The induced permittivity increment of electrorheological fluids in an applied electric field in association with chain formation: A Brownian Dynamics simulation study

We report Brownian Dynamics simulation results for the relative permittivity of electrorheological (ER) fluids in an applied electric field. The relative permittivity of an ER fluid can be calculated from the Clausius-Mosotti (CM) equation in the small applied field limit. When a strong field is applied, however, the ER spheres are organized into chains and assemblies of chains in which case the ER spheres are polarized not only by the external field but by each other. This manifests itself in an enhanced dielectric response, e.g., in an increase in the relative permittivity. The correction to the relative permittivity and the time dependence of this correction is simulated on the basis of a model in which the ER particles are represented as polarizable spheres. In this model, the spheres are also polarized by each other in addition to the applied field. Our results are qualitatively similar to those obtained by Horv\'ath and Szalai experimentally (\textit{Phys. Rev. E}, \textbf{86}, 061403, 2012). We report characteristic time constants obtained from bi-exponential fits that can be associated with formation of pairs and short chains as well as with aggregation of chains. The electric field dependence of the induced dielectric increment reveals the same qualitative behavior that experiments did: three regions with different slopes corresponding to different aggregation processes are identified.