ELECTROSTATIC INTERACTIONS FOR PARTICLE ARRAYS IN ELECTRORHEOLOGICAL FLUIDS I: CALCULATIONS

Abstract

A simple effective charge method and the principle of superposition were used to calculate the total system interaction energy of two-dimensional rectangular and hexagonal arrays of particles in electrorheological suspensions. The calculations gave for static conditions (no shear) that a close-packed hexagonal array of particles was energetically favored over a rectangular array and that for very dilute suspensions a structure consisting of separated single chains was favored over one consisting of clusters. For shearing and assuming that no rotation of the polarization vector takes place, no difference in the maximum force per chain occurred for a two-chain system compared to a single-chain system in either the rectangular or close-packed hexagonal array. This was also the case with rotation of the polarization vector in the rectangular array, although the force was less with rotation compared to without rotation for this array. However, in the case of the dose-packed hexagonal array with rotation of the polarization vector there occurred an order of magnitude enhancement of the maximum force for the two-chain system compared to the single-chain system. This enhancement is comparable to the ratio of the measured strength of ER fluids to that predicted for the structure consisting of separated single chains.