Theory of a Cone-Plate Viscometer for Non-Newtonian Liquids

A general relationship between the torqueMand the angular velocity of a plate is obtained for a time-independent non-Newtonian liquid specified by an arbitrary flow curve. It is assumed that the motion of the liquid is steady and that each liquid particle moves with a constant angular velocity on a circle on a horizontal plane perpendicular to the axis of rotation. The edge effects are neglected. It is shown how to determine the flow curve from the experimental relationship betweenMand for some special cases. Following special cases are considered: i) non-Newtonian liquid obeying power law flow curve, ii) non-Newtonian liquid obeying flow curve expanded into power series, iii) Bingham body. It is shown that the relationship betweenMand for a non-Newtonian liquid obeying power law flow curve is reduced to the well-known formula for a Newtonian liquid when the exponent tends to unity.