Stokes flow past a slender particle

This paper presents a systematic slender–body theory for a slender particle embedded in an arbitrary Stokes flow. Contrary to previous works, the body is not necessary of revolution. The approach consists in gaining the surface stress acting on the particle by asymptotically solving, with respect to a slenderness ratio, a Fredholm boundary integral equation of the first kind. The procedure approximates integrals depending upon a small parameter by invoking systematic formula. Special attention is paid to particles of elliptical cross-section and term–to–term comparisons are given for a slender ellipsoid embedded in a rather simple Stokes flow.