The Mechanical Surface Tension and Stability of Minimal Surface Structures

Abstract

Abstract The principal components of the surface stress tensor, σ in surfactant systems with internal interfaces in the form of infinite periodic minimal surfaces have been determined from general relations derived by Gurkov and Kralchevsky ( Colloids Surf. 47, 45, 1990), and by employing a Helfrich kind of second-order expression for the thermodynamic surface tension, γ, as a function of the mean curvature, H , and the Gaussian curvature, K . For this hypothetical case it is found that the surface stress tensor, σ, is isotropic with a constant, positive value everywhere on the surface. However, in order to avoid mechanical instability, an extra term, e.g., proportional to K 2 has to be entailed in the expression for γ causing the surface stress tensor, σ, to vary somewhat with the position on the surface. Moreover, because of the necessary inclusion of, e.g., a K 2 term, in reality the equilibrium interfacial structure of a bicontinuous microemulsion or an L 3 (sponge) phase will correspond to a slightly distorted infinite periodic minimal surface.