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A double-layer integral equation for the surface tractions on a body movingin a viscous fluid is derived which allows for the incorporation of abackground flow and/or the presence of a plane wall. The Lorentz reciprocaltheorem is used to link the surface tractions on the body to integralsinvolving the background velocity and stress fields on an imaginary boundingsphere (or hemisphere for wall-bounded flows). The derivation requires thevelocity and stress fields associated with numerous fundamental singularitysolutions which we provide for free-space and wall-bounded domains. Two sampleapplications of the method are discussed: we study the tractions on anellipsoid moving near a plane wall, which provides a more detailedunderstanding of the well-studied glancing and reversing trajectories in thecontext of particle sedimentation, and the erosion of bodies by a viscous flow,in which the surface is ablated at a rate proportional to the local viscousshear stress. Simulations and analytical estimates suggest that a sphericalbody in a uniform flow first reduces nearly but not exactly to the dragminimizing profile and then vanishes in finite time. The shape dynamics of aneroding body in a shear flow and near a wall are also investigated. Stagnationpoints on the body surface lead generically to the formation of cusps, whosenumber depends on the flow configuration and/or the presence of nearbyboundaries.

A generalized traction integral equation for Stokes flow, with applications to near-wall particle mobility and viscous erosion