Nearly extensional flows

After defining a nearly extensional flow, the stresses which arise in an incompressible simple fluid undergoing such a motion are determined. Since the linear functionals which arise in this perturbation are similar to those in the infinitesimal viscoelasticity theory of a transversely isotropic solid with rotational and reflectional symmetries, the non-zero linear functionals and interralations between them are determined quite easily. It is then shown that self-consistency demands that certain relations exist between the extensional modulus and these linear functionals. As an application, the speed of propagation of an acceleration wave in a fluid undergoing an extensional flow is considered. Finally, the nearly extensional flow theory is cast in terms of small displacements superposed on the extensional flow. In this form, it may be useful in the study of melt spinning.