Loss of Evolution in the Flow of Viscoelastic Fluids

Abstract For the Maxwell model, it has been proved that an initially evolutionary flow remains so at any time: the property is transported along the streamlines. This is generally not the case for other differential models. A complete study is made of the local properties which are conserved by a Johnson-Segalman fluid flow. Evolution is not preserved, and counter examples are given where the evolutionary character is indeed lost. Two conservation properties are demonstrated and their relationship with the Second Law is also examined. The evolutionary character of a system is a physical requirement which should be satisfied by all models.