Colloids and Surfaces A: Physicochemical and Engineering Aspects
Liquid transport in rectangular microchannels by electroosmotic pumping
Introduction
The study of fluid flow in microchannels is of significant interest to engineers and scientists because of emerging applications in high-tech industries. Examples include miniaturized flow injection analysis systems, micro-reactors for the analysis of biological cells, and heat sinks for cooling microchips and laser diode arrays. Given the small scales involved with microchannels, there are some drawbacks to conventional mechanical fluid propulsion systems, the least of which is that microscale pumps have small moving parts which are difficult to manufacture and repair [1]. A non-mechanical alternative for moving fluids in microchannels is electroosmotic pumping, which takes advantage of the electrical properties of the fluid to induce flow. Although the phenomenon of electroosmosis has been known for nearly two centuries, its application to microscale pumping has only recently been studied [2].
Most surfaces obtain a surface electric charge when they are brought into contact with a polar medium. This may be due to ionization, ion adsorption or ion dissolution. The surface charge, in turn, influences the ion distribution in the polar medium, forming the Electric Double Layer (EDL) [3]. The EDL is the region near the charged surface where counter-ions and co-ions in a polar medium are preferentially distributed, such that the net charge density is not zero. This distribution of ions combined with random thermal motion results in the EDL. Guoy and Chapman modeled the region near the surface as a diffuse double layer, where they linked the non-uniform ion distribution to the competing electrical and thermal diffusion forces [4]. Stern later presented the basis for the current model, in which the Stern plane splits the EDL into an inner, compact layer, and an outer, diffuse layer. In the inner layer or the Stern layer, the geometry of the ions and molecules strongly influences the charge and potential distribution, with the Stern plane located near the surface, at roughly the radius of a hydrated ion. The inner layer between the surface and the Stern plane is considered to be immobile; if the ions are within the Stern plane, thermal diffusion will not be strong enough to overcome electrostatic or Van der Waals forces and they will attach to the surface, becoming specifically adsorbed [4]. In the outer diffuse layer, the ions are far enough away from the surface that they are mobile. Electrokinetic transport phenomena such as electroosmosis can be understood in terms of the surface potential at the surface of shear (approximately the Stern plane), known as the zeta potential, ζ, because these phenomena are only directly related to the mobile part of the EDL [4].
Within the diffuse layer, because of the EDL, the net charge density, ρe is not zero. If an electric field is applied along the length of the channel, a body force is exerted on the ions in the diffuse layer of the EDL. The ions will move under the influence of the applied electrical field, pulling the liquid with them and resulting in electroosmotic flow. The fluid movement is carried through to the rest of the fluid in the channel by viscous forces. This electrokinetic process is called electroosmosis, and was first introduced by Reuss in 1809 [5].
Since the fluid motion is initiated by the electrical body force (the driving force) acting on the ions in the diffuse layer of the EDL, electroosmotic flow depends not only on the applied electrical field but also on the net local charge density in the liquid. Thus, in order to study electroosmotic pumping in rectangular microchannels, it is necessary to understand the EDL field and to calculate the net local charge density in a rectangular microchannel. Earlier studies of EDL and electroosmotic flows were limited to systems with simple geometries, such as cylindrical capillaries with circular cross-sections or a slit-type channel formed by two parallel plates [5], [6], [7]. However, the channels in modern microfluidic devices and MEMS are made by micromachining technologies. The crosssection of these channels is close to a rectangular shape [8]. In such a situation, the EDL field is two-dimensional and will affect the two-dimensional flow field in the rectangular microchannel.
In order to understand the characteristics of electroosmotic flow in rectangular microchannels, and to control electroosmotic pumping as a means of transporting liquids in microstructures, we will investigate the characteristics of electroosmotic flow in rectangular microchannels. In this paper we examine the numerical solutions of the 2D Poisson–Boltzmann equation and the 2D-momentum equation for laminar flows in rectangular microchannels. The EDL field, the flow field and the volumetric flow rate will be studied as functions of the zeta potential, the liquid properties, the channel geometry and the applied electrical field.
Section snippets
Electrical double layer in rectangular microchannels
Referring to Fig. 1, consider a rectangular microchannel of width 2W, height 2H and length L. Assuming symmetry in the potential and velocity fields, the solution domain can be reduced to a quarter section of the channel (as shown in Fig. 1). As mentioned earlier, we are interested in the potential and velocity fields within the diffuse layer, not including the immobile layer of the EDL. As such, the exterior surfaces of the solution domain coincide with the shear plane.
Before considering the
Velocity distribution in rectangular microchannels
The general equation of motion for laminar conditions in a liquid with constant density and viscosity is given by:If we assume that the flow is steady, two-dimensional, and fully developed, then the velocity components are described by:In addition, with this assumption, quadratic and higher order terms are neglected in Eq. (12). If there is no pressure gradient, the first term on the right hand side of Eq. (12) drops out as well. The only force in the
Results and discussion
The above equations and boundary conditions for the EDL and velocity fields in a rectangular microchannel were solved numerically. The physical properties of KCl aqueous solution were used as the properties of the fluid at a concentration of 10−6 M, where ε=80 and μ=0.90×10−3 kgm−1s−1 [11]. An arbitrary reference velocity of U=1 mm s−1 was used to non-dimensionalize the velocity. Using experimental results [12], zeta potential values were varied from 0.100 to 0.200 V, corresponding to three
Conclusion
The velocity profile of electro-osmotic flow (EOF) in rectangular microchannels has been investigated numerically in this paper. The two-dimensional Poisson–Boltzmann equation and the equations of motion are solved for a rectangular microchannel using a finite difference numerical scheme. The results demonstrate the significance of geometry effects on EOF, with EOF enhanced as the aspect ratio of the channel moves away from 1:1. Increases in Dh increase the volumetric flow rate but will have
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