Capillary forces between solid particles in fluid interfaces

Abstract

Floating solid particles in fluid—fluid interfaces will interact with one another, even in the absence of gravity, when they have an irregular wetting perimeter which disturbs the smoothness of the interface. Calculations on a model system show that for a disturbance introduced by a particle with a sinusoidal edge, there can be a significant capillary interaction with similar neighbouring particles. This interaction is based on the minimisation of the total surface area. It results in a capillary force which acts over a distance of the order of the sine's wavelength, with a magnitude proportional to the square of the sine's amplitude. At large distances, the interaction is predominantly attractive. Unless the two approaching particle edges match exactly, there is an equilibrium distance below which the force becomes repulsive. When the sines on the edges of two interacting particles are not in phase, there will also be a lateral force tending to move the particles in tangential direction with respect to one another. Interaction forces of this nature can be of quite significant magnitude and only at very small distances are they overtaken in importance by molecular forces. For particle-covered surfaces they can result in resistance against both dilational and shear deformation. A derivation is given of the associated dilational modulus for a simple model. The possible role of capillary interaction of this nature in thin liquid films and in biological membranes is briefly discussed.