A Surfactant Bridge Model for the Nonlinear Electrorheological Effects of Surfactant-Activated ER Suspensions

Abstract

In surfactant-activated electrorheological (ER) suspensions it is observed that the ER response shows linear ER behavior (F∝E2) at small surfactant concentrations and nonlinear ER behavior (F∝En, n≈1) at large surfactant concentrations. Here, a surfactant bridge model is developed to explain the nonlinear ER behavior of surfactant-activated ER suspensions. The model shows that the formation and size of a surfactant bridge depend on various variables, especially the electric field strength, the surfactant surface tension, and the initially adsorbed amount of surfactants on particles. The predicted dependence of the formation and size of a surfactant bridge on the electric field strength and the initially adsorbed amount of surfactants is consistent with the observations. Also, the model indicates that there is a critical minimum electric field Ecrit for the formation of a surfactant bridge, and the estimated Ecrit shows good agreement with the observations. The force acting between particles is composed of the electrostatic force and force associated with surface tension. However, it is found that the contribution of the force associated with surface tension can be ignored and the electrostatic force is dominant regardless of the formation of surfactant bridges between particles. When surfactant bridges are formed between particles, the predicted force shows nonlinear ER behavior (F∝En, n≈1), consistent with the observed nonlinear ER behavior at large surfactant concentrations. When no surfactant bridge is formed, the predicted force is proportional to the electric field squared (F∝E2), consistent with the interfacial polarization. The model can successfully predict the nonlinear ER behavior at large surfactant concentrations, confirming that the nonlinear ER behavior of surfactant-activated ER suspensions arises from the observed formation of surfactant bridges between particles.