ABSTRACT
Abstract We analyze the hydrodynamic interactions between spherical solid particles which are suspended in a quiescent fluid and in contact with a planar fluid-gas interface. Stick boundary conditions are assumed on the sphere surfaces, and the free surface boundary conditions are accounted for by the method of images. The one-sphere hydrodynamic resistance operator of such a quasi-two-dimensional system is calculated numerically. Using a spherical multipole expansion with symmetry-adjusted basis functions, explicit results are derived for the long-distance terms of the two-sphere mobility tensor up to cubic order in the inverse interparticle distance. The point particle model is also constructed, taking into account the constraint forces necessary to keep the point-particles at a fixed ‘radius’ a apart from the interface. The accuracy of both far field approximations is discussed by comparing them with the precise many-sphere mobility, evaluated by the multipole expansion.
