Abstract
This thesis concerns the response of two-dimensional foams to applied shear based on numerical simulations in the quasistatic limit. The effect of liquid fraction and areadisorder on the discrete topological changes (T1s) which occur as a foam flows are probed at several length scales and related to the response of the ordered hexagonal honeycomb.At the macroscopic scale, many T1s combine and the yielding of the foam can be characterized through the harmonics of the stress. Stress harmonics obtained from simulations of dry two-dimensional foams are in good agreement with experimental data for foams and other yield stress materials.
At the mesoscopic scale, several T1s occur in a certain region of the foam causing the flow to localize in a region of width proportional to the square root of area-disorder. For dry two-dimensional foams I present a one-dimensional measure and a tensorial measure of foam structure which can identify the localized region from a single still image. The width of the localized region increases linearly with liquid fraction and for sufficiently high values of liquid fraction and area-disorder, the T1s fill the channel and no localization is observed.
At the microscopic scale, the links between neighbouring bubbles define a pair of orientations that characterize the local bubble configurations at the instant of a T1. Macroscopic flow behaviour originates at the microscopic scale and I show that the yield stress is directly related to the orientation of the T1 events.
Liquid fraction and area-disorder have, in general, the same effect at each length scale. The yield stress decreases with increasing liquid fraction and area-disorder; and the amount of flowing foam and the orientations of a T1 increase with increasing liquid fraction and area-disorder. The response of disordered foams is shown to be different to that of ordered foams in each case.
| Date of Award | 19 Apr 2010 |
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| Original language | English |
| Awarding Institution |
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| Sponsors | Engineering and Physical Sciences Research Council |
| Supervisor | Simon Cox (Supervisor) & David Binding (Supervisor) |