Capillary forces between colloidal particles confined in a liquid film: The finite-meniscus problem

We consider a system made of two spherical particles confined between two fluid interfaces. The concept is illustrated in experiments with polystyrene micrometer-sized particles located between the two membranes of a bilamellar giant lipid vesicle. The particles locally separate the membranes and form a Plateau border, which is filled with water, Experiments based on optical manipulation and dynamometry readily show that the particles attract each other. The interaction force is long-ranged (several particle radii) and goes through a maximum (about a piconewton) at finite particle separation. We propose a theory of the interaction, based on the linearized Laplace equation for the meniscus profile. The theory predicts that the meniscus around an isolated particle is finite, that is, bounded by a peripheral contact line, outside of which the film surfaces are equidistant. When two particles come near each other, their menisci overlap and fuse to form a unique meniscus with a new peripheral line. This is the source of the capillary interaction. The computation yields a characteristic nonmonotonic force-versus-distance profile, as experimentally observed with the latex particles. The computed profile quantitatively fits to the experimental data, with a single adjustable parameter, the bilayer tension. Other features of the interaction (hysteresis, dependence on particle size) are discussed. We find that the capillary attraction in general is strong enough to cause aggregation of the confined colloidal particles.