| Abstrakt: |
The effect of a layer of an adsorbed monomolecular surfactant film of fluid covering the free surface of a semi-infinite volume of substrate fluid is considered of mortion within both surfactant and substrate fluids caused by the slow rotation of a solid sphere which is partially submerged in the substrate fluid. The boundary condition at the surfactant is derived and agrees with that proposed by Scriven. The resulting boundary-value problem is solved for varying depths of partial submersion of the sphere by a method in which the equations governing the motion in the substrate are satisfied exactly and the error in satisfying the boundary conditions at the sphere surface and surfactant layer is minimized according to a least-squares criterion. A comprehensive set of data is provided for the surface velocity, film, substrate and total torques acting on the sphere, covering a wide range of the parameters defining the depth of partial submersion of the sphere and surface-shear viscosity when the dynamic viscosity of the substrate is given. Close agreement is obtained by the method with data obtained from the exact solution and experiment when the surface viscosity is negligible. |
