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A Brief Summary of L. van Wijngaarden’s Work Up Till His Retirement

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In Fascination of Fluid Dynamics

Part of the book series: Fluid Mechanics and its Applications ((FMIA,volume 45))

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Abstract

This paper attempts to provide an overview of Professor Leen van Wijngaarden’s scientific work by briefly summarizing a number of his papers. The review is organized by topic and covers his work on pressure waves in bubbly liquids, bubble dynamics, two-phase flow, standing waves in resonant systems, and flow cavitation noise. A list of publications up till his retirement in March 1997 is provided in the Appendix.

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References

  • Batchelor G.K., Compression waves in a suspension of gas bubbles in liquid. Fluid Dyn. Trans. 4 (1969) 425–445

    Google Scholar 

  • Batchelor G.K., Sedimentation in a dilute dispersion of spheres. J. Fluid Mech. 52 (1972) 245–268

    Article  ADS  MATH  Google Scholar 

  • Batchelor G.K. and Green J.T., The determination of the bulk stress in a suspension of spherical particles to order c 2. J. Fluid Mech. 56 (1972) 401–427

    Article  ADS  MATH  Google Scholar 

  • Bel Fdhila R. and Duineveld P.C., The effect of surfactants on the rise of a spherical bubble at high Reynolds and Péclet numbers.Phys. Fluids 8 (1996) 310–321

    Article  ADS  Google Scholar 

  • Biesheuvel A., On void fraction waves in dilute mixtures of liquid and gas bubbles. Ph.D. Thesis, University of Twente (1984)

    Google Scholar 

  • Biesheuvel A. and Spoelstra S., The added mass coefficient of a dispersion of spherical gas bubbles in liquid. Int. J. Multiphase Flow 15 (1989) 911–924

    Article  MATH  Google Scholar 

  • Birkhoff G. and Zarantonello E.H.,Jets, Wakes, and Cavities. Academic Press, Duluth, MN (1957)

    MATH  Google Scholar 

  • Broer L.J.F., Some basic properties of relaxation gasdynamics. In: Wegener P.P. (ed.), Nonequilibrium Flows, Vol.I. Dekker, New York (1970) pp. 1–31

    Google Scholar 

  • Caflisch R.E., Miksis M.J., Papanicolaou G.C. and Ting L., Effective equations for wave propagation in bubbly liquid. J. Fluid Mech. 153 (1985) 259–273

    Article  ADS  MATH  Google Scholar 

  • Campbell I.J. and Pitcher A.S., Shock waves in liquid containing gas bubbles. Proc. Roy. Soc. London A243 (1958) 534–545

    ADS  Google Scholar 

  • Chu B.T. and Ying S.J., Thermally driven nonlinear oscillations in a pipe with travelling shock waves. Phys. Fluids 6 (1963) 1625–1637

    Article  ADS  MATH  Google Scholar 

  • d’Agostino L. and Brennen C.E., On the acoustical dynamics of bubble clouds. In: Hoyt J.W. (ed.), Cavitation and Multiphase Flow Forum, ASME FED Vol. 2. ASME, New York (1983) pp. 72–75

    Google Scholar 

  • d’Agostino L. and Brennen C.E., Linearized dynamics of spherical bubble clouds. J. Fluid Mech. 199 (1989) 155–176

    Article  MathSciNet  ADS  Google Scholar 

  • d’Agostino L., Brennen C.E. and Acosta A.J., Linearized dynamics of two-dimensional bubbly and cavitating flows over slender surfaces. J. Fluid Mech. 192 (1988) 485–509

    Article  MathSciNet  ADS  Google Scholar 

  • Duineveld PC, The rise velocity and shape of bubbles in pure water at high Reynolds number. J. Fluid Mech. 292 (1995) 325–332

    Article  ADS  Google Scholar 

  • Duineveld P.C., The influence of an applied sound field on bubble coalescence. J. Acoust. Soc. Am. 99(1996) 622–624

    Article  ADS  Google Scholar 

  • Foldy L.L., The multiple scattering of waves. Phys. Rev. 67 (1945) 107–119

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Galper A. and Miloh T., Generalized Kirchhoff equations for a deformable body moving in a weakly non-uniform flow field. Proc. Roy. Soc. Lond. A446 (1994) 169–193

    MathSciNet  ADS  Google Scholar 

  • Galper A. and Miloh T., Dynamic equations of motion for a rigid or deformable body in an arbitrary non-uniform potential flow field. J. Fluid Mech. 295 (1995) 91–120

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Gidaspow D., Soo S.L., Harlow F.H., Hughes E.D., Wallis G.B. and Hsu Y.Y., Round table discussion: Modeling of two-phase flow. In: Proceedings of the 5th International Heat Transfer Conference, Vol. 7. Japan Society of Mechanical Engineers, Tokyo (1974) pp. 163–170

    Google Scholar 

  • Iordanskii S.V, On the equation of motion for a liquid containing gas bubbles. Zh. Prikl. Mekh. Tekhn. Fiz. 3 (1960) 102–110 [in Russian]

    Google Scholar 

  • Kameda M. and Matsumoto Y, Shock waves in a liquid containing small gas bubbles. Phys. Fluids 8 (1996) 322–335

    Article  MathSciNet  ADS  Google Scholar 

  • Kogarko B.S., One-dimensional unsteady motion of a liquid with an initiation and progression of cavitation. Dokl. Akad. Nauk SSSR. 155 (1964) 779–782 [in Russian]

    Google Scholar 

  • Kok J.B.W., Collision dynamics of bubble pairs moving through a perfect liquid. Appl. Sci. Res. 50 (1993a) 169–188

    Article  MATH  Google Scholar 

  • Kok J.B.W., Dynamics of a pair of gas bubbles moving through liquid. I. Theory. Eur. J. Mech. B Fluids 4 (1993b) 515–540

    MathSciNet  Google Scholar 

  • Kok J.B.W., Dynamics of a pair of gas bubbles moving through liquid. II. Experiment. Eur. J. Mech. B Fluids 4 (1993c) 541–560

    MathSciNet  Google Scholar 

  • Korteweg DJ. and de Vries G., On the change of form of long waves advancing in a rectangular canal and on a new type of long stationary waves. Phil. Mag. 39 (1895) 422–443

    Article  MATH  Google Scholar 

  • Kumar S. and Brennen C.E., Nonlinear effects in the dynamics of clouds of bubbles. J. Acoust. Soc. Am. 89 (1991) 707–714

    Article  ADS  Google Scholar 

  • Kumaran V. and Koch D.L., The effect of hydrodynamic interactions on the average properties of a bidisperse suspension of high Reynolds number, low Weber number bubbles. Phys. Fluids A 5 (1993a) 1123–1134

    Article  ADS  MATH  Google Scholar 

  • Kumaran V. and Koch D.L., The rate of coalescence in a suspension of high Reynolds number, low Weber number bubbles. Phys. Fluids A 5 (1993b) 1135–1140

    Article  ADS  MATH  Google Scholar 

  • Landweber L. and Miloh T., The Lagally theorem for unsteady multipoles and deformable bodies. J. Fluid Mech. 96 (1980) 33–46

    Article  ADS  MATH  Google Scholar 

  • Lighthill M.J., Viscosity effects in sound waves of finite amplitude. In: Batchelor G.K. and Davies R.M. (eds), Surveys in Mechanics. Cambridge University Press, Cambridge (1956) pp. 250–351

    Google Scholar 

  • Nigmatulin R.I. and Khabeev N.S., Heat exchange between a gas bubble and a liquid. Fluid Dyn. 9 (1974) 759–764

    Article  ADS  Google Scholar 

  • Omta R., Oscillations of a cloud of bubbles of small and not so small amplitude. J. Acoust. Soc. Am. 82(1987) 1018–1033

    Article  ADS  Google Scholar 

  • Sangani A.S. and Didwania A.K., Dynamic simulations of flows of bubbly liquids at large Reynolds numbers. J. Fluid Mech. 250 (1993) 307–337

    Article  ADS  MATH  Google Scholar 

  • Sangani A.S., Zhang D.Z. and Prosperetti A., The added mass, basset, and viscous drag coefficients in nondilute bubbly liquids undergoing small-amplitude oscillatory motion. Phys. Fluids A 3 (1991) 2955–2970

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Smereka P., On the motion of bubbles in aperiodic box. J. Fluid Mech. 254 (1993) 79–112

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Spelt P.D.M. and Biesheuvel A., On the motion of gas bubbles in homogeneous isotropic turbulence. J. Fluid Mech. 336 (1997) 221–244

    Article  ADS  MATH  Google Scholar 

  • van Manen J.D., Bent trailing edges of propeller blades of high powered single screw ships. Int. Shipbuilding Prog. 10 (1963) 3–7

    Google Scholar 

  • Watanabe M. and Prosperetti A., Shock waves in dilute bubbly liquids. J. Fluid Mech. 274 (1994) 349–381

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Zandbergen P.J. and Dijkstra D., Von Kármán swirling flows. Ann. Rev. Fluid Mech. 19 (1987) 465–491

    Article  MathSciNet  ADS  Google Scholar 

  • Zhang D.Z. and Prosperetti A., Averaged equations for inviscid disperse two-phase flow. rJ. Fluid Meek. 267 (1994a) 185–219

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Zhang D.Z. and Prosperetti A., Ensemble phase-averaged equations for bubbly flows. Phys. Fluids 6 (1994b) 2956–2970

    Article  MathSciNet  ADS  MATH  Google Scholar 

Appendix

  1. Broer L.J.F. and van Wijngaarden L., On the motion of a charged particle in an almost homogeneous magnetic field. Appl. Sci. Res. B8 (1960) 159–176

    Article  Google Scholar 

  2. Broer L.J.F., Peletier L.A. and van Wijngaarden L., 1960 A mechanical Hall effect. Appl. Sci. Res. B8 (1960) 259–260

    Article  Google Scholar 

  3. Peletier L.A. and van Wijngaarden L., Couette flow of a fully ionized gas, considered as a two-component fluid. Appl. Sci. Res. B9 (1962) 141–150

    Google Scholar 

  4. van Wijngaarden L., Applications of the one-fluid and two-fluid model in magnetohydrodynamics. Ph.D. Thesis, Technische Hogeschool Delft (1962)

    Google Scholar 

  5. Broer LJ.F. and van Wijngaarden L., Magnetohydrodynamic flow along wavy walls. Appl. Sci. Res. B9(1962)451–469

    Google Scholar 

  6. Broer L.J.F. and van Wijngaarden L., The impulsive motion of a wavy plate in a conducting fluid. Appl. Sci. Res. B10 (1963) 91–109

    Google Scholar 

  7. van Wijngaarden L., On the Kramers–Kronig relations, with special reference to gravity waves. Proc. Kon. Ned. Akad. Wetensch B66 (1963) 339–347

    Google Scholar 

  8. van Wijngaarden L., Asymptotic solution of the laminar boundary layer equations for a non-Newtonian fluid. J. Ship Res. 9 (1965) 37–39

    Google Scholar 

  9. Verhagen J.H.G. and van Wijngaarden L., Non-linear oscillations of fluid in a container. J. Fluid Mech. 22 (1965) 737–751

    Article  ADS  MATH  Google Scholar 

  10. van Wijngaarden L., Hydrodynamica en scheepsontwerp (Hydrodynamics and ship design). De Ingenieur 78(10) (1966) W71–W76

    Google Scholar 

  11. van Wijngaarden L., Over de beoefening van de stromingsleer (On the practice of fluid mechanics). Inaugural Lecture, Technische Hogeschool Twente (1966)

    Google Scholar 

  12. van Wijngaarden L., Asymptotic solution of a diffusion problem with mixed boundary conditions. Proc. Kon. Ned. Akad. Wetensch. B69 (1966) 263–276

    Google Scholar 

  13. van Wijngaarden L., On the collective collapse of a large number of gas bubbles in water. In: Görtler, H. (ed.), Proc. 11th Int. Congress of Applied Mechanics, 1964. Springer-Verlag, Berlin (1966) pp. 854–861

    Google Scholar 

  14. van Wijngaarden L., Linear and nonlinear dispersion of pressure pulses in liquid-bubble mixtures. In: Cooper R.D. and Doroff S.W. (eds), Proc. 6th Symposium Naval Hydrodynamics ONR ACR-136 (1966) pp. 115–135

    Google Scholar 

  15. van Wijngaarden L., On the growth of small cavitation bubbles by convective diffusion. Int. J. Heat Mass Transfer 10 (1967) 127–134

    Article  Google Scholar 

  16. van Wijngaarden L., On the equations of motion of liquid and gas bubbles. J. Fluid Mech. 33 (1968) 465–474

    Article  ADS  MATH  Google Scholar 

  17. van Wijngaarden L., On the oscillations near and at resonance in open pipes. J. Engrg. Maths. 2 (1968) 225–240

    Article  MATH  Google Scholar 

  18. Velthuizen H.G.M. and van Wijngaarden L., Gravity waves over a non-uniform flow. J. Fluid Mech. 39(1969)817–829

    Article  ADS  MATH  Google Scholar 

  19. van Wijngaarden L., On the structure of shock waves in liquid-bubble mixtures. Appl. Sci. Res. 22(1970)366–381

    MATH  Google Scholar 

  20. Velthuizen H.G.M. and van Wijngaarden L., The stability of gravity waves on the surface of a flow with non-uniform velocity distribution. In: Leipholz H. (ed.), Proc. IUTAM Symposium on Instability of Continuous Systems. Springer-Verlag, Berlin (1971) pp. 48–54

    Chapter  Google Scholar 

  21. van Wijngaarden L., On the structure of shock waves in a bubble-liquid mixture. Fluid Dyn. Trans. 5 (1971) 289–298

    Google Scholar 

  22. van Wijngaarden L., De Zucht naar een schoner leven (The desire for a more beautiful life). Diesrede, Technische Hogeschool Twente (1972)

    Google Scholar 

  23. van Wijngaarden L., Propagation of shock waves in bubble-liquid mixtures. In: Hetsroni, G. (ed.), Progress in Heat and Mass Transfer, Vol. 6. Pergamon Press, Oxford (1972) pp. 637–649

    Google Scholar 

  24. van Wijngaarden L., One-dimensional flow of liquids containing small gas bubbles. Ann. Rev. Fluid Mech. 4 (1972) 369–396

    Article  ADS  Google Scholar 

  25. Noordzij L. and van Wijngaarden L., Relaxation effects, caused by relative motion, on shock waves in gas-bubble/liquid mixtures. J. Fluid Mech. 66 (1974) 115–143

    Article  ADS  MATH  Google Scholar 

  26. van Wijngaarden L. and Wormgoor J.W., Investigations on resonant acoustic waves in open pipes. In: Bjørnø, L. (ed.), Finite-Amplitude Wave Effects in Fluids. IPC Science and Technology, Copenhagen (1975) pp. 75–80

    Google Scholar 

  27. Boshuisen D.C. and van Wijngaarden L., An investigation on the temperature distribution in thinwalled cylinders during welding up of wear-proof layers. Appl. Sci. Res. 31 (1975) 1–20

    Article  Google Scholar 

  28. Prosperetti A. and van Wijngaarden L., On the characteristics of the equations of motion for a bubbly flow and the related problem of critical flow. J. Engrg. Maths. 10 (1976) 153–162

    Article  MATH  Google Scholar 

  29. van Wijngaarden L., Hydrodynamic interaction between gas bubbles in liquid. J. Fluid Mech. 77 (1976) 27–44

    Article  ADS  MATH  Google Scholar 

  30. van Wijngaarden L., Some problems in the formulation of the equations for gas/liquid flows. In: Koiter W.T. (ed.), Theoretical and Applied Mechanics. North-Holland, Amsterdam (1976) pp. 249–260

    Google Scholar 

  31. van Wijngaarden L., Pressure waves in bubbly liquids. In: Collins D.J., Plesset M.S. and Saffren (eds), Proc. Int. Colloquium on Drops and Bubbles. Jet Propulsion Laboratory, Pasadena, CA (1976) pp. 405–414

    Google Scholar 

  32. van Wijngaarden L., Nonlinear acoustics. In: Hermans A.J. and Oosterveld M.W.C. (eds), Proc. Symposium on Applied Mathematics Dedicated to the Late Prof.Dr. R. Timman Delft University Press, Delft (1978) pp. 51–68

    Google Scholar 

  33. van Wijngaarden L. and Vossers G., Mechanics and physics of gas bubbles in liquids: A report on Euromech 88. J. Fluid Mech. 87 (1978) 695–704

    Article  ADS  MATH  Google Scholar 

  34. Disselhorst J.H.M. and van Wijngaarden L., Resonant gas oscillations in open pipes. Arch. Mech. 31 (1979) 115–124

    Google Scholar 

  35. Disselhorst J.H.M. and van Wijngaarden L., Oscillatory flow around the edge of a flat plate. J. Engrg. Maths. 1 (1979) 271–287

    Article  Google Scholar 

  36. Disselhorst J.H.M. and van Wijngaarden L., Flow in the exit of open pipes during acoustic resonance. J. Fluid Mech. 99 (1980) 293–319

    Article  MathSciNet  ADS  Google Scholar 

  37. van Wijngaarden L., Sound and shock waves in bubbly liquids. In: Lauterborn W. (ed.), Cavitation and Inhomogeneities in Underwater Acoustics. Springer-Verlag, Berlin (1980) pp. 127–140

    Chapter  Google Scholar 

  38. van Wijngaarden L., On the mathematical modelling of two-phase flows. In: Reali M. (ed.), Proc. 4th Int. Meeting on Water Column Separation (1980)

    Google Scholar 

  39. Sluijter F.W. and van Wijngaarden L., A brief summary of L.J.F. Broer’s work up till his retirement. Appl. Sci Res. 37 (1981) 5–19

    Article  MATH  Google Scholar 

  40. van Wijngaarden L., Bubble interactions in liquid/gas flows. Appl. Sci. Res. 38 (1982) 331–340

    Article  MATH  Google Scholar 

  41. Biesheuvel A. and van Wijngaarden L., The motion of pairs of gas bubbles in a perfect liquid. J. Engrg. Maths. 4 (1982) 349–365

    Article  Google Scholar 

  42. van Wijngaarden L., On the motion of gas bubbles in a perfect liquid. Arch. Mech. 34 (1982) 343–349

    MATH  Google Scholar 

  43. van Wijngaarden L., Waves in gas-liquid flows. In: Meyer, R.E. (ed.), Theory of Dispersed Multiphase Flow. Academic Press, Duluth, MN (1983) pp. 251–269

    Google Scholar 

  44. van Wijngaarden L., Gas/liquid flow research in the Netherlands. Int. J. Multiphase Flow 10 (1984) 107–111

    Article  Google Scholar 

  45. Biesheuvel A. and van Wijngaarden L., Two-phase flow equations for a dilute dispersion of gas bubbles in liquid. J. Fluid Mech. 148 (1984) 301–318

    Article  ADS  MATH  Google Scholar 

  46. van Wijngaarden L., On multiple solutions and other phenomena in rotating fluids. Fluid Dyn. Trans. 12 (1985) 157–179

    Google Scholar 

  47. van Wijngaarden L. and Omta R., Hydrodynamics of cavitation noise. In: Proc. Ernst Becker Gedächtnis Kolloquium TH Darmstadt Schriftenreihe Wissenschaft und Technik 28 (1986) pp. 219–226

    Google Scholar 

  48. van Wijngaarden L. and Biesheuvel A., Voidage waves in bubbly flows. In: Afgan N. (ed.), Transient Phenomena in Multiphase Flow. Hemisphere, Washington, DC (1988) pp. 275–289

    Google Scholar 

  49. van Wijngaarden L., Flow of bubbly liquids. In: Germain P., Piau M. and Caillerie D. (eds), Theoretical and Applied Mechanics. North-Holland, Amsterdam (1989) pp. 387–406

    Google Scholar 

  50. van Wijngaarden L. and Kapteyn C., Concentration waves in dilute bubble/liquid mixtures. J. Fluid Mech. 212 (1990) 111–137

    Article  ADS  MATH  Google Scholar 

  51. van Wijngaarden L., Een instabiliteit in gas/vloeistof stromingen (An instability in gas-liquid flow). Versl. Afd. Nath, Kon. Ned. Akad. Wetensch. 99 (1990) 58–60

    Google Scholar 

  52. van Wijngaarden L., Bubble deformation in bubbly liquids and its effect on the stability of voidage waves. In: Miloh T. (ed.), Mathematical Approaches in Hydrodynamics. SIAM, Philadelphia, PA (1991) pp. 38–49

    Google Scholar 

  53. van Wijngaarden L., Geurst’s stability criterion for concentration waves in bubbly flows. Int. J. Multiphase Flow 17 (1991) 809–814

    Article  Google Scholar 

  54. van Wijngaarden L. and Buist J., The emission of sound by statistically homogeneous bubble layers. J. Engrg. Maths. 26 (1992) 195–210

    Article  MATH  Google Scholar 

  55. van Wijngaarden L., The mean rise velocity of pairwise-interacting bubbles in liquid. J. Fluid Mech. 251 (1993) 55–78

    Article  ADS  MATH  Google Scholar 

  56. van Wijngaarden L., Dispersed flow. In: Hewitt G.F. and Lahey Jr R.T. (eds), Multiphase Science and Technology, Vol. 8. Begell House (1994) pp. 195–206

    Google Scholar 

  57. van Wijngaarden L., Bubble dynamics and the sound emitted by cavitation. In: Blake J.R., Boulton-Stone J.M. and Thomas N.H. (eds), Bubble Dynamics and Interface Phenomena. Kluwer Academic Publishers, Dordrecht (1994) pp. 181–193

    Chapter  Google Scholar 

  58. de Lange D.F., de Bruin G.J. and van Wijngaarden L., Observations of cloud cavitation on a stationary 2D profile. In: Blake J.R., Boulton-Stone J.M. and Thomas N.H. (eds), Bubble Dynamics and Interface Phenomena. Kluwer Academic Publishers, Dordrecht (1994) pp. 241–246

    Chapter  Google Scholar 

  59. de Lange D.F., de Bruin G.J. and van Wijngaarden L., On the mechanism of cloud cavitation. Experiment and modelling. In: Kato H. (ed.), Proc. 2nd Int. Symp. on Cavitation, Tokyo, April 1994 (1994) pp. 45–49

    Google Scholar 

  60. van Wijngaarden L., Evolving solitons in bubbly flows. Acta Appl. Math. 39 (1995) 507–516

    Article  MathSciNet  MATH  Google Scholar 

  61. van Wijngaarden L., Turbulent two-phase flow. In: Gavrilakis S., Machiels L. and Monkewitz P.A. (eds), Advances in Turbulence VI. Kluwer Academic Publishers, Dordrecht (1996) pp. 535–541

    Chapter  Google Scholar 

  62. de Lange D.F., de Bruin G.J. and van Wijngaarden L., Numerical modelling of unsteady 2D sheet cavitation. La Houille Blanche 4/5 (1997) 89–95

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD, 21218, USA

    A. Prosperetti

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  1. J.M. Burgers Centre for Fluid Mechanics, University of Twente, Enschede, The Netherlands

    Arie Biesheuvel

  2. J.M. Burgers Centre for Fluid Mechanics, Eindhoven University of Technology, The Netherlands

    Gertjan F. van Heijst

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Prosperetti, A. (1998). A Brief Summary of L. van Wijngaarden’s Work Up Till His Retirement. In: Biesheuvel, A., van Heijst, G.F. (eds) In Fascination of Fluid Dynamics. Fluid Mechanics and its Applications, vol 45. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4986-0_2

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