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

Analytical solutions to the continuum spin and linear velocities as well as the two-dimensional volume flow rate are solved and presented for negative electrorheological Poiseuille flows induced by internal micro-particle Quincke electrorotation using continuum anti-symmetric/couple stress theories with finite spin viscosities and small spin velocities. Theoretical predictions on the volume flow rate and linear velocity profile obtained from the continuum finite spin viscosity small spin velocity theory presented herein agree very well with the experimental measurements in the parametric regime of low or small driving pressure gradients as reported in current literature.