Determination of parameters of a material obeying Casson’s equation by some rheometers

Abstract

It is shown how to determine parameters of a material obeying Casson’s equation by some rheometers. Casson has proposed an equation for the flow of varnishes relating the shear stress F to the rate of shear D. This relation has the form, $\sqrt{\mathrm{(}\mathit{F}\mathrm{)}}={\mathit{k}}_0+{\mathit{k}}_1\sqrt{\mathrm{(}\mathit{D}\mathrm{)}}$ , ${\mathit{k}}_0$ and ${\mathit{k}}_1$ being constants. This equation is generally called Casson’s equation.

We have determined the parameters ${\mathit{k}}_0$ and ${\mathit{k}}_1$ , that is, the viscosity ${\mathit{\eta }}_{\mathit{c}}$ corresponding to ${\mathit{k}}_1^2$ and the yield value ${\mathit{\tau }}_{\mathit{f}}$ corresponding to ${\mathit{k}}_0$ , by a rotating coaxial cylinder viscometer and a cone and plate viscometer. The determination of the parameters can be made by the following procedure. First, we substitute the flow curve for Casson’s equation into the general relationship between the torque M and the angular velocity Ω for a non-Newtonian fluid. From a plot of $\sqrt{\mathit{\Omega }}$ vs. $\sqrt{\mathit{M}}$ we can get an asymptote. Then we can determine ${\mathit{\eta }}_{\mathit{c}}$ from the slope of the asymptote and ${\mathit{\tau }}_{\mathit{f}}$ from the intersection of the asymptote with the abscissa.