Models of wet two dimensional foams

In this thesis I used models and computer simulations to investigate the properties of two dimensional polydisperse foams from the dry limit of zero liquid fraction to the wet limit of 0.16 liquid fraction. Initially I used the Plat software, which implements the standard model of two dimensional foams, to explore the full range of liquid fractions. As the software becomes increasingly less reliable towards the wet limit, we use over 500,000 simulations in order to obtain results in this regime. We found the variation of energy and coordination number with liquid fraction, and the internal distribution of contacts in the foams. We then focus on the variation of the coordination number with liquid fraction close to the wet limit. In particular, we compare the results of the Plat simulation with those of the Soft Disk model, which is widely used in the study of foams. The Soft Disk model is widely used due to its simplicity, but it is approximate, and neglects deformations. A stark difference between the two models is noted, with the Plat simulation exhibiting a linear variation of the coordination number with liquid fraction, and the Soft Disk model exhibiting a square root variation. We investigate the link between the radial density function (and its analog, the distribution of separations), and the variation of the coordination number with liquid fraction in the wet limit. We find a marked difference between the distributions of separations of the two models. This explains the difference in the variation of the coordination number. It appears to be due to the fact that the bubbles in the Plat simulation are deformable, while those in the Soft Disk model are not. In order to explore the wet limit of two dimensional foams further, we develop a new model based on the theory of Morse and Witten. This model is defined for the wet limit, with deformable bubbles. It accurately predicts the response of a bubble of droplet to small deformations. We develop a framework and an algorithm for applying this theory to the case of modeling two dimensional foams. The new simulation based on this model is tested against the Plat simulation. It produces comparable foams, with similar variations of the energy with liquid fraction. It also produces comparable contact changes with changes in liquid fraction. We propose an extension of this model to the case of three dimensional foams. Finally, we demonstrate an additional application of the theory of Morse and Witten in three dimensions to the calculation of the surface tension of bubbles and drops. We derive a simple formula, taking two length measurements, without any free parameters, which predicts the surface tension of bubbles and drops to a reasonable degree of accuracy (within 2%)