The functional similarity between faxén relations and singularity solutions for fluid-fluid, fluid-solid and solid-solid dispersions

Abstract

The functional similarity between Faxén relations (for moments of the appropriate transport flux) and singularity solutions has been noted in the past. For rigid particles (and perfect conductors etc.) it has been noted in the literature that the root of this similarity is linked to the Lorentz reciprocal theorem. However, the duality applies even to more general two-phase problems such as a viscous drop in another solvent, with the relevant singularity distribution taken from the exterior solution. Although two-phase Faxén relations are available for various particle shapes, until now, the root of this duality has not been demonstrated explicitly. The application of the duality is illustrated by the derivation of new Faxén relations for ellipsoidal inclusions.