A cluster of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si43.svg" display="inline" id="d1e1161"> <mml:mi>N</mml:mi> </mml:math> -bubbles driven along a channel at high imposed driving pressure: Bubble areas, film lengths and ver

A two-dimensional foam staircase structure is considered with N bubbles stacked in a zigzag fashion along a channel. A model is analysed for determining the configuration of a staircase set into motion under the action of a high imposed driving pressure. Minimum and also maximum permitted bubble sizes for which the staircase structure survives are identified. Both minimum and maximum sizes are found to be decreasing functions of N . Behaviours in the limit of large N are identified, albeit tentatively, as the methodology for computing the staircase structure is found to be highly stiff. Indeed, as N increases, tiny changes in the staircase configuration at the downstream end lead to large geometric changes at the upstream end, limiting the domain of N values for which structures can be readily computed. • N -bubble staircase structure flowing rapidly along Hele-Shaw channel is considered. • Foam films become flat with known orientations. • Flat film state with correct size bubbles must be constructed. • Minimum and maximum allowed bubbles sizes decrease with N . • Small changes in configuration downstream lead to large changes upstream.