  We define a class of flows with exponential kinematics termed Periodic
Exponential Shear (PES) flow which involve periodic exponential stretching of
fluid elements along with their rotation. We exhibit analytical and numerical
results for PES flow by using the Oldroyd-B model for viscoelastic fluids. We
calculate the growth in the shear and the normal stresses analytically as well
as demonstrate that repeated application of the flow leads to stable
oscillatory shear and normal stresses. We define a material function applicable
to a periodic, unsteady shear flow and show numerically that this material
function exhibits deformation-rate thickening behavior for viscoelastic fluids
subject to PES flow. We demonstrate the feasibility of PES flow by presenting
preliminary experimental results from a controlled-strain rate rheometer, using
a Newtonian mineral oil.
