Dense suspensions have previously been shown to produce a range of anomalous and gravity-defying behaviors when subjected to strong vibrations in the direction of gravity. These behaviors have previously been interpreted in terms of rigid body phenomena and shear-thickening, but here we examine discontinuous shear thickening (DST) as the cause of a negative viscosity effect, i.e. the average shear rate being opposite to the direction of the average shear stress. Using ideas from the Wyart and Cates modeling framework, we show that such a negative viscosity can be achieved in shear flows driven by oscillating stress with both square and sinusoidal wave forms. We extend this same modeling approach to study falling films in a vibrating gravitational field, where we similarly find it is possible to attain an overall flow opposite to the direction of gravity. Preliminary experimental findings are also provided in support of the modeling work.
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