Analysis of the Constant Rate Startup Flow of a Viscoelastic Fluid in Annular, Cylindrical, and Planar Conduits

The unsteady viscoelastic flow problem of velocity profile development in a conduit owing to a step change in volumetric flow rate is considered. Using a three-constant Oldroyd model, analytical solutions describing the time dependence of the velocity and shear stress distributions have been obtained. Particular analytical solutions are derived for conduits of different geometry, namely, annular, tubular, and planar. The analysis indicates that in contrast to Newtonian flow which exhibits a monotonic development of the velocity profile, viscoelastic liquids approach steady state behavior in an oscillatory fashion. The severity of the oscillatory behavior, however, is directly related to the elastic nature of the liquid.