Capillary Interactions of Micro-particles on Curved Interfaces

Microparticles trapped at fluid interfaces interact by capillarity to migrate, form structures and find preferred locations. These phenomena are exploited to organize colloids at fluid interfaces, impacting emulsion stabilization and forming the basis for advanced materials which exploit, e.g. the mechanics or optical properties of the structures which form. Interface curvature plays a strong role in microparticle behavior by acting as a field which directs microparticle migration. Here, we discuss the behavior of microparticles with pinned contact lines at the oil-water interface on interfaces with well-defined curvature fields. Once the particles attach to the interface, they migrate in deterministic paths towards sites of high curvature. These experiments are well described by our analysis. We theoretically determine the disturbance field imposed by particles via an asymptotic analysis, and have quantified the associated capillary energy and the capillary force. Forces can be understood simply in terms of slope variation of the disturbed interface along the contact line. Capillary energies are expressed in closed form as a function of mean and deviatoric curvatures of the interface prior to the particles deposition. Pair interactions between particles will be also discussed.