Review on Processing and Fluid Transport in Porous Metals with a Focus on Bottleneck Structures

  • A. J. OtaruEmail author


The dynamics of fluid in porous metals has earned growing attention due to the increasing worldwide research and technological advancement in harnessing, processing and the use of materials. In this study, a review on the wide range of different structures that metal foams can show, the range of processing methods that can be used to make them, leading to these different structures and their fluid flow behaviour are presented herein. The fluid section of this investigation covers fluid flow models, boundary conditions, permeability and Form drag estimations, Reynolds number and friction factor determinations, state-of-the-art knowledge of experimental and predictive results. It is the hope that the extended review on processing and fluid flow across monomodal “bottleneck” metallic structures covered herein would lend itself useful to the processing of enhanced bimodal “bottleneck” structures for fluid flow application.


Metal foams Processing Fluid flow 



OAJ would like to thank the University of Nottingham Dean of Engineering Research Scholarship for International Excellence for providing me with the needed funds and facilities required for the successful completion of this work. Many thanks to Professor Andrew R. Kennedy (Lancaster University, UK) and Professor Herve P. Morvan (University of Nottingham, UK) for their overwhelming contributions.

Compliance with Ethical Standards

Conflict of interest

The author of this work declares that He has no conflict of interest.


  1. 1.
    P.A. Jorges, J.C. Malcom, Recent-trends in porous sound-absorbing materials. Sound Vib. 44, 12–17 (2010)Google Scholar
  2. 2.
    B. Koo, Y. Yi, M. Lee, B. Kim, Effect of particle size and forming pressure on pore properties of Fe–Cr–Al porous metal by pressureless sintering. Met. Mater. 23(2), 336–340 (2017)CrossRefGoogle Scholar
  3. 3.
    J.H. Jung, V.D. Krstic, H.K. Cho, Numerical analysis of effective thermal conductivity associated with microstructural changes of porous SiC as an inert-matrix. Met. Mater. 7(1), 21–26 (2001)CrossRefGoogle Scholar
  4. 4.
    A.R. Kennedy, Porous Metals and Metal Foams Made from Powders, Powder Metal. (2012). Google Scholar
  5. 5.
    J. Zhou, Porous metallic materials, in Advanced Structural Materials, ed. by W.O. Soboyejo (CRC Press, Taylor & Francis Group, Boca Raton, 2006), p. 22Google Scholar
  6. 6.
    M.F. Ashby, L.U. Tianjin, Metal foams: a survey. Sci. China Ser. (b) 46(6), 521–530 (2003)CrossRefGoogle Scholar
  7. 7.
    E.L. Furman, A.B. Finkelstein, M.L. Cherny, The permeability of aluminium foams produced by replicated-casting. Metals 3, 49–57 (2013)CrossRefGoogle Scholar
  8. 8.
    C.Y. Zhao, Review on thermal transport in high porosity cellular metal foams with open cells. Int. J. Heat Mass Transf. 55, 3618–3632 (2012)CrossRefGoogle Scholar
  9. 9.
    A.J. Otaru, H.P. Morvan, A.R. Kennedy, Modelling and optimisation of sound absorption in replicated microcellular metals. Scripta Mater. 150, 152–155 (2018)CrossRefGoogle Scholar
  10. 10.
    N. Dukhan, Analysis of Brinkman-extended Darcy flow in porous media and experimental verification using metal foam. ASME J. Fluids Eng. 134(7), 071201 (2012)CrossRefGoogle Scholar
  11. 11.
    A.R. Siddiq, A.R. Kennedy, A novel method for the manufacture of porous structures with multi-component, coated pores. Mater. Lett. 196, 324–327 (2017)CrossRefGoogle Scholar
  12. 12.
    M.F. Ashby, A. Evans, A.R. Kennedy, The role of oxidation during compaction on the expansion and stability of Al foams made via a PM route. Adv. Eng. Mater. 8, 568–570 (2006)CrossRefGoogle Scholar
  13. 13.
    P. Habisreuther, N. Djordjevic, N. Zarzalis, Statistical distribution of residence time and tortuosity of flow through open-cell foams. Chem. Eng. Sci. (2009). Google Scholar
  14. 14.
    N. Dukhan, O. Bagci, M. Ozdemir, Experimental flow in various porous media and reconciliation of Forchheimer and Ergun relation. Exp. Thermal Fluid Sci. 57, 425–433 (2014)CrossRefGoogle Scholar
  15. 15.
    P. Ranut, E. Nobile, L. Mancini, High resolution microtomography-based CFD simulation of flow and heat transfer in aluminum metal foams. Appl. Thermal Eng. (2013). Google Scholar
  16. 16.
    F. Garcia-Moreno, Commercial applications of metal foams: their properties and production. Materials 9, 85 (2016)CrossRefGoogle Scholar
  17. 17.
    J. Banhart, Manufacture, characterization, and application of cellular metals and metal foams. Prog. Mater Sci. 46, 559–632 (2001)CrossRefGoogle Scholar
  18. 18.
    B.H. Smith, S. Szyniszewski, J.F. Hajjar, Steel foam for structures: a review of applications, manufacturing and material properties. J. Constr. Steel 71, 1–10 (2012)CrossRefGoogle Scholar
  19. 19.
    L.D. Kenny, Mechanical properties of particles stabilized aluminium foam. Mater. Sci. Forum 217–222, 1883–1890 (1996)CrossRefGoogle Scholar
  20. 20.
    O. Prakash, H. Sang, J.D. Embury, Structure and properties of AlSiC foam. Mater. Sci. Eng. A 199(2), 195–203 (1995)CrossRefGoogle Scholar
  21. 21.
    P. Asholt, in Metal Foams and Porous Metal Structures, ed. by J. Banhart, M.F. Ashby, N.A. Fleck (MIT-Verlag, Bremen, 1999), p. 133Google Scholar
  22. 22.
    L. Ma, Z. Song, Cellular structure of aluminium foams during foaming process of aluminium melt. Scripta Mater. 39(11), 1523 (1998)CrossRefGoogle Scholar
  23. 23.
    V. Shapovalov, in Porous and Cellular Materials for Structural Applications, vol. 521, ed. by D.S. Schwartz et al. (MRS, Warrendale, 1998), p. 281Google Scholar
  24. 24.
    F. Baumgartner, I. Duarte, J. Banhart, Industrialization of powder compact foaming process. Adv. Eng. Mater. 2, 168–174 (2000)CrossRefGoogle Scholar
  25. 25.
    V. Gergely, B. Clyne, The FORMGRIP process: foaming of reinforced metals by gas release in precursors. Adv. Eng. Mater. 2, 175–178 (2000)CrossRefGoogle Scholar
  26. 26.
    M. Fink, O. Anderson, T. Seidel, A. Schlott, Strongly orthotropic open cell porous metal structures for heat transfer applications. Metals 8, 554 (2018)CrossRefGoogle Scholar
  27. 27.
    J. Banhart, Metal foams: production and stability. Adv. Eng. Mater. 8, 781–794 (2006)CrossRefGoogle Scholar
  28. 28.
    Y.Y. Zhao, D.A. Sun, A novel sintering dissolution process for manufacturing Al foams. Script Materialia 44, 106–110 (2001)CrossRefGoogle Scholar
  29. 29.
    M. Bram, C. Stiller, H.P. Buchkremer, D. Stover, H. Bauer, High-porosity titanium, stainless steel and superalloy parts. Adv. Eng. Mater. 2, 196 (2000)CrossRefGoogle Scholar
  30. 30.
    A.J. Otaru, A.R. Kennedy, The permeability of virtual macroporous structures generated by sphere-packing models: comparison with analytical models. Scripta Mater. 124, 30–33 (2016)CrossRefGoogle Scholar
  31. 31.
    J.E. Rehder, Manufacturing of Cast Iron with Pre-Reduced Iron Ore Pellets, United State Patent 44011469 (1983)Google Scholar
  32. 32.
    J. Banhart, J. Baumeister, Deformation characteristics of metal foams. Mater. Sci. 33, 1431–1440 (1998)CrossRefGoogle Scholar
  33. 33.
    A.J. Otaru, H.P. Morvan, A.R. Kennedy, Measurement and simulation of pressure drop across replicated microcellular aluminium in the Darcy–Forchheimer regime. Acta Mater. 149, 265–275 (2018)CrossRefGoogle Scholar
  34. 34.
    A.J. Otaru, H.P. Morvan, A.R. Kennedy, Airflow measurement across negatively infiltration processed porous aluminium structures. AIChE J. (2019). Google Scholar
  35. 35.
    T.J. Lu, F. Chen, D. He, Sound absorption of cellular metals with semi-open cells. J. Acoust. Soc. Am. 108(4), 1697–1708 (2000)CrossRefGoogle Scholar
  36. 36.
    Y. Li, L. Zhendong, F. Han, Airflow resistance and sound absorption behaviour of open-celled aluminium foams with spherical cells. Proc. Mater. Sci. 4, 187–190 (2014)CrossRefGoogle Scholar
  37. 37.
    R. Goodall, A. Marmottant, L. Salvo, A. Mortensen, Spherical pore replicated microcellular aluminium: processing and influence on properties. Mater. Sci. Eng. A 465, 124–135 (2007)CrossRefGoogle Scholar
  38. 38.
    B.N. Asmar, P.A. Langston, A.J. Matchett, A generalized mixing index in discrete element method simulation of vibrated particulate beds. Granul. Matter 4(3), 129–138 (2002)CrossRefGoogle Scholar
  39. 39.
    P. Langston, A.R. Kennedy, Discrete element modelling of the packing of spheres and its application to the structure of porous metals made by infiltration of packed beds of NaCl beads. Powder Technol. 268, 210–218 (2014)CrossRefGoogle Scholar
  40. 40.
    A.J. Otaru, Fluid Flow and Acoustic Absorption in Porous metallic Structures Using Numerical Simulation and Experimentation, Ph.D. thesis, The University of Nottingham, United Kingdom (2018)Google Scholar
  41. 41.
    Q.Z. Wang, D.M. Lu, C.X. Cui, L.M. Liang, Material science and engineering. J. Mater. Process. Technol. 211, 363 (2011)CrossRefGoogle Scholar
  42. 42.
    E. Michael, The Dawn of Fluid Dynamics: A Discipline Between Science and Technology (Wiley, Hoboken, 2006), p. ix. ISBN 3-527-40513-5Google Scholar
  43. 43.
    M.A. Rao, Rheology of Fluid and Semisolid Foods: Principles and Applications, 2nd edn. (Springer, Berlin, 2007), p. 8. ISBN 978-0-387-70929-1CrossRefGoogle Scholar
  44. 44.
    H.K. Versteeg, W. Malasekara, An Introduction to Computational Fluid Dynamics—The Finite Volume Method, 2nd edn. (Pearson Education Limited, London, 2007)Google Scholar
  45. 45.
    CMI, Clay Mathematic Institute, Millennium Prize Problem (2014).
  46. 46.
    D.A. Nield, A. Bejan, Convection in Porous Media, 2nd edn. (Springer, New York, 1992), pp. 8–91CrossRefGoogle Scholar
  47. 47.
    S. Peng, Q. Hu, S. Dultz, M. Zhang, Using x-ray computed tomography pore structure characterization for Berea sandstone: resolution effect. J. Hydrol. 472–473, 254–261 (2012)CrossRefGoogle Scholar
  48. 48.
    K.K. Bodla, J.Y. Murthy, S.V. Garimella, Microtomography-based simulation of transport through open-cell metal foams. Numer. Heat Transf. A Appl. 7, 527–544 (2010)CrossRefGoogle Scholar
  49. 49.
    G.A. Narsilio, O. Buzzi, S. Fityus, T.S. Yun, D.W. Smith, Upscaling of Navier–Stokes equation in porous media: theoretical, numerical and experimental approach. Comput. Geotech. 36, 1200–1206 (2009)CrossRefGoogle Scholar
  50. 50.
    T.P. De Carvalho, H.P. Morvan, D. Hargreaves, H. Oun, A. Kennedy, Pore-scale numerical investigation of pressure drop behaviour across open-cell metal foams. Transp. Porous Media 117(2), 311–336 (2017)CrossRefGoogle Scholar
  51. 51.
    S. Whitaker, Flow in porous media I: a theoretical derivation of Darcy’s law. Transp. Porous Media 1, 3–25 (1986)CrossRefGoogle Scholar
  52. 52.
    H. Darcy, Les Fotaines Publiques de la Ville de Dijon (Dalmont, Paris, 1856)Google Scholar
  53. 53.
    Comsol, Introduction to the Acoustic Module, US Patent, 7, 519, 518; 7, 596, 474 and 7, 623, 991 (2015)Google Scholar
  54. 54.
    M. Le Bars, M.G. Worster, Interfacial conditions between a pure and a porous medium: implications for binary alloy solidification. J. Fluid Mech. 550, 151–170 (2006)Google Scholar
  55. 55.
    H Mifflin, The American Heritage ®, (Science Dictionary, 2014)Google Scholar
  56. 56.
    R.P. Hesketh, Flow Between Parallel Plates-Modified from the COMSOL ChE Library Module (Department of Chemical Engineering, Rowan University, Glassboro, 2008), pp. 3–4Google Scholar
  57. 57.
    A. Dybbs, R.V. Edwards, A new look at porous media fluid mechanics—Darcy to turbulent, in Fundamentals of Transport Phenomena in Porous Media. NATO ASI Series (Series E: Applied Sciences), vol. 82, ed. by J. Bear, M.Y. Corapcioglu (Springer, Dordrecht, 1984)Google Scholar
  58. 58.
    A. Bejan, Convection Heat Transfer (Wiley, Hoboken, 1984)Google Scholar
  59. 59.
    M. Piatek, A. Gancarczyk, M. Iwaniszyn, P.J. Jodlowski, J. Lojewska, A. Kolodziej, Gas-phase flow resistance of metal foams: experiments and modelling. AIChE J. 63(6), 1799–1803 (2017)CrossRefGoogle Scholar
  60. 60.
    D. Edouard, M. Lacroix, C. Pham, M. Mbodji, C. Pham-Huu, Experimental measurements and multiphase flow models in solid SiC foam beds. AIChE J. 54(11), 2823–2832 (2008)CrossRefGoogle Scholar
  61. 61.
    J.L. Lage, P.S. Krueger, A. Narasimham, Protocol for measuring permeability and form coefficient of porous media. Phys. Fluids 17, 088101 (2005)CrossRefGoogle Scholar
  62. 62.
    L. Tadrist, M. Miscevis, O. Rahli, F. Topin, About the use of fibrous materials in compact heat exchangers. Exp. Thermal Fluid Sci. 28, 193–199 (2004)CrossRefGoogle Scholar
  63. 63.
    N. Dukhan, Metal Foams: Fundamental and Applications (DESTECH Publication, Inc. Technology and Engineering, Lancaster, 2013), pp. 1–310Google Scholar
  64. 64.
    UAF, Universal Air Filter, (2014).
  65. 65.
    N. Dukhan, C.A. Minjeur, A two-permeability approach for assessing flow properties in cellular metals. J. Porous Mater. 18(2), 417–424 (2010)Google Scholar
  66. 66.
    B. Antohe, J.L. Lage, D.C. Price, R.M. Weber, Experimental determination of the permeability and inertial coefficients of mechanically compressed aluminium metal layers. ASME J. Fluids Eng. 11, 404–412 (1997)CrossRefGoogle Scholar
  67. 67.
    H. Oun, A.R. Kennedy, Experimental investigation of pressure drop characterization across multilayer porous metal structure. J. Porous Mater. 21, 1133–1141 (2014)CrossRefGoogle Scholar
  68. 68.
    O. Reutter, E. Smirnova, J. Sauerhering, S. Angel, T. Fend, R. Pitz-Paal, Characterization of air flow through sintered metal foams. ASME J. Fluids Eng. 130(5), 051201 (2008)CrossRefGoogle Scholar
  69. 69.
    N. Dukhan, R. Picón-Feliciano, A.R. Álvarez-Hernánde, Air flow through compressed and uncompressed aluminum foam: measurements and correlations. ASME J. Fluids Eng. 128(5), 1004–1012 (2006)CrossRefGoogle Scholar
  70. 70.
    J.J. Lu, A. Hess, M.F. Ashby, Sound absorption of metallic foams. J. Appl. Phys. 99, 07511–07519 (1999)Google Scholar
  71. 71.
    J.F. Despois, A. Mortensen, Permeability of open-pore microcellular materials. Acta Mater. 53, 1381–1388 (2005)CrossRefGoogle Scholar
  72. 72.
    A.J. Otaru, Enhancing the sound absorption performance of porous metals using tomography images. Appl. Acoust. 140, 183–189 (2019)CrossRefGoogle Scholar
  73. 73.
    K. Seah, R. Thampuran, S. Teoh, Parametric studies of the mechanical behaviour of porous titanium. Met. Mater. 4(4), 672–675 (1998)CrossRefGoogle Scholar
  74. 74.
    Y.B. Choi, T. Motoyama, K. Matsugi, G. Sasaki, Influence of the specific surface area of a porous nickel to the intermediate compound generated by reaction of a porous nickel and aluminium. Met. Mater. Int. 20(4), 741–745 (2014)CrossRefGoogle Scholar
  75. 75.
    Y. Champoux, M.R. Stinson, On acoustical models for sound propagation in rigid frame porous materials and the influence of shape factors. J. Acoust. Soc. Am. 92(2), 1120–1131 (1992)CrossRefGoogle Scholar
  76. 76.
    K. Boomsma, D. Poulikakos, The effect of comparison and pore size variations on the liquid flow characteristics in metal foams. ASME J. Fluids Eng. 124, 263–273 (2002)CrossRefGoogle Scholar
  77. 77.
    J.P. Du Plessis, S. Wouldberg, Pore-scale derivation of Ergun equation to enhance its adaptability and generalization. Chem. Eng. Sci. 63, 2576–2586 (2008)CrossRefGoogle Scholar
  78. 78.
    J.M. Coulson, The flow of fluids through granular beds: effects of particle shape and voids in streamline flow. Trans. Inst. Chem. Eng. 27, 237–257 (1949)Google Scholar
  79. 79.
    M. Muskat, H.G. Botset, Flow of gas through porous materials. Physics 1, 27–47 (1931)CrossRefGoogle Scholar
  80. 80.
    S. Ergun, Fluid flow through packed column. Chem. Eng. 48, 89–94 (1952)Google Scholar
  81. 81.
    I. Kececioglu, Y. Jiang, Flow through porous media of packed spheres saturated with water. ASME J. Fluids Eng. 116, 164–170 (1994)CrossRefGoogle Scholar
  82. 82.
    D. Edouard, M. Lacroix, C.P. Huu, F. Luck, Pressure drop modelling on solid foam: state-of-the-art correlation. Chem. Eng. J. 144, 299–311 (2008)CrossRefGoogle Scholar
  83. 83.
    J.P. Bonnet, F. Topin, L. Tadrist, Flow laws in metal foams: compressibility and pore size effects. Trans. Porous Media 73, 149–163 (2008)CrossRefGoogle Scholar

Copyright information

© The Korean Institute of Metals and Materials 2019

Authors and Affiliations

  1. 1.Department of Chemical EngineeringFederal University of TechnologyMinnaNigeria

Personalised recommendations