The theory of capillary excess viscosities

Abstract

A general phenomenological theory of capillary excess or surface viscosities is developed from considerations of momentum balance in the neighbourhood of a fluid phase boundary. It is assumed that a coordinate system may be erected in the interfacial region for which the constitutive equations are anisotropic in the normal direction but tangentially isotropic. This anisotropy together with certain assumptions regarding the continuity of the velocity vector and its derivatives leads to the identification for incompressible fluids of four surface viscosity coefficients k , n , k N and n N . The first two have been recognized since the time of Boussinesq, and experimental data regarding them are accumulating. The second two appear to be new, and experiments to measure them are only in a preliminary stage. In all cases, the surface viscosity coefficients are formally identified as integrals taken through the interfacial region from one bulk phase to the next. The theory is limited to interfacial regions whose curvatures are small with respect to the reciprocal thickness of the transition zone and of greater than ultra-low surface tension.