Summary
In this paper we consider the problem of calculating the resistive torque on a disk rotating slowly with constant angular speed in the surface of a liquid with an adsorbed surface film. Using the method of complementary representations for generalised axially symmetric potential functions, the boundary-value problem for the azimuthal velocity component is reduced to the solution of a Fredholm integral equation of the second kind. This equation is solved numerically and asymptotically for all values of the ratio of the surface shear viscosity of the film to the viscosity of the substrate fluid, and values calculated for the substrate and film torques on the disk. The results are compared with previous work of Goodrich and his co-workers.
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Shail, R. The torque on a rotating disk in the surface of a liquid with an adsorbed film. J Eng Math 12, 59–76 (1978). https://doi.org/10.1007/BF00042804
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DOI: https://doi.org/10.1007/BF00042804