We analyse axisymmetric gravity currents of power-law fluids theoretically and experimentally. We use aqueous suspensions of Xanthan gum in laboratory experiments of constant-volume and constant-flux release to resolve the rheological parameters of the fluid, which we then compare with measurements made using a strain-controlled rheometer. We find that the constant-volume release of highly shearthinning fluids involves an early-time evolution dominated by inertia, and non-convex free surfaces

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... at make the application of similarity solutions of the late-time viscously dominated evolution inefficient at resolving material properties. In contrast, constantflux release of the same fluids can be viscously dominated and consistent with the self-similar solution from early in the evolution, which makes it a more useful method for measuring rheological parameters.