Journal of Non-Newtonian Fluid Mechanics 266 (2019) 46–58 Contents lists available at ScienceDirect Journal of Non-Newtonian Fluid Mechanics journal homepage: www.elsevier.com/locate/jnnfm Electro-osmotic oscillatory flow of viscoelastic fluids in a microchannel Samir H. Sadek, Fernando T. Pinho ∗ CEFT, Departamento de Engenharia Mecânica, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal a r t i c l e i n f o Keywords: Microchannels Electro-osmotic flow (EOF) Viscoelastic fluids Small amplitude oscillatory shear flow (SAOS) Small amplitude oscillatory shear by electro-osmosis (SAOSEO) Multi-mode upper-convected Maxwell (UCM) model a b s t r a c t This work presents an analytical solution for electro-osmotic flow (EOF) in small amplitude oscillatory shear (SAOS) as a measuring tool suitable to characterize the linear viscoelastic properties of non-Newtonian fluids in microchannel flow. The flow in the straight microchannel is driven by applying oscillating sinusoidal electric potentials. Fourier series are used to derive an expression for the velocity field, under an externally imposed generic potential field aimed at the practical application of SAOS in characterizing the rheological properties of viscoelastic fluids. This extensive investigation covers a wide range of parameters and considers the multi-mode upper-convected Maxwell (UCM) model, which represents the rheology of viscoelastic fluids in the limit of small and slow deformations. Particular focus is given to two cases of practical interest: equal wall zeta potentials at both channel walls and negligible zeta potential at one of the walls. The results show that in flows with thin electric double layers (EDL), Reynolds numbers below 0.001, and Deborah numbers below 100, corresponding to a viscoelastic Mach number of 0.32, the velocity field outside the EDLs is linear and has a large enough amplitude of oscillation, which may allow the quantification of the storage and loss moduli in the linear regime. This technique requires the use of significantly smaller sample sizes than the traditional SAOS in a rotational rheometer. List of abbreviations EDL electric double layer EOF electro-osmotic flow EZP equal zeta potential NZP negligible zeta potential PIV particle image velocimetry PTV particle tracking velocimetry SAOS small amplitude oscillatory shear SAOSEO small amplitude oscillatory shear by electro-osmosis 1. Introduction Transport phenomena at the micro-scale is increasingly of interest for applications in a variety of systems given the inherent savings in materi- als and energy, fast reaction times and the ability of today’s technology to fabricate micro-systems with multi-purpose functions. In particular, micro-scale systems are increasingly being used to process bio-fluids and chemicals, in species separation, or mixing, among others. On moving from macro to micro-scale systems, the ratio of volume to surface forces dramatically decreases and surface-based forcing mechanisms become advantageous relative to volume-based methods. Indeed, monitoring and controlling liquid transport accurately by electro-osmosis becomes increasingly easier and more effective at the micro- and nano-scales, whereas the use of the traditional pressure gradient driven flow becomes ∗ Corresponding author. E-mail address: fpinho@fe.up.pt (F.T. Pinho). increasingly less efficient as the size of the channels are reduced due to the significant increase of the pressure gradients [1–3]. Electro-osmosis is an electro-kinetic phenomenon, identified first by Reuss [4] in the 19th century. In electro-osmosis, chemical equilibrium between a polar fluid and a solid dielectric wall results on a spontaneous charge being acquired by the wall and the corresponding counter-charge occurring in near-wall layers on the liquid side. On the liquid side, a very thin wall layer of immobile counter-ions develops and is followed by a thicker layer of diffuse counter-ions, thus creating the so-called elec- tric double layer (EDL). Upon application of an external electric poten- tial field between the inlet and outlet of the microchannel the ensuing motion of the diffuse layer counter-ions drags the remaining core fluid in the channel by viscous forces. An overview of electro-osmosis and of other electro-kinetic flow techniques can be found in [5–7]. Electro- osmosis offers special unique features over other types of pumping meth- ods (e.g. micro-pumps), and has the ability of easily and very quickly (within the viscous time scale) change flow direction and magnitude by changing the applied potential field. The generated flow is defined by the pattern of the imposed electric potential field, so it can be easily driven at constant flow rate, or following an oscillatory pattern [8]. As previously mentioned, chemical and biomedical lab-on-a-chip systems are the most frequent applications of micro-scale liquid flows. The fluids are frequently made from complex molecules which ex- hibit non-linear rheological behavior. These so-called non-Newtonian fluids have such rheological characteristics as variable viscosity and viscoelasticity. The rheological characterization of non-Newtonian flu- ids is performed with various controllable and quasi-controllable flows https://doi.org/10.1016/j.jnnfm.2019.01.007 Received 20 July 2018; Received in revised form 15 January 2019; Accepted 20 January 2019 Available online 13 February 2019 0377-0257/© 2019 Elsevier B.V. All rights reserved.