The effects of surface tension and viscosity on the stability of two superposed fluids

Abstract

ABSTRACTThe effect of surface tension on the stability of two superposed fluids can be described in a universal way by a non-dimensional ‘surface tension number’ S which provides a measure of the relative importance of surface tension and viscosity. When both fluids extend to infinity, the problem can be reduced to the finding of the roots of a quartic equation. The character of these roots is first analysed so as to obtain all possible modes of stability or instability. Two illustrative cases are then considered in further detail: an unstable case for which the density of the lower fluid is zero and a stable case for which the density of the upper fluid is zero, the latter case corresponding to gravity waves. Finally, the variational principle derived by Chandrasekhar for problems of this type is critically discussed and it is shown to be of less usefulness than had been thought, especially in those cases where periodic modes exist.