Approximate Theory for Oscillatory Experiments with a Cone-and-plate Viscometer

IN an earlier communication 1 it was pointed out that, from a theoretical point of view, the cone-and-plate geometry was not a suitable one for the investigation of the linear time-dependent behavior of elastico-viscous liquids. It was suggested that instruments with plane, cylindrical or spherical geometry were to be preferred, since consistent theories for such instruments are to be found in the literature 2–5 . In this communication, some of the specific mathematical difficulties involved in obtaining an oscillatory theory for the cone-and-plate viscometer are pointed out and an attempt is made to obtain an approximate formula which may be useful to those who have adapted the cone-and-plate viscometer to perform oscillatory experiments. This formula is likely to be useful in low-frequency experiments or alternatively in experiments with very viscous materials. In the theory, it is assumed that the angle between the cone and plate is small enough for the free-surface boundary condition to be ignored.