For history-sensitive and slip-sensitive materials, the measurement tool selected can dramatically affect the reported values of a material’s rheological properties. The venerable 4-bladed vane pioneered by Nguyen, Boger and coworkers is the most common rheometric tool of choice and provides the most pragmatic compromise between (relatively) simple kinematics and robust measurements. Here, we introduce a modified vane-like geometry with a fractal structure based on a three-generation Bethe lattice that can be readily manufactured using rapid prototyping methods . The design of this new fixture gives a larger surface area-to-volume ratio to the tool, leading to improved cylindricity of the plastic region at the point of yielding, and was optimized by experiment and by simulation (using an adaptive finite element/augmented Lagrangian method). We describe the use of this fractal vane to measure both the static and dynamic yield stress as well as the steady flow curve of a range of simple and thixotropic yield stress fluids. Moreover, this tool provides an expanded range of measurement compared to traditional 4-bladed vanes with an accuracy within ±3% of roughened cone-and-plate reference measurements for viscous Newtonian fluids and simple yield stress fluids. The vanes in this study are entirely 3D printed using a desktop stereolithography machine, making them inexpensive, disposable, chemically-compatible with a wide range of solvents and readily adaptable to future design innovations. We illustrate the use of these fixtures in determining the thixo-elasto-visco-plastic (TEVP) response of a Carbopol-based hair gel, a jammed emulsion (mayonnaise), and an especially difficult-to-handle particulate suspension (tomato ketchup).
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