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We report Brownian Dynamics simulation results for the relative permittivityof electrorheological (ER) fluids in an applied electric field. The relativepermittivity 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 inwhich case the ER spheres are polarized not only by the external field but byeach other. This manifests itself in an enhanced dielectric response, e.g., inan increase in the relative permittivity. The correction to the relativepermittivity and the time dependence of this correction is simulated on thebasis of a model in which the ER particles are represented as polarizablespheres. In this model, the spheres are also polarized by each other inaddition to the applied field. Our results are qualitatively similar to thoseobtained by Horv\'ath and Szalai experimentally (\textit{Phys. Rev. E},\textbf{86}, 061403, 2012). We report characteristic time constants obtainedfrom bi-exponential fits that can be associated with formation of pairs andshort chains as well as with aggregation of chains. The electric fielddependence of the induced dielectric increment reveals the same qualitativebehavior that experiments did: three regions with different slopescorresponding to different aggregation processes are identified.

physical review. e

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