The temperature field in rotational rheometers and flow curve correction for viscous dissipation

Abstract

A solution is presented for incompressible non-Newtonian liquids of the one-dimensional stationary temperature field which arises due to heat dissipation between two concentric cylinders, the outer fixed and thermostated, the inner rotating at a constant angular velocity. The object of the study is to outline a simple procedure for determining the temperature rise of the liquid and, primarily, to ascertain the corrections of the consistent variables τ and D which enable the experimenter to rectify the rheogram on the basis of measurement of the shear stress τ and the angular velocity Ω. The results obtained are summarized in graphical form as diagrams of the temperature and velocity fields and, to facilitate practical application of the correction procedure, in a table relating the dimensionless temperature function Ψ(ℋ, n, ζ) to the geometry ℋ, the flow behaviour index n, and the coefficient of temperature rise ζ and showing the function Ψ′(1) as well.