Continuum Modeling of Micro-particle Electrorotation in Couette and Poiseuille Flows - the Zero Spin Viscosity Limit

摘要

A continuum mechanical model is developed to analyze the electrorheological responses and flow phenomena of a particle-liquid mixture with the suspended micro-particles undergoing spontaneous electrorotation, or Quincke rotation, for both two dimensional Couette and Poiseuille flow geometries by combining particle electromechanics and continuum anti-symmetric stress analyses in the zero spin viscosity limit. Predicted results show that with a direct current electric field strength higher than the Quincke threshold applied perpendicularly to the flow direction, the spin velocity is increased and the effective viscosity is decreased as compared to the zero electric field value of the electrorheological fluid viscosity for Couette flow at a given driving shear rate. Moreover, it is also found that with a constant driving pressure gradient, the spontaneous internal particle electrorotation increases the electrorheological fluid rotation as well as enhances the flow velocity and the subsequent two-dimensional volume flow rate of Poiseuille flow when the applied direct current electric field perpendicular to the direction of flow has a strength higher than the critical strength for the onset of Quincke rotation. These continuum mechanical results of the effective viscosity and volume flow rate qualitatively agree with those obtained from effective continuum models (based on single particle dynamics) and general experimental observations as found in current literature.