  We analyze the flow of a liquid foam between two plates separated by a gap of
the order of the bubble size (2D foam). We concentrate on the salient features
of the flow that are induced by the presence, in an otherwise monodisperse
foam, of a single large bubble whose size is one order of magnitude larger than
the average size. We describe a model suited for numerical simulations of flows
of 2D foams made up of a large number of bubbles. The numerical results are
successfully compared to analytical predictions based on scaling arguments and
on continuum medium approximations. When the foam is pushed inside the cell at
a controlled rate, two basically different regimes occur: a plug flow is
observed at low flux whereas, above a threshold, the large bubble migrates
faster than the mean flow. The detailed characterization of the relative
velocity of the large bubble is the essential aim of the present paper. The
relative velocity values, predicted both from numerical and from analytical
calculations that are discussed here in great detail, are found to be in fair
agreement with experimental results.
