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A particle placed in soft matter distorts its host and creates an energylandscape. This can occur, for example, for particles in liquid crystals, forparticles on lipid bilayers or for particles trapped at fluid interfaces. Suchenergies can be used to direct particles to assemble with remarkable degrees ofcontrol over orientation and structure. These notes explore that concept forcapillary interactions, beginning with particle trapping at fluid interfaces,addressing pair interactions on planar interfaces and culminating withcurvature capillary migration. Particular care is given to the solution of theassociated boundary value problems to determine the energies of interaction.Experimental exploration of these interactions on planar and curved interfacesis described. Theory and experiment are compared. These interactions provide arich toolkit for directed assembly of materials, and, owing to their closeanalogy to related systems, pave the way to new explorations in materialsscience.

Capillary Interactions on Fluid Interfaces: Opportunities for Directed Assembly