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Recent research has shown that magnetorheological fluid can undergo squeeze-strengthening when flow conditions promote filtration. While a Péclet number has been used to predict filtration in non-magnetic two-phase fluids submitted to slow compression, the approach has yet to be adapted to magnetorheological fluid behavior in order to predict the conditions leading to squeeze-strengthening behavior of magnetorheological fluid. In this article, a Péclet number is derived and adapted to the Bingham rheological model. This Péclet number is then compared to the experimental occurrence of squeeze-strengthening behavior obtained from several squeeze geometries and magnetorheological fluid compositions submitted to pure-squeeze conditions. Results show that the Péclet number well predicts the occurrence of squeeze-strengthening behavior in high-concentration magnetorheological fluid made from various particle sizes and using various squeeze geometries. Moreover, it is shown that squeeze-strengthening occurrence is increased when using annulus geometries or by increasing average particle radius. While lowering concentration increases filtration, tested conditions only led to squeeze-strengthening behavior after concentration had increased close to packing limit. Altogether, results suggest that the Péclet number derived in this study can be used to predict the occurrence of squeeze-strengthening for various magnetorheological fluids and squeeze geometries using the well-known rheological properties of magnetorheological fluids.

Under squeezing flow, magnetorheological fluid can undergo a strengthening phenomenon which results in a drastic increase of its yield stress. This behavior, also known as the super-strong effect, could be used to significantly increase the performance (e.g. torque-to-weight) of rotary magnetorheological fluid devices (e.g. brakes, clutches), but has yet to be exploited due to limited predictability of the phenomenon. To better understand the occurrence of the super-strong effect, a novel test bench capable of small amplitude oscillatory shear is designed to study the behavior of highconcentration magnetorheological fluid submitted to different simultaneous squeeze-shear conditions and magnetic field strengths. Experimental results, obtained up to 5 mm/s compression speed, show that the squeeze-strengthening effect can be correlated to the Péclet number when squeeze flow is dominant, suggesting that the super-strong behavior is governed by solid-liquid phase separation. This super-strong effect, however, is found greatly reduced when the superimposed shear-rate approaches the squeeze-rate order of magnitude.

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