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

Abstract

An analytical solution is derived for the micro-channel flow of viscoelastic fluids by combined electro-osmosis and pressure gradient forcing. The viscoelastic fluid is described by the Phan-Thien-Tanner model with due account for the near-wall layer depleted of macromolecules. This skimming layer is wider than the electric double layer (EDL) and leads to an enhanced flow rate relative to that of the corresponding uniform concentration flow case. The derived solution allows a detailed investigation of the flow characteristics due to the combined effects of fluid rheology, forcing strengths ratio, skimming layer thickness and relative rheology of the two fluids. In particular, when the EDL is much thinner than the skimming layer and simultaneously the viscosity of the Newtonian fluid inside this layer is much lower than that of the fluid outside, the flow is dominated by the characteristics of the Newtonian fluid. Outside these conditions, proper account of the various fluid layers and their properties must be considered for an accurate prediction of the flow characteristics. The analytical solution remains valid for the flow driven by a pressure gradient and its streaming potential, which is determined in the appendix.