Shape optimisation of channels for extensional flow

Studying the rheology of viscoelastic (or otherwise time dependent) fluids can be challenging. Achieving steady state conditions in shear tests is relatively straightforward – the system only needs to be strained for sufficient duration that steady state stresses are achieved, say, by continued rotation of a rheometer geometry. Hopefully the system under test does not settle under gravity or irreversibly degrade over this period!

On the other hand, achieving steady state stresses when studying extensional flows is much more difficult, as fluid elements are continuously being stretched into ever longer and thinner profiles, presenting a point where strain cannot be continued indefinitely on account of factors such as pressure drop, geometric size, fluid velocity, shear rates, etc.

Channels designed to produce constant extension rates are commonly of the hyperbolic profile (i.e. x.y=constant for a planar channel, as sketched above, r^2.x=constant for axisymmetric). Improvements to this theoretical profile have been presented in the literature using shape optimisation techniques (e.g. Zografos et al, 2016) but certain critical aspects of the channel and trade-offs that must be made when practically implementing them have not been addressed/explored in detail in literature, particularly from a fundamental/phenomenological standpoint.

A body of work exploring these aspects has been presented at a couple of conferences and seminars (most recently the INNFM meeting 2023, previously e,g, ICR2020). A new channel profile was presented, whilst also inviting discussion from the community on a complex issue surrounding the measurement of strain rates within fluids which has been encountered. These coupled areas of interest are currently under preparation for publication.