Back of a long bubble train driven along a channel at high imposed driving pressure

A long bubble train propagating along a channel is modelled. The train is arranged in a so-called staircase configuration with films between bubbles zigzagging along the channel. Specifically, the geometry of the back (i.e. upstream) portion of the staircase is computed by determining bubble film lengths and vertex locations where three films meet. The geometry is shown to be distinct from a so-called infinite staircase. Provided upstream conditions are selected correctly (i.e. provided the geometrical shape of the backmost bubble is specified correctly), the configuration can be made to converge towards an infinite staircase moving downstream. Care must be taken, however, in selecting upstream conditions, as computations prove very stiff. To achieve convergence, well-defined ratios are needed for displacements of successive vertices from their infinite staircase counterparts. A minimum allowed bubble area results for the back end of a staircase to avoid breaking (i.e. to avoid a requirement for topological rearrangements of the bubble train), despite the infinite staircase having no minimum bubble area.