Electro-rheological effects of polarizable nano spherical particles

A theoretical study is provided for determining the effective stress and viscosity of ideally conducting uncharged polarized freely spherical solid particles suspended in a Stokes fluid under a uniform DC electric field and constant shear. Due to polarization electric double layer (EDL) is formed in the symmetric electrolyte around the spherical (perfect conductor) particle. Assuming a dilute suspension (ignoring particle-particle interaction) we employ a generalized effective stress formulation which considers the case of applied pure shear (no electric field), the case of ambient electric field (no shear) and finally the coupling between both cases. Comparison between the current analysis and literature has shown commendable agreement. Our analytical predictions can be further simplified for the case of a thin EDL utilizing the Helmholtz-Smoluchowski (HS) slip-velocity model in accordance with the generalized cell- method.