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LIQUID-GAS INTERFACES STUDIED ON THE BASIS OF THE CLASSICAL SURFACE TENSION THEORY AND INTERMOLECULAR FORCE MODELS.
STANFORD UNIV CALIF DEPT OF AERONAUTICS AND ASTRONAUTICS
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Liquid-gas interfaces are studied from two viewpoints. The first method uses the classical surface tension model of the interface. The differential equation defining the equilibrium shape of the interface relates the surface tension with the pressure difference across the interface. The boundary conditions for the equation assume that the contact angles the angles the liquid forms with the container waalls are constant and independent of the body forces. An iterative method for finding the equilibrium shape is developed, for the case of small body forces. The method is used in two cases and compared with results of other methods. The stability of the interface is investigated for a two-dimensional layer spread over a segment of a rigid cylinder with rigid radial walls. The eigenfunctions of the vibrations of layers of nonuniform depth are expanded in terms of the eigenfunctions for the layers of uniform depth. Approximations are made by truncating the series. The coefficients are obtained by minimizing the mean square error along the interface. The results are given in the form of a relationship between a dimensionless stability parameter and the angle between the radial walls for the case of limiting stability. A comparison of the approximate results with known solutions shows good agreement.
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