "On the Motion of Bubbles in Capillary Tubes," (with H. Princen & A. Kiss), J. Fluid Mech. 172, 259 - 275, 1986.
• "Contact-angle Hysteresis and the Shape of the Three-Phase Line," (with S. Garoff), J. Colloid Interf. Sci. 106, 422 - 437, 1985.
• "Finger Breakup in Hele-Shaw Cells," (with A. DeGregoria), Phys. Fluids, 28, 2313 - 2314, 1985.
• "Capillary Hysteresis on Mixed-Wettable Surfaces," (with S. Garoff), Electrochemical Society Proceedings Volume 85-8, 122 -130, 1985.
• "The Nonlinear Evolution of Viscous Fingers - A Water Wave Problem in Disguise," Proc. 1st International Wkshp. on Water Waves & Floating Bodies, 145-150, MIT Cambridge, 1986.
• "Stability of Hele-Shaw Flows; the Wetting-Layer Effect," Phys. Fluids, 29, 3086 -3088, 1986.
• "Simulation of Hele-Shaw Fingering with Finite Capillary-Number Effects Included," (with A. DeGregoria) Phys. Rev. A, 35, 276-280, 1987.
• "Flow in Hele-Shaw Cells - A Canonical Model for Porous Media (?)," in Advances in Multiphase Flow and Related Problems, (G. Papanicoleau, ed.) 181-190, Soc. Ind. Appl. Math. Philadelphia, 1987.
• "Contact Angle Hysteresis on Heterogeneous Surfaces," (with S. Garoff) Langmuir 1, 219 - 230, 1985.
• "Discussion of Computer-Extended Series," Trans. Inst. Engr. Australia 9, 247 -249, 1984.
• "The Calculation of Nonlinear Short-Crested Gravity Waves," (with A. Roberts) Phys. Fluids 26, 2388-2392, 1983.
• "Strongly Nonlinear Waves," (with J. D. Fenton) Ann. Rev. Fluid Mech. 14, 39 - 60, 1982.
• "Free-surface Flow over a Semi-circular Obstruction," (with L. Forbes) J. Fluid Mech. 114, 299-314, 1982.
• "A Semi-analytic Approach to the Self-induced Motion of Vortex Sheets," J. Fluid Mech. 111, 475-490, 1981.
• "Nonlinear Solution for an Applied Overpressure on a Moving Stream," J. Engrg. Math. 15, 147-156, 1981.
• "Supercritical Flow Past Blunt Bodies in Shallow Water," (with L. Forbes), J. Appl. Math & Phys. (ZAMP) 32, 314-328, 1981.
• "Numerical Calculation of Standing Waves in Water of Arbitrary Uniform Depth," (with J.-M. Vanden-Broeck), Phys. Fluids 24, 812-815, 1981.
• "Semi-analytic Solution for Nonlinear Standing Waves in Deep Water," (with A. Whitney), J. Fluid Mech. 107, 147-171, 1981.
• "Numerical Solution of the Exact Equations for Capillary Gravity Waves," (with J.-M. Vanden-Broeck), J. Fluid Mech. 95, 119-139,1979.
• "Numerical Computation of Steep Gravity Waves in Shallow Water," (with J.-M. Vanden-Broeck), Phys. Fluids 22, 1868-1871, 1979.
• "A One-parameter Family of Sequence Transformations," (with J.-M. Vanden-Broeck), S. I. A. M. J. Math. Anal. 10, 653-666, 1979.
• "Divergent Low-Froude-number Series Expansion of Nonlinear Free-Surface Flow Problems," (with J.-M. Vanden-Broeck & E. Tuck), Proc. Roy. Soc. London A361, 207-224, 1978.
• "A High-order Series Solution for Standing Water Waves," (with A. Whitney), Proc. 6th Australasian Hydraulics & Fluid Mechanics Conf. v. 1, 365-359, 1977.
• "Rational Approximations to the Solution of the Blunt-Body and Related Problems", Lecture Notes in Physics 47, 165-188, 1976.
• "On the Analytic Structure of the Taylor-Maccoll Conical Flow Solution," J. Appl. Math. & Phys. (ZAMP) 26, 407-414, 1975.
• "Series Solution for the Planar Asymmetric Blunt-Body Problem," Phys. Fluids 18, 1630-1638, 1975.
• "Hypersonic Flows Generated by Parabolic & Paraboloidal Shock Waves," Phys. Fluids 17, 1816-1821, 1974.
• "Computer Extension and Analytic Continuation of Stokes' Expansion for Gravity Waves," J. Fluid Mech. 62, 553-578, 1974.
• "The Calculation of Nonlinear Interfacial Waves," GFD Summer Symposium Fellowship Lectures, 96-109, Woods Hole Oceanographic Institution, 1972.
• "Drag of Cones at Supersonic Speeds," AIAA Jour. 7, 572, 1969.

REPORTS WITH SUBSTANTIALLY DIFFERENT CONTENT FROM ABOVE

• "Mathematical Modeling and Numerical Simulation of Beverage Container Coating Processes," (with Weidner, D. E. & Eley, R. R.), Glidden Research Report PR&D 93-02, February 2, 1993.
• "Interfacial Waves of Permanent Form in Immiscible Two-Phase Flow," TR 88-3, Center for the Mathematics of Waves, University of Delaware, 1988.
• "Local Extrema in the Solution to the Biharmonic Equation," (with E. K. Hall) Department of Mechanical Engineering Tech. Rpt. No. 288, May 27, 1988, University of Delaware.
• "Two-phase Displacement in Capillary Tubes," Exxon CRL Report CR.9BL.84, 1984.
• "Determination of Maxwell-Model Constants from Experimental Data for Extensional Flow of Polymer Solutions," Exxon CRL Report CR.11BL.84, 1984.
• "Approximate Techniques for the Prediction of Pressure Drop and Flow Fields in a Model Porous Medium," Exxon CRL Report CR.10.BL.84, 1984.
• "Interfacial Waves of Permanent Form in Core-Annular Pipe Flow," Exxon CRL Report CR.2BL.83, 1983.
• "A Simple Analytic Model for Heat Transfer in a Layer of Porous Oil Shale," Exxon CRL Report CR.1.BL.83, 1983.
• "On the Pressure Field of Nonlinear Standing Water Waves," Joint Institute for Aeronautics & Acoustics, Stanford University Report JIAA TR-33, (NASA-CR-1641-81), 1980.
• "Divergent Low-Froude-Number Series Expansion of Nonlinear Free-Surface Flow Problems," (with J.-M. Vanden-Broeck & E. Tuck), Report V-01 Appl. Math Dept., University of Adelaide, 1977.
• "A Propeller Analysis Computer Program," (with S. Bernstein) FRI Note 67, (APL/JHU POR 3686), Flow Research Inc., 1975.