Nonlocal electrostatics in heterogeneous suspensions using a point-dipole model

The electrostatic dipole moment distribution in heterogeneous suspensions is determined via a self-consistent, point-dipole model, which incorporates nonlocal electrostatics. Predictions agree qualitatively with previous asymptotic results for discontinuous concentration profiles. For small fluctuations in concentration, the dipole strength can be expressed as an expansion in gradients of the concentration. This expansion is incorporated into a linearized continuum model for structure evolution in sheared electrorheological suspensions. Prior stability analysis of a fully local continuum model predicts the formation of concentrated particle stripes oriented in the flow direction, in agreement with experimental observations. Incorporating nonlocal electrostatics suppresses the growth of high wave number fluctuations, providing a more realistic finite rate of growth of fluctuations. Incorporating nonlocal electrostatics in the full nonlinear continuum model produces a single particulate stripe at steady state.