Nucleation, bubble growth and coalescence*

In gas-liquid two-phase pipe flows, flow regime transition is associated with changes in the micro-scale geometry of the flow. In particular, the bubbly-slug transition is associated with the coalescence and break-up of bubbles in a turbulent pipe flow. We consider a sequence of models designed to facilitate an understanding of this process. The simplest such model is a classical coalescence model in one spatial dimension. This is formulated as a stochastic process involving nucleation and subsequent growth of ‘seeds’, which coalesce as they grow. In a development of this, we allow for bubble fragmentation, and we study the evolution of the bubble size distribution both analytically and numerically. We also present some ideas concerning ways in which the model can be extended to more realistic two- and three-dimensional geometries.