Skip to main content
Article thumbnail
Location of Repository

The mathematics of foam

By C. J. W. Breward


The aim of this thesis is to derive and solve mathematical models for the flow of liquid in a foam. A primary concern is to investigate how so-called `Marangoni stresses' (i.e. surface tension gradients), generated for example by the presence of a surfactant, act to stabilise a foam. We aim to provide the key microscopic components for future foam modelling. We begin by describing in detail the influence of surface tension gradients on a general liquid flow, and various physical mechanisms which can give rise to such gradients. We apply the models thus devised to an experimental configuration designed to investigate Marangoni effects. Next we turn our attention to the flow in the thin liquid films (`lamellae') which make up a foam. Our methodology is to simplify the field equations (e.g. the Navier-Stokes equations for the liquid) and free surface conditions using systematic asymptotic methods. The models so derived explain the `stiffening' effect of surfactants at free surfaces, which extends considerably the lifetime of a foam. Finally, we look at the macroscopic behaviour of foam using an ad-hoc averaging of the thin film models

Topics: Partial differential equations, Fluid mechanics, Numerical analysis
Year: 1999
OAI identifier:

Suggested articles


  1. (1994). A counter-example to Kelvin’s conjecture on minimal surfaces. doi
  2. (1997). A mathematical model for drying paint layers.
  3. (1996). A new model for drainage of static foams. doi
  4. (1990). A numerical and asymptotic study of some third-order ordinary differential equations relevant to draining and coating flows. doi
  5. (1994). A soluble model for foam drainage. doi
  6. (1987). A theory of extensional viscosity for flowing foams and concentrated emulsions. doi
  7. (1995). Adsorption dynamics of surfactants at the airwater interface: a critical review of mathematical models and mechanisms.
  8. (1967). An introduction to fluid dynamics.
  9. (1986). Aqueous foams.
  10. (1995). Capillary pinning of foam in porous media.
  11. (1983). Computer simulation of a two-dimensional soap froth i. Method and motivation. doi
  12. (1984). Computer simulation of a two-dimensional soap froth ii. Analysis of results. doi
  13. (1992). Dimple formation and behavior during axisymmetrical foam film drainage.
  14. (1998). Drainage of a thin free film.
  15. (1992). Dynamics and transport of a localised soluble surfactant on a thin film. doi
  16. (1996). Effect of material properties on the drainage of symmetric, plane parallel, mobile foam films. doi
  17. (1997). Elastic-plastic behaviour of a Kelvin foam. In
  18. (1997). Experimental comparisons with a numerical model of surfactant effects on the burst of a single bubble.
  19. (1997). Experimental observations in the foam rig. Private communication,
  20. (1994). Extensional thin layer flows. DPhil thesis, Mathematics Department,
  21. (1982). Flow through a plateau border of cellular foam.
  22. (1997). Foam destruction using a hot wire gauze. Private communication,
  23. (1999). Foam destruction using a hot wire spiral. Private communication,
  24. (1988). Foam flows.
  25. (1997). Foam patterning in porous media.
  26. (1994). Foam stability and structure in adsorption and distillation. AIChE,
  27. (1997). Foaming in beer and breweries: problems, challenges and solutions.
  28. (1995). Foams in distillation columns. Private communication,
  29. (1994). Foams in porous media as a problem in polymer physics.
  30. (1998). Gravitational drainage of a tangentially-immobile thick film.
  31. (1990). Hydrodynamics of the rupture of thin liquid films.
  32. (1995). Insoluble surfactant spreading on a thin viscous film: shock evolution and film rupture.
  33. (1997). Invasive and non-invasive measurements of dynamic surface tensions.
  34. (1997). Long-scale evolution of this liquid films.
  35. (1997). Measurement of dynamic interfacial properties in an overflowing cylinder by ellipsometry.
  36. (1998). Measurement of the dynamic surface excess in an overflowing cylinder by neutron reflection.
  37. (1985). Mechanics of Polymer Processing.
  38. (1998). Micromechanics of foam flows. PhD thesis,
  39. (1995). Modeling axisymmetric flows.
  40. (1995). Modelling an experiment to study surface dilation effects. Master’s thesis, Mathematics Department,
  41. (1997). Modelling foam drainage.
  42. (1995). Modelling foaming behaviour.
  43. (1996). Modelling the generation and collapse of aqueous foams.
  44. (1996). Models for thin viscous sheets.
  45. (1994). Nonlinear evolution equations for thin liquid films with insoluble surfactants.
  46. (1993). Nonlinear rupture of free films.
  47. (1989). On a mathematical model for fibre tapering.
  48. (1974). On spherical bubbles rising steadily in dilute surfactant solutions. doi
  49. On the division of space with minimum partitional area. doi
  50. (1999). On the evolution of nonaxisymmetric viscous fibres with surface tension, inertia and gravity.
  51. (1962). Phisicochemical Hydrodynamics.
  52. (1982). Physical chemistry of surfaces, 4th Ed.
  53. (1996). Simple shearing flow of a dry Kelvin soap foam. doi
  54. (1997). Slag foams. Private Communication,
  55. (1994). Soap film drainage: Theory and experiment.
  56. Statique expe´rimentale et the´orique des liquides soumis aux seules forces mole´culaires.
  57. (1973). Surface ages in vibrating jet experiments. doi
  58. (1990). Surface dilation and fluid-dynamical behaviour of Newtonian liquids in an overflowing cylinder. i. pure liquids.
  59. (1994). Surface dilation and fluiddynamical behaviour of Newtonian liquids in an overflowing cylinder. ii. surfactant solutions.
  60. (1992). Surface dilational behaviour of surfactant solutions.
  61. (1999). Surface tension changes with temperature. Private Communication,
  62. (1999). The draining of a two-dimensional bubble.
  63. (1990). The dynamics of a localised surfactant on a thin film.
  64. (1998). The dynamics of surfactant adsorption. DPhil thesis, Physical and Theoretical Chemisrty Laboratory,
  65. (1992). The Elements of Physical Chemistry.
  66. (1996). The foam drainage equation. doi
  67. (1958). The influence of surface phenomena on the performance of distillation columns. doi
  68. (1993). The levelling of paint films. doi
  69. (1996). The linear elastic behaviour of a bidisperse Weaire-Phelan soap foam.
  70. (1996). The linear elastic behaviour of dry soap films.
  71. (1973). The Mathematics of Diffusion.
  72. (1996). The microrheology of wet foams.
  73. (1981). The Principles of Chemical Equilibrium, 4th Ed.
  74. (1988). The rear stagnation point of a bubble rising steadily in a dilute surfactant solution. doi
  75. (1995). The spreading of insoluble surfactant at the free surface of a deep fluid layer.
  76. (1946). The three-dimensional shape of bubbles in foam-an analysis of the role of surface forces in three dimensional cell shape determination.
  77. (1996). Thin film rupture.
  78. (1998). Thin films with high surface tension.
  79. (1990). Unsteady state drainage of a standing foam. AIChE
  80. (1998). Velocity data fits. Private Communication,
  81. (1995). Viscous Flow.

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.