Mathematical modelling of electrorheological nanofluids

Abstract

This paper provides a review of theoretical and experimental advancements in electrorheological (ER) fluids. Experimental results and theoretical models for these novel fluids and their impact in the field of nanotechnology are discussed. This paper reviews their development since the ER phenomenon was first described in the 1940s as well as some recent theoretical results of the authors. These include a description of the multipole re-expansion method for calculating the electrostatic force of attraction between dielectric particles in an externally applied electric field; the description of a critical ratio of particle sizes in a bidisperse systems which provides a genuine maximum for the force of attraction between particles; and how the multipole re-expansion method may be extended to provide a solution for conducting particles with a dielectric coating. Finally, a new general result for thinly coated conducting bodies in an applied electric field is given.