Effect of the skimming layer on electro-osmotic - Poiseuille flows of viscoelastic fluids

Abstract

An analytical solution is derived for the microchannelflow of viscoelastic fluids by combined electroosmosisand pressure gradient forcing. The viscoelasticfluid is described by the Phan-ThienTanner model withdue account for the near-wall layer depleted of macromolecules.This skimming layer is wider than the electricdouble layer (EDL) and leads to an enhanced flow raterelative to that of the corresponding uniform concentrationflow case. The derived solution allows a detailed investigationof the flow characteristics due to the combinedeffects of fluid rheology, forcing strengths ratio, skimminglayer thickness and relative rheology of the two fluids. Inparticular, when the EDL is much thinner than the skimminglayer and simultaneously the viscosity of the Newtonianfluid inside this layer is much lower than that of thefluid outside, the flow is dominated by the characteristics ofthe Newtonian fluid. Outside these conditions, properaccount of the various fluid layers and their properties mustbe considered for an accurate prediction of the flow characteristics.The analytical solution remains valid for theflow driven by a pressure gradient and its streamingpotential, which is determined in the appendix.