Structure parameter of electrorheological fluids in shear flow

A structure parameter, Sn = η(c)γ/τ(E), is proposed to represent the increase of effective viscosity due to the introduction of particles into a viscous liquid and to analyze the shear behavior of electrorheological (ER) fluids. Sn can divide the shear curves of ER fluids, τ/E(2) versus Sn, into three regimes, with two critical values Sn(c) of about 10(-4) and 10(-2), respectively. The two critical Sn(c) are applicable to ER fluids with different particle volume fractions φ in a wide range of shear rate γ and electric field E. When Sn < 10(-4), the shear behavior of ER fluids is mainly dominated by E and by shear rate when Sn > 10(-2). The electric current of ER fluids under E varied with shear stress in the same or the opposite trend in different shear rate ranges. Sn(c) also separates the conductivity variation of ER fluids into three regimes, corresponding to different structure evolutions. The change of Sn with particle volume fraction and E has also been discussed. The shear thickening in ER fluids can be characterized by Sn(c)(L) and Sn(c)(H) with a critical value about 10(-6). As an analogy to friction, the correspondence between τ/E(2) and friction coefficient, Sn and bearing numbers, as well as the similarity between the shear curve of ER fluids and the Stribeck curve of friction, indicate a possible friction origin in ER effect.