Modelling the induced force of attraction in electrorheological nanofluids

The problem of electric-field induced force between spheres is fundamental to electrorheological fluids. In this paper we summarize recent work, and in particular present an exact solution to the electrostatic problem of dielectric spheres subject to an externally applied electric field. The numerical results are compared to published experimental data and the solution is shown to accurately predict the low-frequency experimental results at all measured interstices and particularly is applicable to nanosized spheres in close proximity. This method is applicable to nonidentical spheres and results indicate a genuine maximum in the attractive force between spheres exists, which depends on relative particle size and the electrostatic permittivity of the particles and that of the medium. These maxima have not previously been reported in the literature and the existing published work of the present authors constitutes the first published material on this topic.