Theory of Dilute Electro-Rheological Fluids

The stress versus rate of strain relationship for a dilute suspension of conducting spherical particles in a dielectric fluid is worked out under conditions of simple steady shearing flow in a transverse electric field. The relationship is found to be nonlinear and multivalued so that under certain simple circumstances hysteresis and catastrophic changes in stress or strain rate can occur. The work is of interest in the general study of electro-rheological fluids.