Mathematical Modelling of Waves in Guinness

  • Simon Kaar
  • William Lee
  • Stephen O’Brien
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 26)


We provide a simple two-dimensional model of bubbly two-phase flow which can be used to investigate why waves form and propagate downward while a pint of Guinness is settling. We start out with the basic equations of the two-phase flow and use the large timescale difference of beer convection and rising bubbles in order to treat the convection flow as quasistatic. Using this argument we further simplify the two-phase mixture equations to that of a single liquid whose density varies with bubble concentration. A stability analysis shows that waves can occur through an instability analogous to the Kelvin-Helmholtz instability which forms in parallel shear flow. We provide a description of the form of these waves, and compare them to observations. Our theory provides a platform for the description of waves in more general bubbly two-phase shear flows.



The authors acknowledge the support of MACSI, the Mathematics Applications Consortium for Science and Industry (, funded by the Science Foundation Ireland Investigator Award 12/IA/1683.


  1. 1.
    Benilov, E.S., Cummins, C.P., Lee, W.T.: Why do bubbles in Guinness sink? Am. J. Phys. 81, 88 (2013)CrossRefGoogle Scholar
  2. 2.
    Boycott, A.E.: Sedimentation of blood corpuscles. Nature 104, 532 (1920)CrossRefGoogle Scholar
  3. 3.
    Brennen, C.E.: Fundamentals of Multiphase Flow. Cambridge University Press, Cambridge (2005)CrossRefzbMATHGoogle Scholar
  4. 4.
    Drazin, P.G., Reid, W.H.: Hydrodynamic Stability. Cambridge University Press, Cambridge (2004)CrossRefzbMATHGoogle Scholar
  5. 5.
    Rankine, W.J.M.: On the thermodynamic theory of waves of finite longitudinal disturbances. Philos. Trans. R. Soc. 160, 277–288 (1870)CrossRefGoogle Scholar
  6. 6.
    Robinson, M., Fowler, A.C., Alexander, A.J., O’Brien, S.B.G.: Waves in Guinness. Phys. Fluids 20, 067101 (2008)CrossRefGoogle Scholar
  7. 7.
    Wallis, G.B.: One-Dimensional Two-Phase Flow. McGraw-Hill, New York (1969)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  1. 1.MACSIUniversity of LimerickLimerickIreland
  2. 2.Department of MathematicsUniversity of PortsmouthPortsmouthUK

Personalised recommendations