Maximising the electrorheological effect for bidisperse nanofluids from the electrostatic force between two particles

A multipole re-expansion solution for two nonidentical dielectric spheres in a parallel electric field is used to determine the critical ratio of particle radii which leads to the strongest force of attraction between the spheres at various interstices and under varying dielectric properties. These critical ratios provide genuine optimal dimensions, in the sense that the force of attraction decreases for both increasing and decreasing ratios. Numerical results are compared with experimental results from the literature and discussed from the perspective of the impact on the design of electrorheological nanofluids.