Cone-and-Plate Flow

In this example we will examine the stability of another simple shear flow which has application in rheometry. Consider a sample of viscoelastic fluid placed between an inverted cone and a coaxial plate (figure 6.1). Assume that the plate is fixed and the cone rotates at a constant angular speed $\omega$. The governing equations for an Oldroyd-B fluid are given in Appendix 1. These equations are valid when the gap angle $\alpha$ is small [3]. The independent variables are $\rho=r^{1/\alpha}$ and $\psi=(\pi/2-\theta)/\alpha$, so that $\psi$ ranges from 0 to 1.

 

Figure 6.1: Cone-and-plate system