ABSTRACT
The interface between two immiscible fluids can be described as a two dimensional continuum; in the Gibbs convention, an interface possesses negligible thickness and therefore cannot support bending moments. The principal curvatures K1 and K2 in the two surface directions characterize the shape of the interface, and the forces within the interface can be expressed as a surface stress tensor which has units of force per unit length. For a pure fluid, the in-plane stresses can be described in terms of a single isotropic tension γ , the thermodynamic surface tension, which can be related to attractive intermolecular interactions in the bulk phase and the loss of coordination associated with molecules at the interface. The conditions of mechanical equilibrium can be used to derive the classical Young-Laplace relationship, shown in Eq. (1). Equation (1) describes the shape of a fluid interface by relating Bubble and Drop Interfaces © Koninklijke Brill NV, Leiden, 2011
the isotropic interfacial tension, the curvature of the interface, and the pressure jump [p] across it:
γ (K1 +K2)= [p]. (1) When amphiphilic molecules adsorb at a fluid interface, the surface excess con-
centration increases and the thermodynamic surface tension γ () decreases from the pure fluid surface tension γ ( = 0) according to the Gibbs adsorption equation [1]. However, in the absence of deformation, the surface tension remains isotropic. As an interface is stretched, interfacial stresses can develop in response to the applied strain. When surface molecules do not interact, i.e., an ideal surface gas, the interfacial stress remains isotropic. The existence of interactions between adsorbed molecules necessitates additional considerations, see for example, Refs [2, 3]. One common way to assess the interactions between surface molecules is the use of interfacial dilational rheology [4]. In these experiments, the surface of a pendant drop or bubble is expanded or contracted, and the interfacial stress response as a function of deformation is measured. When surface molecules interact to form an elastic interfacial network, the inflation of a pendant drop can result in anisotropic surface stresses. Here we discuss a mechanical framework for describing the inflation of a pendant drop or bubble and the associated interfacial strains and tensions for fluid interfaces that can support anisotropic stresses. We specifically treat purely elastic interfaces, although extension to viscoelasticity is straightforward. Purely dissipative interfaces can be described by Eq. (1).
