Elastic instabilities in cone-and-plate flow: Small gap theory (Q1905439)

A cone-and-plate flow is obtained in the region bounded by a flat plate and a cone whose apex touches the plate. In rheology, measurements of viscosity have been performed by instruments which use this flow concept. Here the non-inertial flow of an Oldroyd-B fluid is considered when the gap angle is small. This flow becomes unstable when the Deborah number reaches a critical value, but the analysis does not explain the instabilities found in time-dependent and oscillatory experiments. A new asymptotic theory presented by the author uses a special choice of coordinate transformation. Now the critical Deborah number depends on the square root of the gap angle. Results are in agreement with experiments.