(326e) Pair Capillary Interaction of Particles with Pinned Contact Lines on Curved Fluid Interfaces

Capillary interactions of microparticles at interfaces are ubiquitous. They are exploited classically to stabilize emulsions, interfacial gels and encapsulation of materials within particle stabilized drops. More recently, they are exploited in bottom up assembly schemes to organize particles for advanced materials applications. Capillary interactions arise spontaneously when the interfacial area or wetted particle surface depends on particle position. On a planar interface, pair interactions between microparticles are well established. On a curved interface, pair interactions are not yet well understood.
In this presentation, we focus on pair capillary interaction of two disks at oil-water interface where the curvature field was imposed by molding the interface around a vertical cylindrical micropost. The  shape of interface close to the micropost has zero mean curvature and position dependent deviatoric curvature. We study circular disks with sharp edges, which pin the contact line when they are trapped at the interface. On planar interfaces, the pair particles interact very weakly. On curved interfaces, however, they migrate to sites of high curvature and interact with each other to form chains and other structures. The observed trajectories of the pair disks were substantially different from the isolated one due to pair capillary interaction.
We theoretically capture the force and torque on a pair disks with pinned contact lines. Our analysis indicated first, the force on each particle is simply due to the slope variation of the  disturbed interface along the contact line, which in turn is altered  in the presence of the second particle. The imposed curvature field on the other hand, exerts a torque on a pair which ultimately align the pair center to center line with the curvature gradient axis . We develop an asymptotic analysis to determine the disturbance field created by the pair particles and the associated  energy landscape. Our analysis is in agreement with experimental measurement. Preliminary discussions for interactions on interfaces with bending energy and tensions are also presented.