On the slow motion of a solid submerged in a fluid with a surfactant surface film

Summary This paper continues the work of Shail and Gooden [1–4] on the motion generated in a semi-infinite fluid by a singularity or submerged solid moving particle when the surface of the fluid is contaminated with a surfactant film. The fluid motion is assumed to be slow and quasi-steady, but the restriction to axially symmetric flows of earlier investigations is removed. The various linearised models of Shail and Gooden [3,4] governing the variation of film concentration are discussed, the constitutive properties of the film being expressed in terms of Boussinesq coefficients of surface shear and dilatational viscosities. The resulting film boundary conditions are applied to solve the non-axially symmetric problem of a Stokeslet placed in the bulk fluid with its axis parallel to the surface (assumed planar throughout the motion), and the results used to calculate approximate expressions for the resistive force on a particle which translates far from and parallel to the surface. A similar analysis is given for the case of a rotelet whose axis is parallel to the surface.