A cluster of N -bubbles driven along a channel at high imposed driving pressure: film orientations and bubble pressures

A cluster of N bubbles (with N odd) arranged in a channel in a zigzag staircase configuration is modelled. A limiting case is considered in which the staircase is set into motion by the application of a high driving pressure. In this limit, foam films between bubbles are predicted to become asymptotically flat. Angles at which these flat films are oriented and also bubble pressures are then determined. For N bubbles, the film orientations and bubble pressures differ from predictions for a staircase in the limit of an infinite number of bubbles. Differences are significant towards the downstream end of a staircase, but decay moving upstream. However, the decay is gradual. Hence, a very large N is needed for a finite staircase to align its film orientations towards its upstream end with the orientations in an infinite staircase.