  To enable robust rheological measurements of the properties of yield stress
fluids, we introduce a class of modified vane fixtures with fractal-like
cross-sectional structures. A greater number of outer contact edges leads to
increased kinematic homogeneity at the point of yielding and beyond. The vanes
are 3D printed using a desktop stereolithography machine, making them
inexpensive (disposable), chemically-compatible with a wide range of solvents,
and readily adaptable as a base for further design innovations. To complete the
tooling set, we introduce a textured 3D printed cup, which attaches to a
standard rheometer base. We discuss general design criteria for 3D printed
rheometer vanes, including consideration of sample volume displaced by the
vanes, stress homogeneity, and secondary flows that constrain the parameter
space of potential designs. We also develop a conversion from machine torque to
material shear stress for vanes with an arbitrary number of arms. We compare a
family of vane designs by measuring the viscosity of Newtonian calibration oils
with error <5% relative to reference measurements made with a cone-and-plate
geometry. We measure the flow curve of a simple Carbopol yield stress fluid,
and show that a 24-arm 3D printed fractal vane agrees within 1% of reference
measurements made with a roughened cone-and-plate geometry. Last, we
demonstrate use of the 24-arm fractal vane to probe the
thixo-elasto-visco-plastic (TEVP) response of a Carbopol-based hair gel, a
jammed emulsion (mayonnaise), and a strongly alkaline carbon black-based
battery slurry.
