Modelling the behaviour of the wetting front in non-standard forced foam drainage scenarios

Forced foam drainage experiments, in which liquid is added at a constant rate at the top of the foam, are studied numerically. The aim of these experiments is to investigate the change in liquid fraction as the resulting drainage wave propagates through the system. A finite element implementation of the foam drainage equation is used to carry out two-dimensional simulations, taking advantage of mesh adaptivity techniques to accurately resolve the dynamics of the wetting front. First, the effects of changes in the liquid addition area at the top of a rectangular container are studied, showing that the variation of the position of the wave front exhibits a power law with time not only for the vertical displacement but also for the horizontal propagation. Then, for uniform addition scenarios, the effect of changes in the geometry of the container are analysed, finding that a power law also describes well the position of the different regions of the drainage wave with time.