University of Cambridge > > Microstructure Engineering Cluster Seminar > Vane Rheometer re-visited: effect of viscosity

Vane Rheometer re-visited: effect of viscosity

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A well-known rheometer uses a cylindrically-symmetric vane tool of radius r1 rotated coaxially in a cylindrical fluid-cup. A cup internal radius r2 = 3r1 is typical. The wide gap r2 – r1 = 2r1 is useful to accommodate large particles suspended in the fluid. A torque applied to the rotor gives a shear stress τ(r ) proportional to r^-2 at a radius r from the common axis. Thus a fluid having a yield-stress τ_0 may yield where τ(r ) > τ_0 (closer to the rotor) and may remain unyielded if τ(r ) is less than or equal to τ_0 (farther from the rotor).

Many workers have used a vane rotor in a wide-gap rheometer for slip-free measurement of the yield stress of visco-plastic fluids but have neglected the existence of viscosity. We analyse partially-yielded coaxial-cylinders flow of a fluid described by the Herschel-Bulkley relation τ = τ_0 + kγn where for a shear rate γ the parameter k is a measure of the viscosity and n is a shear-thinning index. We show the neglect of viscosity by previous workers will erroneously enhance the measured yield stress. Our conclusions apply equally to vane-tool and non-slipping cylindrical rotors. Measurements for yield-stress fluids and soft solids confirm the model’s validity and show how τ_0, k, and n may be measured.

Keywords Coaxial-cylinders rheometry, large-gap rheometry, narrow-gap rheometry, Couette rheometry, vane rheometry, yield-stress fluid, Herschel-Bulkley fluid, wall slip, partial yield

This talk is part of the Microstructure Engineering Cluster Seminar series.

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