AN EXACT SOLUTION TO THE VISCOELASTIC DAMPING OF A TORSION PENDULUM BY A SURFACE-FILM

A theoretical basis for the investigation of viscoelastic behavior of surface films has been established by obtaining the exact solution to the boundary value problem of a film-covered fluid set in free (decaying) oscillatory motion by a torsion pendulum rotor in a shear trough. Because the motions of both the surface film and the substrate contain the time variable in the same exponential form, the Navier-Stokes equations of the fluid phase can be reduced to partial differential equations with respect to spatial variables alone. It then becomes possible to apply the finite Hankel transformation, resulting in ordinary differential equations, which are easily solved. The finite Hankel transformation is further applied to the stress equilibrium boundary condition in the surface film by taking into account the fact that there is a discontinuity of velocity gradient at the edge of the rotor. This discontinuity may, in turn, be related to the torque exerted by the film on the rotor. An explicit formula is thus deduced to compute the complex shear viscosity or the complex shear modulus of the surface film from the experimental measurements of the frequencies and the damping times of the rotor in the presence and absence of the surface film.