The slow rotation of an axisymmetric solid submerged in a fluid with a surfactant surface layer—I The rotating disk in a semi-infinite fluid

A formulation in terms of a Fredholm integral equation of the first kind is given for the axisymmetric problem of a solid rotating in a bounded viscous fluid whose surface is contaminated with an immiscible surfactant film. The particular case of a rotating thin circular disk immersed in a semi-infinite body of fluid is studied in detail, the problem being reduced to the solution of a Fredholm integral equation of the second kind. This equation is solved both asymptotically and numerically, and the resistive torque on the disk and surface velocity profiles are computed for varying values of the ratio of the coefficient of surface shear viscosity to the coefficient of viscosity of the substrate fluid, and depth of the disk below the surface.