The Unsteady expansion and contraction of a two-dimensional vapour bubble confined between superheated or subcooled plates

This talk describes the results of a theoretical investigation of the unsteady expansion and contraction of a vapour bubble in a narrow channel. Specifically we construct and analyse a mathematical model for a long, two-dimensional bubble confined between superheated or subcooled parallel plates, whose motion is driven by mass transfer between the liquid and the vapour. The present model is similar to that previously proposed by Wilson, Davis and Bankoff (1999), but differs from it in one crucial respect, namely that, unlike the earlier work, it includes significant mass transfer from and/or to the semi-circular cap regions at the nose of the bubble as well as from and/or to the thin liquid films attached to the plates. The inclusion of this additional contribution to the overall mass transfer significantly alters the dynamics of the bubble. When both plates are superheated the bubble always expands. In this case there are two possible constant-velocity travelling-wave solutions for the expansion of the bubble, namely an unstable fast mode and a stable slow mode. The evolution of the bubble is calculated numerically for a range of values of the parameters. In particular, these calculations show that eventually the bubble expands either with the constant velocity of the slow mode or exponentially. When both plates are subcooled the bubble always collapses to zero length in a finite time.When one plate is subcooled and the other plate is superheated the situation is rather more complicated.