Capillary surface

Abstract: We study the stability of steady nonlinear waves on the surface of an infinitely deep fluid [1, 2]. In section 1, the equations of hydrodynamics for an ideal fluid with a free surface are transformed to canonical variables: the shape of the surface η(r, t) and the hydrodynamic potential ψ(r, t) at the surface are expressed in terms of these variables. By introducing canonical variables, we can consider the problem of the stability of surface waves as part of the more general problem of nonlinear waves in media with dispersion [3,4]. The resuits of the rest of the paper are also easily applicable to the general case.

Abstract: Fluid motion along a smooth, solid surface is examined when the free surface forms a final visible angle with the solid boundary. The dependence of this angle on the velocity with allowance for capillary forces is determined. The Reynolds number is small. The problem of the motion of the phase interface in a capillary and the spreading of viscous fluid drops on solid surfaces are solved. Experimental results are explained. Up to now, not only were analytical results lacking in this field, but also there was not even a precise formulation of the problem (see the review in [1]).

Abstract: A distinction is made between the surface Helmholtz free energy F, and the surface tension γ. The surface energy is the work necessary to form unit area of surface by a process of division: the surface tension is the tangential stress (force per unit length) in the surface layer; this stress must be balanced either by external forces or by volume stresses in the body. The surface tension of a crystal face is related to the surface free energy by the relation γ=F+A(dF/dA), where A is the area of the surface. For a one-component liquid, surface free energy and tension are equal. For crystals the surface tension is not equal to the surface energy. The standard thermodynamic formulae of surface physics are reviewed, and it is found that the surface free energy appears in the expression for the equilibrium contact angle, and in the Kelvin expression for the excess vapour pressure of small drops, but that the surface tension appears in the expression for the difference in pressure between the two sides of a curved surface. The surface tensions of inert-gas and alkali-halide crystals are calculated from expressions for their surface energies and are found to be negative. The surface tensions of homopolar crystals are zero if it is possible to neglect the interaction between atoms that are not nearest neighbours.