The viscosity of an electrorheological fluid in an electric field is s
tudied by computer simulations. The fluid viscosity increases with the
field through three stages. In a weak field, the fluid remains Newton
ian although its viscosity increases. At this stage, while drifting in
the flow direction, particles diffuse in the direction perpendicular
to the flow. In an intermediate electric field, the fluid has tilted a
nd broken chains moving with the flow and the fluid becomes non-Newton
ian. The viscosity eta and the shear rate gamma has the following rela
tionship eta = eta(0) epsilon(-gamma tau) where tau is the relaxation
time and eta(0) is exponentially proportional to the dipolar interacti
on energy and the volume fraction. In a strong electric field, the flu
id contains condensed chains which provide yield stress and hysteresis
.