Stability of Helium II Flow Down an Inclined Plane

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Abstract
The stability of a layer of helium II flowing down an inclined plane is investigated on the basis of the two fluid theory. The expression of mutual friction as suggested by Gorter and Mellink is used in the analysis. In the limit that essentially only the normal fluid is present, the Yih-Benjamin result is recovered. A similar stability criterion holds for the limit that essentially only the superfluid is present. In general, the flow system is stable only when the fluid layer is fairly thin. Then the system may be stable for certain intermediate compositions even when the fluid is flowing down the under-side of the plane. The results may have some bearing on the problem of film flow in superfluid helium.