The stability of an air film in a liquid flow

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Abstract
A number of processes in which air is entrained in a flow appear to involve the formation of a thin air film between a relatively fast liquid stream and a region of slow recirculation. Eventually, the film breaks into bubbles. This study addresses a possible mechanism causing this process. The linear stability of a vertical film of a viscous gas bounded by liquid in uniform motion on one side, and by liquid at rest on the other side, is studied. Instabilities are found that, depending on the parameter values of the undisturbed flow, are controlled by two basic mechanisms. One is due to the velocity jump across the film and can be related to the usual Kelvin–Helmholtz instability. The second one is controlled by the viscosity jump across the air liquid interfaces. The relation between the remainder of the discrete spectrum and the spectrum of other parallel shear flows bounded by solid or free surfaces is also discussed.