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

Abstract

IN an earlier communication¹ 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.