Continuum modeling of micro-particle electrorotation in Couette and Poiseuille flows—The zero spin viscosity limit

A continuum mechanical model is presented to analyze the negative electrorheological responses of a particle-liquid mixture with the suspended micro-particles undergoing Quincke rotation for both Couette and Poiseuille flow geometries by combining particle electromechanics and continuum anti-symmetric/couple stress analyses in the zero spin viscosity limit. We propose a phenomenological polarization relaxation model to incorporate both the micro-particle rotation speed and macro-continuum spin velocity effects on the fluid polarization during non-equilibrium motion. Theoretical predictions of the Couette effective viscosity and Poiseuille flow rate obtained from the present continuum treatment are in good agreement with the experimental measurements reported in current literature.