Disappearing bodies and ghost vortices

Abstract

In many dispersed multiphase flows bubbles, droplets, and particles move and disappear due to a phase change. Practical examples include vapour bubbles condensing in subcooled liquids, fuel droplets evaporating in a hot gas and ice crystals melting in water. After these ‘bodies’ have disappeared, they leave behind a remnant ‘ghost’ vortex as an expression of momentum conservation. A general framework is developed to analyse why and how a ghost vortex is generated. A study of these processes is incomplete without a detailed discussion of the concept of momentum for unbounded flows. We show how momentum can be defined unambiguously for unbounded flows and show its connection with other expressions, particularly that of Lighthill. We apply our analysis to interpret new observations of condensing vapour bubbles and discuss droplet evaporation. We show that the use of integral invariants, widely applied in turbulence, introduces a new perspective to dispersed multiphase flows.