Negative electrorheological responses of micro-polar fluids in the finite spin viscosity small spin velocity limit. I. Couette flow geometries

Negative electrorheological responses induced by micro-particle electrorotation in two-dimensional Couette flow geometries are analyzed by a set of continuum modeling field equations originating from anti-symmetric/couple stress theories in the finite spin viscosity small spin velocity (FSV) limit. Analytical solutions are obtained for the first time to express the spin velocity, linear velocity, and effective viscosity in terms of the electric field strength, driving shear rate, boundary condition selection parameter, and spin viscosity. Good agreement is achieved between the FSV theoretical predictions presented herein and the experimental measurements reported in recent literature for the effective viscosity for low driving shear rates.