Dynamic polarizability of rotating particles in electrorheological fluids

TL;DR

This paper develops a dynamic effective medium theory for rotating particles in electrorheological fluids, revealing off-diagonal polarization responses akin to the Hall effect and how these responses depend on rotational speed and particle interactions.

Contribution

It generalizes existing EMT to include particle interactions and rotational dynamics, predicting off-diagonal polarization responses in 2D configurations.

Findings

Off-diagonal polarization response resembles the Hall effect.

Diagonal response decreases with increasing rotational speed.

Off-diagonal response peaks at a specific rotational velocity.

Abstract

A rotating particle in electrorheological (ER) fluid leads to a displacement of its polarization charges on the surface which relax towards the external applied field ${\bf E}_0$, resulting in a steady-state polarization at an angle with respect to ${\bf E}_0$. This dynamic effect has shown to affect the ER fluids properties dramatically. In this paper, we develop a dynamic effective medium theory (EMT) for a system containing rotating particles of finite volume fraction. This is a generalization of established EMT to account for the interactions between many rotating particles. While the theory is valid for three dimensions, the results in a special two dimensional configuration show that the system exhibits an off-diagonal polarization response, in addition to a diagonal polarization response, which resembles the classic Hall effect. The diagonal response monotonically decreases with an increasing rotational speed, whereas the off-diagonal response exhibits a maximum at a reduced rotational angular velocity $\omega_0$ comparing to the case of isolated rotating particles. This implies a way of measurement on the interacting relaxation time. The dependencies of the diagonal and off-diagonal responses on various factors, such as $\omega_0$, the volume fraction, and the dielectric contrast, are discussed.