Steady and unsteady isochoric simple extensional flows

The steady tubeless-siphon (Fano) flow of 0.5% Dow Separan AP-30 in glycerine was experimentally studied. It was found that the inertial effects were generally not negligible, resulting in bulging and contraction of the column according to Coleman and Noll's predictions for the extension of a circular cylinder. In an attempt to develop a free-boundary isochoric simple extensional flow which does not have a surface geometry modification as a result of inertial effects, a general unsteady accelerating D'Almbert-type flow is investigated. It is shown that for the Coleman-and-Noll-type extension of a (perpetually) circular cylinder, a specific D'Almbert motion exists which does not have inertial induced surface-geometry changes. However, no D'Almbert-type Fano flow exists which meets this criterion. The interpretation of extensional viscosity is also discussed for these flows.