Analytical solution of mixed electro-osmotic/pressure driven flows of viscoelastic fluids in microchannels

Abstract

Analytical solutions are presented for the flow of viscoelastic fluids in micron sized ducts, namely between parallel plates and pipes under the combined influence of electrokinetic and pressure forces using the Debye-Huckel approximation, including the limit case of pure electro-osmotic flow. The viscoelastic fluids used are described by the simplified Phan-Thien-Tanner model (sPTT), with linear kernel for the stress coefficient function, and zero second normal stress difference, and the FENE-P model, based on the kinetic theory for finitely extensible dumbbells with a Peterlin approximation for the average spring force. The solution is non-linear with a significant contribution arising from the coupling between the electric and pressure potentials. This term acts as a drag reducer and a drag increaser under favorable and adverse pressure gradients, respectively and contrasts with the Newtonian flow case, for which it does not exist, demonstrating that the superposition principle valid for Newtonian fluids no longer applies when non-linear viscoelastic fluid models are considered. The combined effects of fluid rheology, electro-osmotic and pressure gradient forcing on the fluid velocity distribution and fluid stresses are also discussed. The analysis of the streaming potential is also included.