Stability analysis of the mechanism of jet attachment to walls

The attachment of fluid jets to walls when blown closed to these walls is known by the name of the Coanda effect and is widely used in practice, e.g., for the ventilation and air-conditioning of rooms. When a jet of air cooler than the ambient air is blown horizontally along the ceiling, the jet adheres to the ceiling over a given distance even though it is heavier than the ambient air. The aim of this paper is to provide a satisfactory explanation for the phenomenon, on the basis of a theoretical analysis of the equilibrium of a layer of fluid that is denser than the ambient fluid, when it is driven by a translation movement in relation to the ambient fluid and is located under a flat wall in a gravity field. The analysis makes it possible to formulate the separation distance of the jet depending on its properties at the blowing slot. That distance is then compared with the available experimental results.