Dynamic simulation of an electrorheological fluid

Abstract

A molecular‐dynamics‐like method is presented for the simulation of a suspension of dielectric particles in a nonconductive solvent forming an electrorheological fluid. The method accurately accounts for both hydrodynamic and electrostatic interparticle interactions from dilute volume fractions to closest packing for simultaneous shear and electric fields. The hydrodynamic interactions and rheology are determined with the Stokesian dynamics methodology, while the electrostatic interactions, in particular, the conservative electrostatic interparticle forces, are determined from the electrostatic energy of the suspension. The energy of the suspension is computed from the induced particle dipoles by a method previously developed [R. T. Bonnecaze and J. F. Brady, Proc. R. Soc. London, Ser. A 4 3 0, 285 (1990)]. Using the simulation, the dynamics can be directly correlated to the observed macroscopic rheology of the suspension for a range of the so‐called Mason number, Ma, the ratio of viscous to electrostatic forces. The simulation is specifically applied to a monolayer of spherical particles of areal fraction 0.4 with a particle‐to‐fluid dielectric constant ratio of 4 for Ma=10⁻⁴ to ∞. The effective viscosity of the suspension increases as Ma⁻¹ or with the square of the electric field for small Ma and has a plateau value at large Ma, as is observed experimentally. This rheological behavior can be interpreted as Bingham plastic‐like with a dynamic yield stress. The first normal stress difference is negative, and its magnitude increases as Ma⁻¹ at small Ma with a large Ma plateau value of zero. In addition to the time averages of the rheology, the time traces of the viscosities are presented along with selected ‘‘snapshots’’ of the suspension microstructure. In particular, at small Ma, the suspension dynamics exhibit two distinct motions: a slow elastic‐body‐like deformation where electrostatic energy is stored, followed by a rapid microstructural rearrangement where energy is viscously dissipated. It is suggested that the observed dynamic yield stress is associated with these dynamics.