Force balance of particles trapped at fluid interfaces

We study the effective forces acting between colloidal particles trapped at afluid interface which itself is exposed to a pressure field. To this end weapply what we call the ``force approach'', which relies solely on the conditionof mechanical equilibrium and turns to be in a certain sense less restrictivethan the more frequently used ``energy approach'', which is based on theminimization of a free energy functional. The main goal is to elucidate theadvantages and disadvantages of the force approach as compared to the energyapproach. First, we derive a general stress-tensor formulation of the forces atthe interface and work out a useful analogy with 2D electrostatics in theparticular case of small deformations of the interface relative to its flatconfiguration. We apply this analogy to compute the asymptotic decay of theeffective force between particles trapped at a fluid interface, extending thevalidity of previous results. Second, we address the case of deformations of anon-flat interface. We compute the deformation of a spherical droplet due tothe electric field of a charged particle trapped at its surface and concludethat the interparticle capillary force is unlikely to explain certain recentexperimental observations. Finally we discuss the application to a generallycurved interface and show as an illustrative example that a nonsphericalparticle deposited on an interface forming a minimal surface is pulled toregions of larger curvature.Comment: 17 pages, 5 eps-figures. In this new version, the order of sections has been reshuffled and a new subsection has been adde