Extensional rheometry of mobile fluids. Part I: OUBER, an optimized uniaxial and biaxial extensional rheometer

Numerical optimization of a “six-arm cross-slot” device yields several three-dimensional shapes of fluidic channels that impose close approximations to an ideal uniaxial (biaxial) stagnation point extensional flow under the constraints of having four inlets and two outlets (two inlets and four outlets) and for Newtonian creeping flow. One of the numerically designed geometries is considered suitable for fabrication at the microscale, and numerical simulations with the Oldroyd-B and Phan-Thien and Tanner models confirm that the optimal flow fields are observed in the geometry for both constant viscosity and shear thinning viscoelastic fluids. The geometry, named the optimized uniaxial and biaxial extensional rheometer (OUBER), is microfabricated with high precision by selective laser-induced etching of a fused-silica substrate. Employing a refractive index-matched viscous Newtonian fluid, microtomographic-particle image velocimetry enables the measurement of the flow field in a substantial volume around the stagnation point. The flow velocimetry, performed at low Reynolds number (<0.1), confirms the accurate imposition of the desired and predicted flows, with a pure extensional flow at an essentially uniform deformation rate being applied over a wide region around the stagnation point. In Part II of this paper [Haward et al., J. Rheol. 67, 1011–1030 (2023)], pressure drop measurements in the OUBER geometry are used to assess the uniaxial and biaxial extensional rheometry of dilute polymeric solutions, in comparison to measurements made in planar extension using an optimized-shape cross-slot extensional rheometer [OSCER, Haward et al., Phys. Rev. Lett. 109, 128301 (2012)].