Rotating electroosmotic flow of an Eyring fluid

Abstract

A perturbation analysis is presented in this paper for the electroosmotic (EO) flow of an Eyring fluid through a wide rectangular microchannel that rotates about an axis perpendicular to its own. Mildly shear-thinning rheology is assumed such that at the leading order the problem reduces to that of Newtonian EO flow in a rotating channel, while the shear thinning effect shows up in a higher-order problem. Using the relaxation time as the small ordering parameter, analytical solutions are deduced for the leading- as well as first-order problems in terms of the dimensionless Debye and rotation parameters. The velocity profiles of the Ekman–electric double layer (EDL) layer, which is the boundary layer that arises when the Ekman layer and the EDL are comparably thin, are also deduced for an Eyring fluid. It is shown that the present perturbation model can yield results that are close to the exact solutions even when the ordering parameter is as large as order unity. By this order of the relaxation time parameter, the enhancing effect on the rotating EO flow due to shear-thinning Eyring rheology can be significant.