DYNAMIC DILATIONAL PROPERTIES OF COMPOSITE SURFACES

The properties of surfaces (or interfaces) in dilation and compression, as expressed by their dilational moduli, have so far only been studied for uniform, homogeneous surfaces. However, in real systems, in technology, biology, and in everyday life, surfaces are often non-uniform. Such composite surfaces can contain floating solid particles, droplets of a third fluid phase or, in the case of biological membranes, could be composed of a mosaic of lipid bilayers with composition and strength varying from one place to the other. General relationships are derived describing the dynamic dilational modulus of a composite surface in terms of the moduli and area fractions of the component surfaces. Force equilibrium is supposed to be maintained in the surface, during deformation also, and interaction forces between different parts of the surface are assumed to be absent. The simplest case considered is that of undeformable solid particles which float in a deformable surface, occupying a constant area. In this case the ability of the composite surface to resist compression and expansion is simply affected through an area exclusion effect. However, if the area occupied can vary, as is the case for floating solid spheres with a wetting angle dependent on the state of compression of the fluid surface, a more complex behaviour is found. For contact angles close to pi/2, the area exclusion effect dominates, while for angles near 0 and pi the particles can cause a dramatic decrease in the surface's overall resistance against compressional deformation. For surfaces containing droplets and bubbles, an effective dilational modulus can be derived which takes into account mechanical and physicochemical equilibrium conditions near the three-phase contact lines. In this case the composite modulus depends not only on the moduli of the component surfaces but also on the tensions of the curved surfaces. The more the fluid particles approach a spherical shape, the more important these latter terms become. An interesting situation arises at the point of incipient dewetting of superficial droplets where an abrupt decrease of the composite modulus can occur. This gives rise to spots of high extensibility which could be related to the rupture of foam lamellae.