 Extensional flow

An extensional flow stretches material along one or more directions while contracting it along others. A local ideal model of planar extension has velocity $\mathbf{u}=(\dot{ϵ}x,-\dot{ϵ}y,0)$: its rate-of-strain tensor is $\mathrm{diag}(\dot{ϵ},-\dot{ϵ},0)$ and it is an incompressible flow. Uniaxial extensional flow instead contracts both transverse directions. These geometries probe extensional viscosity and can stretch polymers.