Electroosmosis of a viscoelastic fluid over non-uniformly charged surfaces: Effect of fluid relaxation and retardation time

Abstract

We investigate the electroosmotic flow of a quasi-linear viscoelastic fluid over a surface having charge modulation in narrow confinements. We obtain analytical solutions using a combination of regular and matched asymptotic expansions in order to describe the viscoelastic flow field and apparent slip velocity besides pinpointing variations of the flow rate and ionic currents due to the surface charge modulation. We demonstrate excellent agreement between the asymptotic analytical solution for the flow field and the full numerical solution in the limiting condition of a thin electrical double layer and weakly viscoelastic fluid. For a wide range of flow governing parameters, we analyze the flow velocity, vortex dynamics, flow rates, and streaming current. We demonstrate that the magnitude of the observed electroosmotic slip velocity is more sensitive to the thickness of the electrical double layer rather than the viscoelasticity of the fluid. We have observed that the contribution of fluid elasticity is prominent in breaking the axial symmetry in the electroosmotic flow with the presence of periodic charge distributions, which is in contrast to the symmetric electroosmotic flow field of a Newtonian fluid over the same charge modulated walls. The results hold the key toward understanding the flow of biological fluids in microfluidic flows by leveraging electrokinetic transport over charge modulated surfaces. We believe that the results of net throughput, streaming current, and vortex dynamics will aid our understanding of the complex fluid behavior and microfluidic mixers.