Conductivity under an oscillatory mechanical field

If the shear stress of an ER fluid is generated from fibrillated chains, the oscillatory frequency of shear stress obviously should be equivalent to that of the dc current. This is the exact case for OP suspension, and the angular frequency of the shear stress doubles that of the applied oscillatory strain. However, for the PS suspension the frequency of shear stress is almost identical to that of imposed strain but is only half of the frequency of dc 

If a vertical oscillatory field is applied, a.ssuming original gap between two electrodes is d and a vertical oscillation is yx = yo sin ot, then fibrillated chains would vertically elongated, and the conductivity could be expressed 

In summary, the dc current absorption is observed in the oxidized polyacrylonitrile based-ER fluids. The conductive behaviors of ER suspensions with or without an oscillatory mechanical field are confined by the microstructure—the fibrillated chain structure induced by an external electric field. The de current oscillates with the mechanical frequency and strain amplitude, implying that ER suspensions could be used as a mechanical sensor transferring a mechanical signal to an electric one. The conductive mechanism of an oxidized polyacrylonitrile-based ER suspension can be well described by a Quasi-Id-VRH model, where the localized charges hop from one localized state to another along the chains. This conduction model can be used to quantitatively describe the dc current oscillation phenomena. 

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