  Directed assembly of colloids is an exciting field in materials science to
form structures with new symmetries and responses. Fluid interfaces have been
widely exploited to make densely packed ordered structures. We have been
studying how interface curvature can be used in new ways to guide structure
formation. On a fluid interface, the area of the deformation field around
adsorbed microparticles depends on interface curvature; particles move to
minimize the excess area of the distortions that they make in the interface.
For particles that are sufficiently small, this area decreases as particles
move along principle axes to sites of high deviatoric curvature. We have
studied this migration for microparticles on a curved host interface with zero
mean curvature created by pinning an oil-water interface around a micropost.
Here, on a similar interface, we demonstrate capillary curvature repulsion,
that is, we identify conditions in which microparticles migrate away from high
curvature sites. Using theory and experiment, we discuss the origin of these
interactions and their relationship to the particle's undulated contact line.
We discuss the implications of this new type of interaction in various contexts
from materials science to microrobotics.
