Department of Mechanical Engineering

University of Delaware

Newark, Delaware 19716

(302)831-6830/2421

Email: schwartz@me.udel.edu

FAX: (302)831-3619

- All areas of fluid mechanics spanning the speed range from creeping motions to hypersonic flow.
- Specific applications to coating flow, free- and moving-boundary flows, flow in porous media, naval hydrodynamics, geophysical fluid dynamics, classical aerodynamics and gas dynamics, non-Newtonian flows.
- Applied mathematics, fluid mechanics, analytical mechanics, heat transfer.
- Numerical solution of linear and nonlinear problems
- Perturbation techniques,
- Mathematical modeling.

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

- 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.

Board of Directors, International Society of Coating Science and Technology, 1997 - pres.

Editorial Board, Journal of Engineering Mathematics, 1986 - present.

Visiting Professor of Civil and Chemical Engineering, Univ. of Melbourne, 2003.

Visiting Professor of Mechanical Engineering, Naval Postgraduate School, 2002.

Visiting Professor of Applied Mathematics, Univ. of Adelaide, 1994.

Visiting Professor, Department of Mechanical and Aerospace Engineering, Rutgers University, 1986 -1987.

Visiting Professor, Joint Institute for Aeronautics & Acoustics, Stanford University, 1980.

Member, NASA Microgravity Review Panel, 1992, 1993, 1997.

Member, National Science Foundation Fluid Dynamics Panel, 1985.

Visiting Research Scholar, Dept. of Naval Architecture, Univ. of California (Berkeley), 1977.

Summer Fellow, Woods Hole Oceanographic Institution, 1972.

Numerous consultancies to industry.

- 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)

- "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.

- "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.