Electro-rheological effect of nano spherical particles

A theoretical study is provided for determining the effective stress and viscosity of ideally conducting polarized freely spherical solid particles suspended in a Stokes dilute suspension (symmetric electrolyte) under ambient DC electric field and far shear field by developing a linear model that neglects particle-particle interactions. Firstly, we discuss the cell model of suspension without the electric field but under ambient uniform shear field. By applying an effective-field methodology similar to that of Miloh-Benveniste (1989) we recover Einstein's classical formulation for the apparent viscosity of the dilute suspension. The second part of this work deals with the electrical field effect following the procedure of Yariv-Miloh (2008). The applied electric field causes the formation of an electric double layer (EDL) around the spherical particle which interacts with the induced electroosmotic flow. Finally, by assuming thin EDL we employ the Helmholtz-Smolochowski (H-S) slip-velocity model and by using the generalized cell model method, we obtain (yet under the dilute suspension limit) an analytic expression for the effective viscosity depending on both ambient shear and electric field.