Mechanical model for a spherical interface with low tension

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Abstract
The conventional treatment of a spherical interface models the mechanical properties of the system by regarding it as two bulk phases of uniform pressure separated by an infinitely thin membrane of uniform tension σ. This membrane is located at the surface of tension which is positioned so that the resultant forces and their first moments about the centre of the sphere in the model system match those in the real system. In this paper the basic results of this treatment including the relationship between mechanical and thermodynamic viewpoints are rederived in a simple yet illuminating way and without recourse to the assumption that bulk properties must be established within the interior of the sphere. When the difference between parallel and perpendicular components of the stress tensor changes sign within the interfacial region and this leads to a very small value of σ, the surface of tension may be located well away from the interfacial region and in particular cases is not even definable. To deal with this situation a more appropriate description in terms of two surfaces of tension with tensions of opposite sign is developed. This alternative description, which is akin to the notion of a duplex film, enables the limitations of the conventional treatment to be displayed clearly. Particular attention is focussed on the work of forming the drop from the homogeneous material at the same temperature and chemical potentials which surround it. It is anticipated that the new treatment will be of value in describing systems of practical interest such as microemulsion droplets, vesicles and even lyotropic liquid crystals and micelles.

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