Cone-and-plate flow

Olagunju, D.O. and Cook, L. P., 1993. Secondary flows in cone and plate flow of an Oldroyd-B fluid. J. Non-Newtonian Fluid Mech. 46, 29-47. 

Example 3.2 Cone-and-Plate Flow Rheometry The cone-and-plate flow apparatus is shown schematically in Fig. E3.2a. The polymer melt flows in the space formed by the rotating cone and stationary plate. 

The preceding relationship establishes that the cone-and-plate flow is viscometric, where cf> is direction 1, that is, the direction of motion, 6 is direction 2, that is, the direction in which the velocity changes, and r is direction 3, that is, the neutral direction. Furthermore, the flow field is such that shear rate is constant in the entire flow field, as it is in the flow between parallel plates. 

Shear stress The shear stress in the four mentioned geometries can be determined by measuring the moment M (in Nm), or pressure AP (in N/m2) during flow. For the Couette flow and the cone and plate flow the relationships for shear stress and shear rate are easy to handle in order to determine the viscosity. For the parallel plates flow and Poisseuile flow, however, more effort is needed to determine the shear stress at the edge of the plate, qR, in parallel plates flow or the shear rate at the wall, qw, in Poisseuile flow. In Table 15.1 equations for shear stresses and shear rates are shown. 

For cone-and-plate flow, the strain in the sample is uniform, so the damping of the... 

Write the governing equations and boundary conditions in dimensionless form. Solve for the velocity profile in the cone-and-plate flow as a regular perturbation problem for small Reynolds numbers. The solution will be very similar to that of the parallel plate problem. 

Cone and plate flow Parallel plate flow... 

Being based on the assumption of a shear-rate-independent viscosity, Eq. (3.29) is not generally true for viscoelastic liquids. Unlike cone-and-plate flow, the shear... 

Flows in category I are called viscometric flows they include simple shear, Poiseuille and plane Poiseuille, Couette, helical, torsional and cone-and-plate flows. Category II flows are called fourth order flows they include superposition... 

---