Electrokinetic mixing at high zeta potentials: Ionic size effects on cross stream diffusion Alireza Ahmadian Yazdi a , Arman Sadeghi b,⇑ , Mohammad Hassan Saidi a a Center of Excellence in Energy Conversion (CEEC), School of Mechanical Engineering, Sharif University of Technology, Tehran 11155-9567, Iran b Department of Mechanical Engineering, University of Kurdistan, Sanandaj 66177-15175, Iran article info Article history: Received 3 September 2014 Accepted 21 November 2014 Available online 3 December 2014 Keywords: Electroosmotic flow Micromixer Steric effects abstract The electrokinetic phenomena at high zeta potentials may show several unique features which are not normally observed. One of these features is the ionic size (steric) effect associated with the solutions of high ionic concentration. In the present work, attention is given to the influences of finite ionic size on the cross stream diffusion process in an electrokinetically actuated Y-shaped micromixer. The method consists of a finite difference based numerical approach for non-uniform grid which is applied to the dimensionless form of the governing equations, including the modified Poisson–Boltzmann equation. The results reveal that, neglecting the ionic size at high zeta potentials gives rise to the overestimation of the mixing length, because the steric effects retard liquid flow, thereby enhancing the mixing effi- ciency. The importance of steric effects is found to be more intense for channels of smaller width to height ratio. It is also observed that, in sharp contrast to the conditions that the ions are treated as point charges, increasing the zeta potential improves the cross stream diffusion when incorporating the ionic size. Moreover, increasing the EDL thickness decreases the mixing length, whereas the opposite is true for the channel aspect ratio. Ó 2014 Elsevier Inc. All rights reserved. 1. Introduction In the recent years, micro-electro-mechanical-systems (MEMS) have attracted much attention because of wide practical applica- tions, especially in medical and biological related industries where the microfluidic devices, called lab-on-a-chip (LOC), are becoming more and more popular. Lab-on-a-chip devices are microscale lab- oratories on a microchip that can perform clinical diagnoses. The main advantages of these devices are ease of use, speed of analysis, and low sample consumption [1]. Fluid delivery in LOCs is a challenging task because of small length scales involved. Among various techniques being proposed for fluid pumping in these devices, electroosmosis has been favored due to its advantages over other flow actuation mecha- nisms. For example, electroosmotic pumps need no moving parts and, as a result, have much simpler design and easier fabrication. Also, precise flow control can be easily achieved by controlling the external electric field [2]. The fundamental origin of electroosmotic transport lies in the fact that when a surface is brought into contact with an electrolyte solution, it usually takes a net charge. Due to the electroneutrality principle, the liquid takes on an opposite charge in the electric dou- ble layer (EDL) near the surface. The electric double layer contains an immobile inner layer and an outer diffuse layer [3]. If an electric field is applied tangentially along the surface, a force will be exerted on the ions within the mobile diffuse electric layer, result- ing in their motion [4]. Owing to viscous drag, the liquid is drawn by the ions and therefore flows tangential to the surface. Mixing is a physical process with the goal of achieving a uni- form distribution of different components in a mixture, usually within a short period of time. This definition includes the integra- tion of two or more fluids into one phase, most often accompanied by volume contraction or expansion, or the interdispersion of sol- ids [5]. Mixing is one of the essential functions in LOC systems, since it is vital in different processes such as cell activation, enzyme reaction, protein folding, sequencing or synthesis of nucleic acids, and so on [6]. Among various micromixers being developed is the Y/T-shaped micromixer, shown in Fig. 1. In most cases, this micromixer is used to bring two or more fluid streams into contact running side-by-side [7]. Although simple in design, such a device is a useful mixer, and hence has been applied in a number of cases [5]. Despite its macroscale counterpart, mixing in Y/T-shaped micromixer occurs primarily via molecular diffusion at the http://dx.doi.org/10.1016/j.jcis.2014.11.059 0021-9797/Ó 2014 Elsevier Inc. All rights reserved. ⇑ Corresponding author. E-mail addresses: ar_ahmadianyazdi@mech.sharif.edu (A. Ahmadian Yazdi), a. sadeghi@eng.uok.ac.ir (A. Sadeghi), saman@sharif.edu (M.H. Saidi). Journal of Colloid and Interface Science 442 (2015) 8–14 Contents lists available at ScienceDirect Journal of Colloid and Interface Science www.elsevier.com/locate/jcis