Analytical solutions for mass transfer and hydrodynamic dispersion by electroosmotic flow of viscoelastic fluids in heterogeneous microchannels

Abstract

Consideration is given to the hydrodynamic dispersion of a very thin solute band of arbitrary height by the steady and fully-developed electroosmotic flow (EOF) in parallel-plate microchannels with asymmetric wall zeta potentials. This is meant to be a model for sample transfer by EOF in rectangular glass-PDMS microchannels for which there is a non-uniform distribution of the zeta potential due to surface heterogeneity. The side-wall effects are ignored for better mathematical tractability, which is a reasonable assumption given that glass-PDMS microchannels are usually shallow and the processes taking place in these microchannels take short. Given the fact that many working fluids in microfluidic devices are biofluids with complex rheology, the simplified Phan-Thien-Tanner (sPTT) viscoelastic rheological model is used for better applicability of the results to real-life problems. Adopting the generalized dispersion theory and assuming the zeta potentials to be low enough to allow applying the Debye-Hückel approximation, analytical solutions are obtained for the convection and dispersion coefficients as well as for the mean and local concentrations. The results indicate that while asymmetry significantly increases the dispersion coefficient for thin electric double layers it may slightly decrease the dispersion for very thick double layers. Moreover, the viscoelasticity is found to drastically amplify the hydrodynamic dispersion, which highlights the importance of considering non-linear rheology in the pertinent simulations. Finally, complicated variations of the dispersion coefficient are observed with the relative double layer thickness, sometimes with local minimums, indicating the feasibility of minimizing the dispersion of solutes by adjusting the channel height.