A model system for theory and experiment that is relevant to foam fractionation consists of a column of foam moving through an inverted U-tube between two pools of surfactant solution. The foam drainage equation and its variants are used for a theoretical analysis of this process. In the limit in which the lengths of the two legs is large (L -> infinity),exact analytic formulae may be derived for the key properties of the system. Numerical computations and experiments support these results.