A frequency-dependent surfactant bridge model for the electrorheological behaviors of surfactant-activated suspensions

In surfactant-activated electrorheological (ER) suspensions, the ER response shows linear ER behavior (Τ∞Eo2 at small surfactant concentrations and nonlinear ER behavior (Τ∞Eon,n>2) at large surfactant concentrations. A surfactant bridge model was proposed to explain the nonlinear ER behavior at large surfactant concentrations with some assumptions. The proposed model successfully predicted the qualitative nonlinear ER behavior of surfactant-activated ER suspensions at large surfactant concentrations. Here, the surfactant bridge model is expanded to predict the electric field frequency dependent ER behavior of surfactant-activated ER suspensions. The developed surfactant bridge model can predict both the linear ER behavior at small surfactant concentrations and the nonlinear ER behavior at large surfactant concentrations. Furthermore, this model can predict two different types of the electric field frequency dependent ER behaviors of surfactant-activated ER suspensions, which depend on the amount of surfactants.