Mobility of a particle immersed in a liquid film between two fluids.

The mobility of a particle immersed in a liquid film between two viscous fluids is calculated in point approximation. The mobility in the direction parallel to the film diverges logarithmically as the ratio of the sum of outside viscosities to the film viscosity tends to zero, as in the [Saffman-Delbruck, Proc. Natl. Acad. Sci. U.S.A. 72, 3111 (1975)] expression for the mobility of a particle embedded in a membrane. A simple expression for the limiting behavior is derived. For any values of the parameters the mobility tensor can be evaluated by numerical quadrature of two one-dimensional integrals.