  The rheological behaviors of suspension of ideally conductive particles in an
electric field are studied using large-scale numerical simulations in the limit
of zero-shear-rate flow. Under the action of an electric field, the particles
undergo the nonlinear electrokinetic phenomenon termed as dipolophoresis, which
is the combination of dielectrophoresis and induced-charge electrophoresis. For
ideally conductive particles, the dynamics of the suspension are primarily
controlled by induced-charge electrophoresis. To characterize the rheological
properties of the suspension, the particle stress tensor and particle pressure
are calculated in a range of volume fraction up to almost random close packing.
The particle normal stress and particle pressure are shown to behave
non-monotonically with volume fraction, especially in concentrated regimes. In
particular, the particle pressure is positive for volume fraction up to 30\%,
after which it becomes negative, indicating a change in the nature of the
particle pressure. The microstructure expressed by pair distribution function
and suspension entropy is also evaluated. Visible variations in the local
microstructure seem to correlate with the non-monotonic variation in the
particle normal stresses and particle pressure. These non-monotonic behaviors
are also correlated with the change in the dominant mechanism of particle
pairing dynamics observed in our recent study [Mirfendereski \& Park, J. Fluid
Mech. \textbf{875}, R3 (2019)]. Lastly, the effects of confinement on the
particle stress and particle pressure are investigated. It is found that the
particle pressure changes its nature very quickly at high volume fractions as
the level of confinement increases. This study should motivate control
strategies to fully exploit the distinct changing nature of the pressure for
rheological manipulation of such suspension system.
