The surface of tension of a drop of liquid

Abstract

We obtain in mean-field approximation two forms of the pressure tensor at the planar liquid surface of the penetrable-sphere model and use them to show, both explicitly and by a symmetry argument, that they lead to an unambiguous identification of the surface of the tension. This result is peculiar to this model and does not hold for liquids in general. We use it to verify the correctness of (a) Tolman's equation for the change of surface tension with curvature and (b) a statistical expression for the tension of a spherical surface. We examine a different statistical expression, recently proposed by Percus, and show that it agrees with ours in the planar limit, but it has not been shown to describe correctly the change of tension with curvature.