Structure and Dynamics of Foams
The Foams group in Aberystwyth is interested in modelling the structure and dynamics of foams and related materials. This involves solving partial differential equations, developing numerical simulations and devising related experiments. This work has industrial support and is regularly presented at conferences and workshops, and students can expect to travel widely and interact with a number of research groups around the world.
Minimal surfaces: Each soap film in a static foam is a surface of constant mean curvature. Plateau's equilibrium rules determine the local geometry of a foam but not the topology. To examine different foam structures, we take the foam energy to be its total surface area, and then seek local minima of this energy using the Surface Evolver software. In particular, we seek candidates to the global minimum, representing the optimal packings of bubbles. A recent extension to this work is in finding the global minimum of a confined foam, with possible applications to morphological development in biology.
Rheology: The flow of foams is studied both numerically, by assuming that the foam passes through a sequence of equilibrium states, and experimentally, using the facilities of the rheology laboratory. Our simulations are used to design networks for "discrete microfluidics" - the use of ordered foams and emulsions for automated testing of gas and liquid samples. We are currently extending the celebrated Stokes problem to the motion of spheres through a foam, and developing models of the dissipation that occurs in soap films as they move.
Drainage: A standing foam loses liquid from between the bubbles due to gravity, a problem that we study by deriving partial differential equations for the liquid content of the foam as a function of space and time. Recent work has extended this theory to the case when the acceleration due to gravity is reduced or negligible, such as in microgravity experiments on the International Space Station, and has included the effects of solidification, such as in the fabrication of metallic foams.